Wireless Power Transmission

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In present world, transmission and distribution losses are the main concern of power technology. Much of this power is wasted during transmission from power plant generators to the consumer .The resistance of the wire used in the electrical grid distribution system causes a loss of 26-30% of the energy generated. In this condition our present system of electrical distribution is only 70-74% efficient.
A system of power distribution with little or no loss would conserve energy. It would reduce pollution and expenses resulting from the need to generate power to overcome and compensate for losses in the present grid system.

The   proposed   project would demonstrate a method   of   energy distribution  calculated to be 90-94% efficient.   An   electrical distribution system, based on this method would eliminate the need for an inefficient, costly, and capital intensive grid of cables, towers, and substations.  The system would reduce the cost of electrical energy used by the consumer and rid the landscape of wires, cables, and transmission towers.
So, we should need to think alternate state of art technology to transmit and distribute the electricity. Now a day’s global scenario has been changed a lot and there are tremendous developments in every field. If we don’t think alternative way for development of new power technology we have to face a decreasing trend in the development of power sector. The transmission of power without wires may be one noble alternative way for electricity transmission.

 1.1    Introduction of Wireless power transmission System (WPT System):

Wireless energy transfer or wireless power transmission is the process that takes place in any system where electrical energy is transmitted from a power source to an electrical load, without interconnecting wires. Wireless transmission is useful in cases where instantaneous or continuous energy transfer is needed, but interconnecting wires are inconvenient, hazardous, or impossible.
 1.2    Some History of wireless energy transfer
1820: André-Marie Ampère describes Ampere’s law showing that electric current produces a magnetic field.
1831: Michael Faraday describes Faraday’s law of induction, an important basic law of electromagnetism.
1864: James Clerk Maxwell synthesizes the previous observations, experiments and equations of electricity, magnetism and optics into a consistent theory, and mathematically models the behavior of electromagnetic radiation.
1888: Heinrich Rudolf Hertz confirms the existence of electromagnetic radiation. Hertz’s "apparatus for generating electromagnetic waves" was a VHF or UHF wave spark gap transmitter.
1891: Nikola Tesla improves Hertz-wave transmitter RF power supply.
1893: Nikola Tesla demonstrates the wireless illumination of phosphorescent lamps of his design at the World's Columbian Exposition in Chicago.
1894: Hutin & LeBlanc, espouse long held view that inductive energy transfer should be possible, they file a U.S. Patent describing a system for power transfer at 3 kHz.
1894: Nikola Tesla wirelessly lights up single-terminal incandescent lamps.
1894: Jagdish Chandra Bose (Indian) ignites gunpowder and rings a bell at a distance using electromagnetic waves, showing that communications signals can be sent without using wires.
1895: Jagdish Chandra Bose transmits signals over a distance of nearly a mile.
1896: Nikola Tesla transmits signals over a distance of about 48 kilometers (30 mi).
1897: Guglielmo Marconi uses ultra low frequency radio transmitter to transmit Morse code signals over a distance of about 6 km.
 1.3     Present Condition of WPT system :
Consumer research suggests that a universal standard is the preferred solution, so it is now up to the companies interested in developing and manufacturing these solutions to develop a standard that will allow consumers around the world to power their devices across a broad range of brands and power needs under a single, interoperable standard.
This solution will, like the Wi-Fi Alliance did for wireless networking, create a new protocol for how people interact with power.
It has a tremendous economic impact to human society Many countries will benefit from this service. Monthly electric utility bills from old-fashioned, fossil-fuelled, loss prone electrified wire-grid delivery services will be optional much like “cable TV” of today.Today we will be in a wonder world of transmission of plenty of power using the technology of wireless electricity.
1.4      Recent developed in WPT system:
2007: A physics research group, led by Prof. Marin Soljačić, at MIT confirm the earlier (1980's) work of Prof. John Boys by wireless powering of a 60W light bulb with 40% efficiency at a 2 meters (6.6 ft) distance using two 60 cm-diameter coils.
2008: Bombardier offers new wireless transmission product PRIMOVE, a power system for use on trams and light-rail vehicles.
2008: Industrial designer Thanh Tran, at Brunel University made a wireless light bulb powered by a high efficiency 3W LED.
2008: Intel reproduces Nikola Tesla's 1894 implementation and Prof. John Boys group's 1988's experiments by wirelessly powering a nearby light bulb with 75% efficiency.
2009: A Consortium of interested companies called the Wireless Power Consortium announced they were nearing completion for a new industry standard for low-power Inductive charging
2009: Texas Instruments releases the first device.
2009: Reference introduced an Ex approved Torch and Charger aimed at the offshore market. This product was developed by Wireless Power & Communication, a Norway based company.
2010: Haier Group debuts the world's first completely wireless LCD television at CES 2010 based on Prof. Marin Soljacic's research on wireless energy transfer and Wireless Home Digital Interface (WHDI).
 1.5     Advantages of WPT System:
Wireless Power Transmission system would completely eliminates the existing high tension power transmission line cables, towers and sub stations between the generating station and consumers and facilitates the interconnection of electrical generation plants on a global scale. It has more freedom of choice of both receiver and transmitters. Even mobile transmitters and receivers can be chosen for the WPT system. The cost of transmission and distribution become less and the cost of electrical energy for the consumer also would be reduced. The power could be transmitted to the places where the wired transmission is not possible. Loss of transmission is negligible level in the Wireless Power Transmission; therefore, the efficiency of this method is very much higher than the wired transmission. Power is available at the rectenna as long as the WPT is operating.
The power failure due to short circuit and fault on cables would never exist in the transmission and power theft would be not possible at all.
Biological Impacts of WPT system:
Common beliefs fear the effect of microwave radiation. But the studies in this domain repeatedly proves that the microwave radiation level would be never higher than the dose received while opening the microwave oven door, meaning it is slightly higher than the emissions to operate with power densities at or below the ANSI/IEEE exposure standards.

1.6     Wireless energy transfer applications

 The transmission of information

Several 20th century technology that use wireless power (and are in widespread use) included AM, FM, and TV broadcasting. Telecommunications and wireless internet was an application that began in the last decade of the 20th century. Wireless transmission of electricity aids navigation by the Global Positioning System.

The transmission of power

Devices using this principle to charge portable consumer electronics such as cell phones are commercially available. (Splash Power; Battery powered devices can be charged by placing them on an induction mat.) The Powercast system is applicable for a number of devices with low power requirements. This could include LEDs, computer peripherals, wireless sensors, and medical implants. A company called eCoupled unveiled their own take on inductive coupling, which will soon be used on "Herman Miller" desks to recharge devices wirelesly. Examples include the transcutaneous energy transfer (TET) systems in artificial hearts like AbioCor and induction stove tops (and microwave ovens).
Using of Lunar Wireless Power Transfer and wireless power transmissions from generation plant to consumers are also increasing day by day.
So, we want to say that, do not need cables, pipes, or copper wires to receive power. We can send power to we like a cell phone call – where we want it, when we want it, in real time.

  1. Introduction

­The wireless transmission of energy is common in much of the world. Radio waves are energy, and people use them to send and receive cell phone, TV, radio and Wi-Fi signals every day. The radio waves spread in all directions until they reach antennae that are tuned to the right frequency.
The most common form of wireless power transmission is carried out using induction, followed by induction. Other viable technologies for wireless power include those based upon microwaves and lasers. In this chapter we will discuss about different theoretical aspect of wireless power transmission.
2.2   Components of WPT System
The Primary components of Wireless Power Transmission are ,
1. Microwave Generator,
2. Transmitting antenna
3.  Receiving antenna (Rectenna).
These components are described in this chapter.

                   Figure 2.1. Functional Block Diagram of Wireless Power Transmission System
2.2.1      Microwave Generator
The microwave transmitting devices are classified as Microwave Vacuum Tubes (magnetron, klystron, Travelling Wave Tube (TWT), and Microwave Power Module (MPM)) and Semiconductor Microwave transmitters (GaAs MESFET, GaN pHEMT, SiC MESFET, AlGaN/GaN HFET, and InGaAS).
Magnetron is widely used for experimentation of WPT. The microwave transmission often uses 2.45GHz or 5.8GHz of ISM band. The other choices of frequencies are 8.5 GHz, 10 GHz and 35 GHz .The highest efficiency over 90% is achieved at 2.45 GHz among all the frequencies. A magnetron, which is well-known as a microwave heating source in a microwave oven, is used for a microwave power source of a WPT system, because its DC-RF conversion efficiency is higher, it costs less, and it has smaller weight/power ratio than solid state devices. However, a magnetron has a wide oscillation bandwidth and it generates spurious noises in various frequency bands. Thus, we have been studying on a low-noise transmitting system with a magnetron.
Magnetron noise reduction
The wideband oscillation will lead to great fluctuation of a microwave beam from a WPT transmitting system, because of degradation of its frequency and phase stability. The spurious noise will interfere in the other communication systems when it is radiated from the WPT transmitting system. Therefore, narrowband oscillation and spurious noise reduction of a magnetron are essential for a low noise WPT system. With regard to the narrowband oscillation, Brown mentioned that the “internal feedback mechanism” contributed to a quiet magnetron operation. The internal feedback mechanism most effectively takes place by turning off the filament current during the oscillation. Additionally, we found that the narrowband oscillation and the spurious noise reduction were effectively realized when a magnetron was operated by a dc stabilized power supply and the filament current was turned off during the operation. this operating method worked well in reducing sideband noise up to 60dB as well as the narrowband oscillation, shown in Fig.2.2 (a), spurious noise up to 50dB in high frequency bands (4GHz~10GHz), shown in Fig.2.2 (b), and line conductive noise up to 40dB in low frequency bands (~1GHz), shown in Fig.2.2 (c), although the method resulted in some degradation of dc-RF efficiency.

a) Fundamental bands (2.43GHz~2.47GHz)

(b) Spurious noise (4GHz~10GHz)

(c) Line conductive noise (~1GHz)
Fig. 2.2 Magnetron spectra. (thin line: the filament current is turned on, thick line: the filament current is turned off.)
Phase-controlled magnetron
The operating method for the magnetron noise reduction also contributes to development of a phase-controlled magnetron (PCM). The PCM is basically implemented in a phase locking of a magnetron in a phase of a reference signal. Our developed PCM consists of an injection locking method and an anode current control system with phase-locked loop (PLL),in order to realize both the frequency locking and the phase locking. First, the reference signal is injected into a magnetron. Then the anode current control system automatically locks frequency and phase of the magnetron to those of the reference signal. Owing to the accomplishment of the PCM, the experimental equipments with a phased array using PCMs at 2.45GHz and 5.8GHz, which are named SPORTS (Space Power Radio Transmission System)2.45 and SPORTS5.8 respectively, were developed  The SPORTS 2.45, shown in Fig.2.3a, has 12 PCMs, and each PCM has a 5-bit phase shifter. The total microwave output is about 3.6kW. There are two choices for the transmitting antenna section. One is the 4 by 3 horn antenna array. The horn antenna array system has low energy loss, but a broad beam pattern. The other is the 96 dipole antenna array with additional 2-bit phase shifter. The microwave power from a PCM is divided into 8 and connected to 8 dipole antennas. Each dipole antenna has a 2-bit phase shifter to get the microwave beam focused more precisely. The dipole antenna system has a sharp beam pattern but large energy loss. The rectenna array receives and converts microwave power to dc. The SPORTS 5.8, shown in Fig. 2.3.b,    has a choice of two transmitting systems. One consists of 9 PCMs and 288 antenna elements. Its total microwave output is more than 1.26kW. The other consists of a solid-state amplifier and 144 antenna elements. Its microwave output is more than 7.2W. Although the solid-state amplifier system has low efficiency and low microwave output, it cancontrol microwave beam with high resolution

Fig. 2.3.a    SPORTS 2.45

Fig. 2.3b SPORTS 5.8
A light microwave power transmitter at 5.8GHz named COMET (Compact Microwave Energy Transmitter), shown in Fig.2.3.a was also developed by our research group. The size of the COMET is 310mm in diameter and 99mm in thickness. It provides 270W microwave output and its weight is 7kg. So the weight per power ratio is less than 26g/W. Moreover, we succeeded to develop a Phase-and-Amplitude-Controlled Magnetron (PACM) by tuning both the anode current and the external magnetic field simultaneously.

Fig. 2.3c   COMET
5.8GHz CW magnetron
5.8GHz CW magnetrons, shown in Fig2.3c, The Development of 5.8GHz CW magnetrons contributes to reduction in size and weight of the SPS transmitting system, compared to the conventional 2.45GHz magnetron. Our research group experimentally measured and evaluated fundamental performance of the 5.8GHz magnetrons, such as DC-RF conversion efficiency, a curve of anode current vs. free-running frequency, a Q value, etc.

8GHz CW magnetron and 2.45GHz oven magnetron
From experimental results, DC-RF conversion efficiency of 5.8GHz CW magnetrons was measured to be about 40%; on the contrary, 2.45GHz cooker-type magnetrons have around 70% DC-RF conversion efficiency, when a magnetron is operated by a DC stabilized power supply. The Q value of 5.8GHz magnetrons degraded more than 10 times compared to that of 2.45GHz magnetrons. The results come from overheat of the cathode filament due to excessive back bombardment energy. The back bombardment energy in 5.8GHz CW magnetrons was estimated to be generated twice more than that in cooker-type 2.45GHz magnetrons.
The following subjects on CW magnetrons should be conducted for WPT and SPS transmitting systems in the near future: higher-efficiency operation, thermal treatment under vacuum environment, life test, and noise reduction. Some of these subjects are linked together: for example, the high-efficiency operation will help longevity of a magnetron due to reduction of heat loss. Since a magnetron is too complicated to analyze theoretically, the 3-D computer simulations will therefore be expected as a powerful tool for solving these subjects. Also, a low-loss and lightweight power divider and a low-loss phase shifter are necessary for the high-efficient phased array WPT system.
2.2.2 Transmitting Antenna
The slotted wave guide antenna, micro strip patch antenna, and parabolic dish antenna are the most popular type of transmitting antenna. The slotted waveguide antenna is ideal for power transmission because of its high aperture efficiency (> 95%) and high power handling capability. Below 2.3 and 2.4 article, we describe briefly about Antennaa.
.2.2.3 Rectenna
The concept, the name „rectenna‟ and the rectenna was conceived by W.C. Brown of Raytheon Company in the early of 1960s .The rectenna is a passive element consists of antenna, rectifying circuit with a low pass filter between the antenna and rectifying diode. The antenna used in rectenna may be dipole, Yagi – Uda, microstrip or parabolic dish antenna. The patch dipole antenna achieved the highest efficiency among the all. The performance of Various printed rectenna is shown in Table I. Schottky barrier diodes(GaAs-W, Si, and GaAs) are usually used in the rectifying circuit due to the faster reverse recovery time and much lower forward  voltage drop and good RF characteristics. The rectenna efficiency afor various diodes at different frequency is shown in below table 2.1 and 2.2.

Figure 2.4 : McSpadden's (1998) Rectenna Design
Table 2.1. Performance of Printed Rectenna

Type of


Measured Peak
Efficiency (%)

Printed Dipole



Circular Patch



Printed dual



Square patch



Table 2.2. Rectenna Efficiency for Various Diodes at Different Frequency

















2.3  definition & Classification of antenna.
An antenna (or aerial) is a transducer designed to transmit or receive electromagnetic waves. In other words, antennas convert electromagnetic waves into electrical currents and vice versa. They are used with waves in the radio part of the electromagnetic spectrum, that is, radio waves, and are a necessary part of all radio equipment. Antennas are used in systems such as radio and television broadcasting, point-to-point radio communication, wireless LAN, cell phones, radar, and spacecraft communication.
Antennas are most commonly employed in air or outer space, but can also be operated under water or even through soil and rock at certain frequencies for short distances.
Physically, an antenna is an arrangement of one or more conductors, usually called elements in this context. In transmission, an alternating current is created in the elements by applying a voltage at the antenna terminals, causing the elements to radiate an electromagnetic field. In reception, the inverse occurs: an electromagnetic field from another source induces an alternating current in the elements and a corresponding voltage at the antenna's terminals. Some receiving antennas (such as parabolic and horn types) incorporate shaped reflective surfaces to collect EM waves from free space and direct or focus them onto the actual conductive elements.
There are two fundamental types of antenna on the basis of directional patterns,
A. Omni-directional (radiates equally in all directions), such as a vertical rod (in the horizontal plane)
B. Directional (radiates more in one direction than in the other).
A.  Omni directional antenna

Figure 2.5: Vertical polarized VHF- UHF biconical antenna 170 – 1100 MHz with omni directional H-plane pattern.
An omnidirectional antenna is an antenna system which radiates power uniformly in one plane with a directive pattern shape in a perpendicular plane. This pattern is often described as "donut shaped".
Omnidirectional antenna can be used to link multiple directional antennas in outdoor point-to-multipoint communication systems including cellular phone connections and TV broadcasts.
The only 3 dimensional omnidirectional antenna is the unity gain isotropic antenna, a theoretical construct derived from actual antenna radiation patterns and used as a reference for specifying antenna gain and radio system effective radiated power. Antenna gain (G) is defined as antenna efficiency (e) multiplied by antenna directivity (D) which is expressed mathematically as: G = eD. A useful relationship between omnidirectional radiation pattern directivity (D) in decibels and half-power beamwidth (HPBW) based on the assumption of a sinbθ / bθ pattern shape is:
 D = 10\log_{10} {\left ({101.5\over {HPBW - 
0.00272(HPBW)^2}}\right )} \;\; dB
Practical antennas approach omni directionality by providing uniform radiation or response only in one reference plane, usually the horizontal one parallel to the earth's surface.
Common low gain omnidirectional antennas are the whip antenna, a vertically orientated dipole antenna, the discone antenna, and the horizontal loop antenna (or halo antenna) (Sometimes known colloquially as a 'circular aerial' because of the shape).
Higher gain omnidirectional antennas are the Coaxial Colinear (COCO) antenna and Omnidirectional Microstrip Antenna (OMA).
Omnidirectional antennas are generally realized using colinear dipole arrays. These arrays consist of half-wavelength dipoles with a phase shifting method between each element that ensures the current in each dipole is in phase. The Coaxial Colinear or COCO antenna uses transposed coaxial sections to produce in-phase half-wavelength radiators. A Franklin Array uses short U-shaped half-wavelength sections whose radiation cancels in the far-field to bring each half-wavelength dipole section into equal phase .

B.   Directional antenna

Figure 2.6 : Log-periodic dipole array
A directional antenna or beam antenna is an antenna which radiates greater power in one or more directions allowing for increased performance on transmit and receive and reduced interference from unwanted sources. Directional antennas like yagi antennas provide increased performance over dipole antennas when a greater concentration of radiation in a certain direction is desired.
All practical antennas are at least somewhat directional, although usually only the direction in the plane parallel to the earth is considered, and practical antennas can easily be omni directional in one plane.
The most common types are the yagi antenna, the log-periodic antenna, and the corner reflector, which are frequently combined and commercially sold as residential TV antennas. Cellular repeaters often make use of external directional antennas to give a far greater signal than can be obtained on a standard phone. For long and medium wavelength frequencies, tower arrays are used in most cases as directional antennas.
2.4    Most common antennas:
         Common antenna’s are

  1. Waveguide slotted antenna

  2. Yagi Uda antenna

  3. Horn Antenna

4.      Dipole antenna

1.  Waveguide slotted antenna

This antenna, called a slotted waveguide, is a very low loss transmission line. It allows propagating signals to a number of smaller antennas (slots). The signal is coupled into the waveguide with a simple coaxial probe, and as

It travels along the guide it traverses the slots. Each of these slots allows a little of the energy to radiate. The slots are in a linear array pattern. The waveguide antenna transmits almost all of its energy at the horizon, usually exactly where we want it to go.
Its exceptional directivity in the elevation plane gives it quite high power gain. Additionally, unlike vertical collinear antennas, the slotted waveguide transmits its energy using horizontal polarization, the best type for distance transmission.

                          Figure 2. 7:   2320MHz (13cm) Slotted waveguide Antenna
 2. Yagi antenna
Figure 2.8:  A Yagi-Uda antenna. From left to beam right, the elements mounted on the boom are called the reflector, driven element, and director. The reflector is easily identified as being a bit (5%) longer than the driven element, and the director a bit (5%) shorter.
A Yagi-Uda Antenna, commonly known simply as a Yagi antenna or Yagi, is a directional antenna system consisting of an array of a dipole and additional closely coupled parasitic elements (usually a reflector and one or more directors). The dipole in the array is driven, and another element, typically 5% longer, effectively operates as a reflector. Other parasitic elements shorter than the dipole may be added in front of the dipole and are referred to as directors. This arrangement gives the antenna increased directionality compared to a single dipole. Directional antennas, such as the Yagi-Uda, are also commonly referred to as beam antennas  or high-gain antennas (particularly for transmitting). Many common television antennas are Yagi antennas with added corner reflectors and/or UHF elements.
The bandwidth of a Yagi-Uda antenna, which is usually defined as the frequency range for which the antenna provides a good match to the transmission line to which it is attached, is determined by the length, diameter and spacing of the elements. For most designs, bandwidth is low, typically only a few percent of the design frequency.
Yagi-Uda antennas can be designed to operate on multiple bands. Such designs are more complicated, using pairs of resonant parallel coil and capacitor combinations (called a "trap" or LC) in the elements. The trap serves to isolate the outer portion of an element from the inner portion at the trap design frequency. In practice, the higher frequency traps are located closest to the boom of the antenna. Typically, a tri-band beam will have two pairs of traps per element. For example, a tri-band design covering the 10, 15 and 20 meter bands would have traps for the 10 and 15 meter bands. The use of traps is not without cost, as they reduce the bandwidth of the antenna on each band and reduce its overall efficiency.

3.  Horn Antenna

Figure 2.9:  Horn Antenna
A horn antenna is used for the transmission and reception of microwave signals. It derives its name from the characteristic flared appearance. The flared portion can be square, rectangular, or conical. The maximum radiation and response corresponds with the axis of the horn. In this respect, the antenna resembles an acoustic horn. It is usually fed with a waveguide.
horn_antenna.gif (2247 bytes)
In order to function properly, a horn antenna must be a certain minimum size relative to the wavelength of the incoming or outgoing electromagnetic. If the horn is too small or the wavelength is too large (the frequency is too low), the antenna will not work efficiently.
Horn antennas are commonly used as the active element in a dish antenna. The horn is pointed toward the center of the dish reflector. The use of a horn, rather than a dipole antenna or any other type of antenna, at the focal point of the dish minimizes loss of energy (leakage) around the edges of the dish reflector. It also minimizes the response of the antenna to unwanted signal snot in the favored direction of the dish





4.  Dipole antenna


    Figure 2.10: A schematic of a half-wave dipole antenna that a shortwave listener might build.
A dipole antenna, created by Heinrich Rudolph Hertz around 1886,is an antenna that can be made by a simple wire, with a center-fed driven element for transmitting or receiving radio frequency energy. These antennas are the simplest practical antennas from a theoretical point of view; the current amplitude on such an antenna decreases uniformly from maximum at the center to zero at the ends.
Power transfer Equation for a Dipole Antenna
                                                  ^                                                   P(r, θ,φ)
Consider for half wave dipole,
I= IocosßZ
Where, Io=Maximum value of the current
Now for transmitting antenna, the magnetic field intensity will be:-
^                     -jβr                                     ^
H= j/2πr (Io ℮       ) [cos (π/2cosθ)/sinθ] aφ
               jπ/2       -jβr      ^                                    
  = Hφ ℮          ℮              aφ      [where, Hφ=Io/2πr [cos (π/2cosθ)/sinθ]
              -j (βr-π/2)     ^
  = Hφ ℮                     aφ   ——————————– (i)
Again, for transmitting antenna the electric field intensity will be,
^    ^            -j(βr-π/2)    ^
E = η Hφ ℮                   aφ
             -jθη          -j(βr-π/2)  ^
   =‌‌‌‌‌│η‌‌‌│℮        Hφ ℮                 aφ
                     -j(βr-π/2-θη)  ^
   =‌‌‌‌‌│η‌‌‌│Hφ ℮                        aφ —————————- (ii)
Consider the medium between the antennas have a conductivity of α. Then the electric and magnetic field of the receiver end would be,
^                   -αr     -j(βr-π/2-θη)  ^
E=│η‌‌‌│Hφ ℮      ℮                       aφ——————– (iii)
 ^              -αr    -j(βr-π/2)      ^
 H = Hφ ℮      ℮                     aφ   ———————– (iv)
So the power density of the receiving end will be,
                    ^     ^
Sav= ½ Re (E x H)
                               -αr      –j(βr-π/2)   jθη              -αr     –j(βr-π/2)     ^ 
=1/2 Re {│η‌‌‌│Hφ ℮        ℮                 ℮        x Hφ ℮        ℮                  } ar
                              -2αr    jθη      ^
=1/2 Re {│η‌‌‌│Hφ²℮         ℮       }  ar
                         -2αr            ^
=1/2│η‌‌‌│Hφ²℮        cosθη ar
                                         -2αr          ^
= (1/2│η‌‌‌│) (│η‌‌‌│Hφ) ² ℮         cosθη ar
                              -2αr     ^
= (1/2│η‌‌‌│) Eo² ℮         cosθη ar ————————- (v)
[where (│η‌‌‌│Hφ) =Eo]
Since the electric field makes an angle of (90º-θ) with the axis of the receiver, then the voltage induced,
Vo=Eo ℮     .l sinθ [where l is the length of the antenna]
When the load impedance is matched to the antenna, the load impedance, ZL=Ra-jXa, further more for a lossless antenna Ra= Rrad. So, the total impedance of antenna and load is 2Rrad.
Hence, the power delivered to the load,
Pr = ½ [Vo/2Rrad] ² Rrad
= (1/8 Rrad) Eo²l² ℮        sin²θ ———————— (vi)
The radiation resistance of half wave dipole antenna,
 Rrad= (1.219/2π) │η‌‌‌│cosθη
Putting this value in (vi), then we have,
Pr = [2π/8(1.219) │η‌‌‌│cosθη] Eo²l² ℮        sin²θ
Now for a magnetic dipole antenna which radius is a. So the equation of the magnetic and electric field will be,
→                     →          -jβr  ^
Eφ= (ωμβ/4πr) M sinθ℮       aφ
             →      →
Where, M=πa²I is the magnetic dipole moment
and I= Io is the phasor equipment of i(t)=Io cosωt
         →                       →            -jβr
and Hθ= – (ωμβ/4πrη) M sinθ ℮     
Now the voltage induced in the antenna
→   →           -αr
Et= Eφ sinθ ℮
Now, induced voltage at the receiving antenna,
Vo= Et.l
=│Eφ │sinθ l ℮
=(ωμβ/4πr) │M│sinθl℮
So, the power delivered to the load,
Pr = 1/2‌│Vo/2Rrad‌│²Rrad
    =1/8 (Vo²/Rrad)
    =1/8 {(ωμβ/4πr) │M│sinθl} ²℮        /Rrad
     Where, Rrad=8/3π³η (πa²/λ²) cosθη

2.5   Different Parameters of Antenna

There are several critical parameters affecting an antenna's performance that can be adjusted during the design process. These are resonant frequency, impedance, gain, aperture or radiation pattern, propagation, polarization, efficiency and bandwidth. Transmit antennas may also have a maximum power rating, and receive antennas differ in their noise rejection properties. All of these parameters can be measured through various means.

(a) Resonant frequency

The "resonant frequency" and "electrical resonance" is related to the electrical length of an antenna. The electrical length is usually the physical length of the wire divided by its velocity factor (the ratio of the speed of wave propagation in the wire to c0, the speed of light in a vacuum). Typically an antenna is tuned for a specific frequency, and is effective for a range of frequencies that are usually centered on that resonant frequency. However, other properties of an antenna change with frequency, in particular the radiation pattern and impedance, so the antenna's resonant frequency may merely be close to the center frequency of these other more important properties.
Antennas can be made resonant on harmonic frequencies with lengths that are fractions of the target wavelength; this resonance gives much better coupling to the electromagnetic wave, and makes the aerial act as if it were physically larger.
Some antenna designs have multiple resonant frequencies, and some are relatively effective over a very broad range of frequencies. The most commonly known type of wide band aerial is the logarithmic or log periodic, but its gain is usually much lower than that of a specific or narrower band aerial.

(b) Gain

Gain as a parameter measures the efficiency of a given antenna with respect to a given norm, usually achieved by modification of its directionality. An antenna with a low gain emits radiation with about the same power in all directions, whereas a high-gain antenna will preferentially radiate in particular directions. Specifically, the Gain, Directive gain or Power gain of an antenna is defined as the ratio of the intensity (power per unit surface) radiated by the antenna in a given direction at an arbitrary distance divided by the intensity radiated at the same distance by a hypothetical isotropic antenna.
The gain of an antenna is a passive phenomenon – power is not added by the antenna, but simply redistributed to provide more radiated power in a certain direction than would be transmitted by an isotropic antenna. If an antenna has a gain greater than one in some directions, it must have a gain less than one in other directions, since energy is conserved by the antenna. An antenna designer must take into account the application for the antenna when determining the gain.
High-gain antennas have the advantage of longer range and better signal quality, but must be aimed carefully in a particular direction. Low-gain antennas have shorter range, but the orientation of the antenna is relatively inconsequential. For example, a dish antenna on a spacecraft is a high gain device that must be pointed at the planet to be effective, whereas a typical Wi-Fi antenna in a laptop computer is low-gain, and as long as the base station is within range, the antenna can be in any orientation in space. It makes sense to improve horizontal range at the expense of reception above or below the antenna. Thus most antennas labelled "omnidirectional" really have some gain.
In practice, the half-wave dipole is taken as a reference instead of the isotropic radiator. The gain is then given in dBd (decibels over dipole):
NOTE: 0 dBd = 2.15 dBi. It is vital in expressing gain values that the reference point be included. Failure to do so can lead to confusion and error.

(c) Radiation pattern

The radiation pattern is a graphical depiction of the relative field strength transmitted from or received by the antenna. As antennas radiate in space often several curves are necessary to describe the antenna. If the radiation of the antenna is symmetrical about an axis (as is the case in dipole, helical and some parabolic antennas) a unique graph is sufficient. Each antenna supplier/user has different standards as well as plotting formats. An antenna radiation pattern allows to easily seeing side lobes and back lobes. Each format has its own advantages and disadvantages. Radiation pattern of an antenna can be defined as the locus of all points where the emitted power per unit surface is the same. The radiated power per unit surface is proportional to the squared electrical field of the electromagnetic wave. The radiation pattern is the locus of points with the same electrical field. In this representation, the reference is usually the best angle of emission. It is also possible to depict the directive gain of the antenna as a function of the direction. Often the gain is given in decibels.
The graphs can be drawn using Cartesian (rectangular) coordinates or a polar plot. This last one is useful to measure the beamwidth, which is, by convention, the angle at the -3dB points around the max gain. The shape of curves can be very different in Cartesian or polar coordinates and with the choice of the limits of the logarithmic scale. The four drawings below are the radiation patterns of a same half wave antenna.

Figure 2.11(a): Radiation pattern of a half-wave dipole antenna. Linear scale.

Figure 2.11(b): Gain of a half-wave dipole. The scale is in dBi.

Figure 2.11(c): Gain of a half-wave dipole. Cartesian representation.

Figure 2.11(d): 3D Radiation pattern of a half-wave dipole antenna.

(d) Impedance

As an electromagnetic wave travels through the different parts of the antenna system (radio, feed line, antenna, free space) it may encounter differences in impedance (E/H, V/I, etc). At each interface, depending on the impedance match, some fraction of the wave's energy will reflect back to the source, forming a standing wave in the feed line.
The ratio of maximum power to minimum power in the wave can be measured and is called the standing wave ratio (SWR). A SWR of 1:1 is ideal. A SWR of 1.5:1 is considered to be marginally acceptable in low power applications where power loss is more critical, although an SWR as high as 6:1 may still be usable with the right equipment. Minimizing impedance differences at each interface (impedance matching) will reduce SWR and maximize power transfer through each part of the antenna system.
Complex impedance of an antenna is related to the electrical length of the antenna at the wavelength in use. The impedance of an antenna can be matched to the feed line and radio by adjusting the impedance of the feed line, using the feed line as an impedance transformer.
More commonly, the impedance is adjusted at the load (shown below) with an antenna tuner, a balun, a matching transformer, matching networks composed of inductors and capacitors, or matching sections such as the gamma match.

 (e)  Propagation

Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is unphysical in light of causality), which adds to the expressions for the electro-dynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wave packet of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle.
Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν, where E is the energy of the photon, h = 6.626 × 10-34 J·s is Planck's constant, and ν is the frequency of the wave.
One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer, regardless of the observer's velocity. (This observation led to Albert Einstein's development of the theory of special relativity.)
In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum

(f) Efficiency

Efficiency is the ratio of power actually radiated to the power put into the antenna terminals. A dummy load may have an SWR of 1:1 but an efficiency of 0, as it absorbs all power and radiates heat but not RF energy, showing that SWR alone is not an effective measure of an antenna's efficiency. Radiation in an antenna is caused by radiation resistance which can only be measured as part of total resistance including loss resistance. Loss resistance usually results in heat generation rather than radiation, and reduces efficiency. Mathematically, efficiency is calculated as radiation resistance divided by total resistance.
We classify the MPT efficiency roughly into three stagesDC-RF conversion efficiency which
includes losses caused by beam forming, beam collection efficiency which means ratio of all
radiated power to collected power on a receiving antenna, and RF-DC conversion efficiency.
RF-DC Conversion Efficiency
The RF-DC conversion efficiency of the rectenna or the CWC is over 80 % of experimental
results as shown in Fig.6.1. Decline of the efficiency is caused by array connection loss, change of
optimum operation point of the rectenna array caused by change of connected load, trouble of the
rectenna, and any losses on the systems, for example, DC/AC conversion, cables, etc. However, it is
easier to keep high efficiency than that on the other two stages

     Fig. 2.12        Typical characteristic of RF-DC conversion efficiency of Rectenna
Beam Collection Efficiency
The beam collection efficiency depends on the transmitter and receiver aperture areas, the wavelength, and the separation distance between the two antennas as shown in the section 1. For example, it was calculated approximately 89% in the SPS reference system with the parameters as follows; the transmitter aperture is 1 kmφ, the rectenna aperture is 10×13 km, the wavelength is 12.24 cm (2.45GHz), and the distance between the SPS and the rectenna 36,000km.They assume 10dB Gaussian power taper on the transmitting antenna. The beam pattern on the ground is shown in Fig 2.13  Decline of the efficiency is caused by phase/frequency/amplitude error on a phased array. Phase/frequency/amplitude error on a phased array causes difference of beam direction and rise of
sidelobes. If we have enough large number of elements, the difference of the beam direction is negligible. The rise of the sidelobe decreases antenna gain and beam collection efficiency. If antenna planes separate each other structurally, grating lobes, whose power level is the same as main beam may occur and power can not be concentrated to the rectenna array. This problem occurs in module-type phased array. The idea of random array has risen in order to suppress the grating lobes. However, a sidelobe level increases, beam collection efficiency decreases and have to search for special techniques. Power in grating lobes diffuses not to a main lobe but to sidelobes. Therefore, we have to fundamentally suppress the grating lobes for a MPT system.

Fig. 2.13    Beam Pattern on the Ground
DC-RF Conversion Efficiency
If we do not have to steer a microwave beam electrically in a MPT, we can use a microwave transmitter with high DC-RF conversion efficiency over 70-80 % like microwave tubes. However, if we need to steer a microwave beam electrically without any grating lobes, we have to use phase shifters with high loss. Especially in the SPS system, the optimum and economical size of the transmitting phased array and microwave power are calculated as around a few km and over a few GW, respectively. It means that microwave power from one antenna element is much smaller than that from one microwave tube or high power (over a several tens watts) semiconductor amplifier. It also means that phase shifter have to be installed after the microwave generation/amplification if microwave beam will be steered to directions of larger than 5 degrees without grating lobes.
(g) Bandwidth
The bandwidth of an antenna is the range of frequencies over which it is effective, usually centered on the resonant frequency. The bandwidth of an antenna may be increased by several techniques, including using thicker wires, replacing wires with cages to simulate a thicker wire, tapering antenna components (like in a feed horn), and combining multiple antennas into a single assembly and allowing the natural impedance to select the correct antenna. Small antennas are usually preferred for convenience, but there is a fundamental limit relating bandwidth, size and efficiency.

(h) Polarization

The polarization of an antenna is the orientation of the electric field (E-plane) of the radio wave with respect to the Earth's surface and is determined by the physical structure of the antenna and by its orientation. It has nothing in common with antenna directionality terms: "horizontal", "vertical" and "circular". Thus, a simple straight wire antenna will have one polarization when mounted vertically, and a different polarization when mounted horizontally. "Electromagnetic wave polarization filters" are structures which can be employed to act directly on the electromagnetic wave to filter out wave energy of an undesired polarization and to pass wave energy of a desired polarization.
Reflections generally affect polarization. For radio waves the most important reflector is the ionosphere – signals which reflect from it will have their polarization changed unpredictably.
For signals which are reflected by the ionosphere, polarization cannot be relied upon. For line-of-sight communications for which polarization can be relied upon, it can make a large difference in signal quality to have the transmitter and receiver using the same polarization; many tens of dB differences are commonly seen and this is more than enough to make the difference between reasonable communication and a broken link.
Polarization is largely predictable from antenna construction but, especially in directional antennas, the polarization of side lobes can be quite different from that of the main propagation lobe. For radio antennas, polarization corresponds to the orientation of the radiating element in an antenna. A vertical omni directional WiFi antenna will have vertical polarization (the most common type).
An exception is a class of elongated waveguide antennas in which vertically placed antennas are horizontally polarized. Many commercial antennas are marked as to the polarization of their emitted signals.
Polarization is the sum of the E-plane orientations over time projected onto an imaginary plane perpendicular to the direction of motion of the radio wave. In the most general case, polarization is elliptical (the projection is oblong), meaning that the antenna varies over time in the polarization of the radio waves it is emitting. Two special cases are linear polarization (the ellipse collapses into a line) and circular polarization (in which the ellipse varies maximally). In linear polarization the antenna compels the electric field of the emitted radio wave to a particular orientation. Depending on the orientation of the antenna mounting, the usual linear cases are horizontal and vertical polarization.
In circular polarization, the antenna continuously varies the electric field of the radio wave through all possible values of its orientation with regard to the Earth's surface. Circular polarizations, like elliptical ones, are classified as right-hand polarized or left-hand polarized using a "thumb in the direction of the propagation" rule. Optical researchers use the same rule of thumb, but pointing it in the direction of the emitter, not in the direction of propagation, and so are opposite to radio engineer’s use.
In practice, regardless of confusing terminology, it is important that linearly polarized antennas be matched, lest the received signal strength be greatly reduced. So horizontal should be used with horizontal and vertical with vertical. Intermediate matchings will lose some signal strength, but not as much as a complete mismatch. Transmitters mounted on vehicles with large motional freedom commonly use circularly polarized antennas so that there will never be a complete mismatch with signals from other sources. In the case of radar, this is often reflections from rain drops.

(i) Transmission and reception

All of the antenna parameters are expressed in terms of a transmission antenna, but are identically applicable to a receiving antenna, due to reciprocity. Impedance, however, is not applied in an obvious way; for impedance, the impedance at the load (where the power is consumed) is most critical. For a transmitting antenna, this is the antenna itself. For a receiving antenna, this is at the (radio) receiver rather than at the antenna. Tuning is done by adjusting the length of an electrically long linear antenna to alter the electrical resonance of the antenna.
Antenna tuning is done by adjusting an inductance or capacitance combined with the active antenna (but distinct and separate from the active antenna). The inductance or capacitance provides the reactance which combines with the inherent reactance of the active antenna to establish a resonance in a circuit including the active antenna. The established resonance being at a frequency other than the natural electrical resonant frequency of the active antenna. Adjustment of the inductance or capacitance changes this resonance.
Antennas used for transmission have a maximum power rating, beyond which heating, arcing or sparking may occur in the components, which may cause them to be damaged or destroyed. Raising this maximum power rating usually requires larger and heavier components, which may require larger and heavier supporting structures. This is a concern only for transmitting antennas, as the power received by an antenna rarely exceeds the microwatt range.
Antennas designed specifically for reception might be optimized for noise rejection capabilities. An antenna shield is a conductive or low reluctance structure (such as a wire, plate or grid) which is adapted to be placed in the vicinity of an antenna to reduce, as by dissipation through a resistance or by conduction to ground, undesired electromagnetic radiation, or electric or magnetic fields, which are directed toward the active antenna from an external source or which emanate from the active antenna. Other methods to optimize for noise rejection can be done by selecting a narrow bandwidth so that noise from other frequencies is rejected, or selecting a specific radiation pattern to reject noise from a specific direction, or by selecting a polarization different from the noise polarization, or by selecting an antenna that favors either the electric or magnetic field.
For instance, an antenna to be used for reception of low frequencies (below about ten megahertz) will be subject to both man made noise from motors and other machinery, and from natural sources such as lightning. Successfully rejecting these forms of noise is an important antenna feature. A small coil of wire with many turns is more able to reject such noise than a vertical antenna. However, the vertical will radiate much more effectively on transmit, where extraneous signals are not a concern.

2.6 Electromagnetic waves Derivation

Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. If we inspect Maxwell's equations without sources (charges or currents) then we will find that, along with the possibility of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell's equations for free space:
\nabla \cdot \mathbf{E} = 0  \qquad \qquad 
\qquad \ \ (1)
\nabla \times \mathbf{E} = -\frac{\partial 
\mathbf{B}}{\partial t}  \qquad \qquad \ (2)
\nabla \cdot \mathbf{B} = 0 \qquad \qquad 
\qquad \ \ (3)
\nabla \times \mathbf{B} = \mu_0 \epsilon_0 
\frac{\partial \mathbf{E}}{\partial t}  \qquad \quad \ (4)
\nabla  is a vector differential operator (Del).
One solution,
\mathbf{E}=\mathbf{B}=\mathbf{0}, is trivial.
To see the more interesting one, we utilize vector identities, which work for any vector, as follows:
\nabla \times \left( \nabla \times \mathbf{A} 
\right) = \nabla \left( \nabla \cdot \mathbf{A} \right) - \nabla^2 
To see how we can use this take the curl of equation (2):
\nabla \times \left(\nabla \times \mathbf{E} 
\right) = \nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} 
\right) \qquad \qquad \qquad \quad \ \ \ (5) \,
Evaluating the left hand side:
 \nabla \times \left(\nabla \times \mathbf{E} 
\right) = \nabla\left(\nabla \cdot \mathbf{E} \right) - \nabla^2 
\mathbf{E} =  - \nabla^2 \mathbf{E} \qquad \ \ (6) \,
Where we simplified the above by using equation (1).
Evaluate the right hand side:
\nabla \times \left(-\frac{\partial 
\mathbf{B}}{\partial t} \right) = -\frac{\partial}{\partial t} \left( 
\nabla \times \mathbf{B} \right) = -\mu_0 \epsilon_0 \frac{\partial^2 
\mathbf{E}}{\partial t^2} \quad \ \ \ \ (7)
Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely
                     \nabla^2 \mathbf{E} = \mu_0 \epsilon_0 
\frac{\partial^2 \mathbf{E}}{\partial t^2} 
Applying a similar pattern results in similar differential equation for the magnetic field:
                \nabla^2 \mathbf{B} = \mu_0 \epsilon_0 
\frac{\partial^2 \mathbf{B}}{\partial t^2}       
These differential equations are equivalent to the wave equation:
\nabla^2 f = \frac{1}{{c_0}^2} 
\frac{\partial^2 f}{\partial t^2} \,
Co is the speed of the wave in free space and
f describes a displacement
Or more simply:
\Box f = 0
Where \Box is d'Alembertian:
\Box = \nabla^2 - \frac{1}{{c_0}^2} 
\frac{\partial^2}{\partial t^2} = \frac{\partial^2}{\partial x^2} + 
\frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} - 
\frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} \
Notice that in the case of the electric and magnetic fields, the speed is:
c_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}}
Which, as it turns out, is the speed of light in free space. Maxwell's equations have unified the permittivity of free space ε0, the permeability of free space μ0, and the speed of light itself, c0. Before this derivation it was not known that there was such a strong relationship between light and electricity and magnetism.
But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. Let's consider a generic vector wave for the electric field.
\mathbf{E} = \mathbf{E}_0 f\left( 
\hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)
Here  \mathbf{E}_0 is the constant amplitude, f is any second differentiable function,  
\hat{\mathbf{k}} is a unit vector in the direction of propagation, and  {\mathbf{x}}  is a position vector. We observe that       f\left( 
\hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)    is a generic solution to the wave equation.
 In other words
\nabla^2 f\left( \hat{\mathbf{k}} \cdot 
\mathbf{x} - c_0 t \right) = \frac{1}{{c_0}^2} 
\frac{\partial^2}{\partial t^2} f\left( \hat{\mathbf{k}} \cdot 
\mathbf{x} - c_0 t \right),
For a generic wave traveling in the \hat{\mathbf{k}} direction.
This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?
\nabla \cdot \mathbf{E} = \hat{\mathbf{k}} 
\cdot \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t 
\right) = 0
\mathbf{E} \cdot \hat{\mathbf{k}} = 0
The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.
\nabla \times \mathbf{E} = \hat{\mathbf{k}} 
\times \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t 
\right) = -\frac{\partial \mathbf{B}}{\partial t}
\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} 
\times \mathbf{E}
The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of \mathbf{E},\mathbf{B}.
Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, E0 = c0B0, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as\mathbf{E} 
\times \mathbf{B}.
From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization. On a quantum level, it is described as photon polarization
2.7 Near field
Near field is a wireless transmission technique over distances comparable to, or a few times the diameter of the device(s), and up to around a quarter of the wavelengths used. Near field energy itself is non radioactive, but some radioactive losses will occur.
The term near-field region (also known as the near field or near zone) has the following meanings with respect to different telecommunications technologies:

  • The close in region of an antenna where the angular field distribution is dependent upon the distance from the antenna.

  • In the study of diffraction and antenna design, the near field is that part of the radiated field that is below distances shorter than the Fresnel parameter S = D2/(4λ) from the source of the diffracting edge or antenna of longitude or diameter D.

  • In optical fiber communications, the regions close to a source or aperture.

The diffraction pattern in the near field typically differs significantly from that observed at infinity and varies with distance from the source.
 2.8   Far field
Means for long conductors of electricity forming part of an electric circuit and electrically connecting said ionized beam to an electric circuit. Far field methods achieve longer ranges, often multiple kilometer ranges, where the distance is much greater than the diameter of the device(s). With radio wave and optical devices the main reason for longer ranges is the fact that electromagnetic radiation in the far-field can be made to match the shape of the receiving area (using high directivity antennas or well-collimated Laser Beam) thereby delivering almost all emitted power at long ranges. The maximum directivity for antennas is physically limited by diffraction
In the far field, the shape of the antenna pattern is independent of distance. If the source has a maximum overall dimension D (aperture width) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2/(4λ), S > 1.For a beam focused at infinity, the far-field region is sometimes referred to as the Fraunhofer region. Other synonyms are far field, far zone, and radiation field.
Methods, Recent Technologies, Researches and Invention of WPT system

 In this chapter, we classified WPT system and describe recent technologies, researches and invention of WPT system.
3.1    WIRELESS POWER TRANSMISSION METHODS (based on near field and Far Field)
At least four methods exist by which electrical energy can be transferred from a source to a load without the use of manmade conductors. These are: electromagnetic induction, electromagnetic radiation, evanescent wave coupling, and electrical conduction. The second method is radiative; the others are non-radiative. Only electro-magnetic Radiation is used for Far field, other three methods are use for near field.

3.1.1      Electro dynamic induction
The "electrodynamic inductive effect" or "resonant inductive coupling" has key implications in solving the main problem associated with non-resonant inductive coupling for wireless energy transfer; specifically, the dependence of efficiency on transmission distance. Electromagnetic induction works on the principle of a primary coil generating a predominantly magnetic field and a secondary coil being within that field so a current is induced in the secondary. Coupling must be tight in order to achieve high efficiency. As the distance from the primary is increased, more and more of the magnetic field misses the secondary. Even over a relatively small range the simple induction method is grossly inefficient, wasting much of the transmitted energy.
Faraday's law of electromagnetic induction states that:
 \mathcal{E} = -{{d\Phi_B} \over dt},
\mathcal{E}is the electromotive force (emf) in volts
ΦB is the magnetic flux in webers
For the common but special case of a coil of wire, composed of N loops with the same area, Faraday's law of electromagnetic induction states that
 \mathcal{E} = - N{{d\Phi_B} \over dt}
\mathcal{E}is the electromotive force (emf) in volts
N is the number of turns of wire
ΦB is the magnetic flux in webers through a single loop
A corollary of Faraday's Law, together with Ampere's and Ohm's laws is Lenz's law:
The emf induced in an electric circuit always acts in such a direction that the current it drives around the circuit opposes the change in magnetic flux which produces the emf.
Electromagnetic induction underlies the operation of generators, all electric motors, transformers, induction motors, synchronous motors, solenoids, and most other electrical machines.
Wireless Power Transmission is occurred by using electro-dynamic induction. It is done by three procedures. This are-
a) Inductive coupling
b) Resonant coupling
c) Capacitive coupling
(a) Inductive coupling
Inductive coupling is an example of a near field method. Inductive coupling is the transfer of energy from one circuit (such as a conductive antenna and associated circuitry) to another by means of mutual inductance between the two circuits. Now-a-days inductive coupling is known as ecoupled.
The action of an electrical transformer is the simplest instance of inductive coupling. The coupling between two wires can be increased by winding them into coils and placing them close together on a common axis, so the magnetic field of one coil passes through the other coil. The two coils may be physically contained in a single unit, as in the primary and secondary sides of a transformer, or may be separated. The battery chargers of a mobile phone or the transformers in the street are examples of how this principle can be used. Induction cookers and many electric toothbrushes are also powered by this technique.figure-3.1 shows the process of inductive coupling.
Figure3.1: the process of inductive coupling
The main drawback to induction, however, is the short range. The receiver must be in relatively close proximity to the transmitter (or “induction unit") in order to inductively couple with it.
 (b) Resonant coupling
From the beginning of inductive power transmission, resonant circuits are used to enhance the inductive power transmission. Already Nicola Tesla used resonances in his first experiments about inductive power transmission more than hundred years ago. Especially for systems with a low coupling factor, a resonant receiver can improve the power transfer. Resonant power transmission is a special, but widely used method of inductive power transmission and is limited by the same constraints of magnetic fields emissions and efficiency.
To understand the effect, it can be compared to mechanical resonances. Consider a string tuned to a certain tone as mechanical resonator. Even a far away and low level sound generator can excite the string to vibration, if the tone pitch is matched .Here, the resonator in the receiver consists of the receiver inductance and a capacitor. Also the transmitter can have a resonator. The transmitter and receiver coils LTx and LRx can be considered as weakly coupled transformer.
In this diagram, also the resistances of the windings are shown. The diagram shows clearly, that the resonant capacitors cancel out the stray inductance in the receiver and the magnetizing inductance in the transmitter. Now, the only remaining limit for the power transmission is the winding resistances of the coils, which impedance is one or two orders of magnitude lower than that of the inductances. Therefore, for a given generator source, much more power can be received. Using resonance can help efficiency dramatically. If resonant coupling is used, the coils are individually capacitively loaded so as to form a tuned LC circuit. If the primary and secondary coils are resonant at a common frequency, it turns out that significant power may be transmitted between the coils over a range of many times the coil diameters.
 (c) Electrostatic induction / capacitive coupling
The "electrostatic induction effect" or "capacitive coupling" is a type of high field gradient or differential capacitance between two elevated electrodes over a conducting ground plane for wireless energy transmission involving high frequency alternating current potential differences transmitted between two plates or nodes. The electrostatic forces through natural media across a conductor situated in the changing magnetic flux can transfer energy to a receiving device (such as Tesla's wireless bulbs).Sometimes called "the Tesla effect" it is the application of a type of electrical displacement, i.e., the passage of electrical energy through space and matter, other than and in addition to the development of a potential across a conductor.

Figure 3.2: Tesla illuminating two exhausted tubes by means of a powerful, rapidly alternating electrostatic field created between two vertical metal sheets suspended from the ceiling on insulating cords. (This image is rotated 90deg counterclockwise.)
Advantages of induction

  1. low in cost.

  2.  highly efficient for transforming power in near field.

  3. Easy to design.

Disadvantages of induction
  1.  some times simple induction method is grossly inefficient, wasting much of the    transmitted energy .
               2. The distances between the coils must be very small.
               3. It can be effected by environment.
3.1.2      Electromagnetic radiation
Electromagnetic radiation in the form of either radio waves or light can also be used to transfer energy wirelessly. While systems based upon this method are used mostly for information transfer, a high degree of efficiency in power transmission is also achievable under certain circumstances. This beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its exceptional performance characteristics and robustness such as a Yagi antenna. Efficient power transmission via radio waves can be achieved by using shorter wavelengths of electromagnetic radiation, typically in the microwave range. A rectenna may be used to convert the microwave energy back into electricity. Conversion efficiencies exceeding 95% have been achieved in this manner. Power beaming using microwaves has been proposed for the transmission of energy from orbiting solar power satellites to earth and the beaming of power to spacecraft leaving orbit has been considered. In the case of light, power can be transmitted by converting electricity into a laser beam that is then fired at a solar cell receiver. Conversion to light, such as a laser, is usually very inefficient (although quantum cascade lasers improve this) Conversion back into electricity is also typically very inefficient, with the absolute best modern solar cells achieving 40% efficiency.  Atmospheric absorption causes losses. As with microwave beaming, this method requires a direct line of sight with the target. Photovoltaic cells can also be used to receive energy from Earth's strongest natural source of electromagnetic radiation, the Sun.
Note:  Laser wave and radio / microwave are included in Electro magnetic radiation
3. 1.2.1       Wireless transmission by Radio or microwave
The earliest work in the area of wireless transmission via radio waves (etheric force) was performed by Thomas Edison in 1875. Later, Guglielmo Marconi worked with a modified form of Edison's transmitter. Yagi and Uda published their first paper on the tuned high-gain directional array now known as the Yagi antenna. While it did not prove to be particularly useful for power transmission, this beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its excellent performance characteristics. Power transmission via radio waves can be made more directional, allowing longer distance power beaming, with shorter wavelengths of electromagnetic radiation, typically in the microwave range.

Fig 3.3   Block diagram of microwave power transmission
Process of a microwave power transmission
Wireless power transfer through microwaves/radio waves is a three-step process:

  1. Direct current (DC) or alternating current (AC) electrical power is converted into radio frequency (RF) power.

  2. The RF power is transmitted through space or atmosphere to some distant point and the power is collected and converted back into DC power at the receiving point.


Advantages of microwave power transmission

  1. Microwave/radio wave is very useful for both short and long distances. Experiments in the tens of kilowatts have been performed at Goldstone in California in 1975 and more recently (1997) at Grand Bassin on Reunion Island.

  2. Its efficiency is much higher than electromagnetic induction.

  3. This technology is fairly mature.

Disadvantages of microwave power transmission

  1. The power beaming of microwave in atmosphere has some harmful effects for users.

In order to separate users from any risk of safety problems, a wireless power transfer system must remain below FCC regulations. In addition to abiding by the FCC regulations a WPT system should the user to turn the system on or off manually.

  1. Frequency allocation is always a problem for this method. This is because attenuation of microwaves due to dust particles, rain drops, cloud droplets, ice crystals, snow etc occurs.

Satellite with microwave wireless power transmission
wired helicopter
Increase DC-RF-transmission-RF-DC efficiency and etc.    Wireless transmission by Laser beam
With a laser beam centered on its panel of photovoltaic cells, a lightweight model plane makes the first flight of an aircraft powered by a laser beam inside a building at NASA Marshall Space Flight Center. In the case of electromagnetic radiation closer to visible region of spectrum (10s of microns (um) to 10s of nm), power can be transmitted by converting electricity into a laser beam that is then pointed at a solar cell receiver. This mechanism is generally known as "Power Beaming" because the Power is beamed at a receiver that can convert it to usable electrical energy. There are quite a few unique advantages of Laser based energy transfer that outweigh the disadvantages. Collimated monochromatic wave front propagation allows narrow beam cross-section area for energy confinement over large ranges. Compact size of solid state lasers-photovoltaic semiconductor diodes allows ease of integration into products with small form factors.
Ability to operate with zero radio-frequency interference to existing communication devices i.e. Wi-Fi and cell phones..Control of Wireless Energy Access, instead of Omni-directional transfer where there can be no authentication before transferring energy.
These allow laser-based Wireless Energy Transfer concept to compete with conventional energy transfer methods..Its drawbacks are:
A laser consists of a gain medium inside a highly reflective optical cavity, as well as a means to supply energy to the gain medium. The gain medium is a material with properties that allow it to amplify light by stimulated emission. In its simplest form, a cavity consists of two mirrors arranged such that light bounces back and forth, each time passing through the gain medium. Typically one of the two mirrors, the output coupler, is partially transparent. The output laser beam is emitted through this mirror.

Design or Laser Construction

Fig 3.4 Principal components from above figure
1. Gain medium    2. Laser pumping energy             3. High reflector              4. Output coupler    5. Laser beam
Light of a specific wavelength that passes through the gain medium is amplified (increases in power); the surrounding mirrors ensure that most of the light makes many passes through the gain medium, being amplified repeatedly. Part of the light that is between the mirrors (that is, within the cavity) passes through the partially transparent mirror and escapes as a beam of light.
The process of supplying the energy required for the amplification is called pumping. The energy is typically supplied as an electrical current or as light at a different wavelength. Such light may be provided by a flash lamp or perhaps another laser. Most practical lasers contain additional elements that affect properties such as the wavelength of the emitted light and the shape of the beam.
Conversion to light, such as with a laser, is moderately inefficient (although quantum cascade lasers improve this)
Conversion back into electricity is moderately inefficient, with photovoltaic cells achieving 40%-50% efficiency. (Note that conversion efficiency is rather higher with monochromatic light than with insolation of solar panels). Atmospheric absorption causes losses. As with microwave beaming, this method requires a direct line of sight with the target. The Laser "Power Beaming" technology has been mostly explored in military weapon sand aerospace applications and is now being developed for commercial and consumer electronics Low-Power applications. Wireless energy transfer system using laser for consumer space has to satisfy Laser safety requirements standardized under IEC 60825. To develop an understanding of the trade-offs of Laser ("a special type of light wave"-based system):  Propagation of a laser beam  (on how Laser beam propagation is much less affected by diffraction limits) Coherence and the range limitation problem (on how spatial and spectral coherence characteristics of Lasers allows better distance-to-power capabilities) Airy disk (on how most fundamentally wavelength dictates the size of a disk with distance) Applications of laser diodes (on how the laser sources are utilized in various industries and their sizes are reducing for better integration) Geoffrey Landis is one of the pioneers of Solar Power Satellite and Laser-based transfer of energy especially for Space and Lunar missions. The continuously increasing demand for safe and frequent space missions has resulted in serious thoughts on a futuristic Space elevator that would be powered by Lasers. NASA's Space elevator would need wireless power to be beamed to it for it to climb a tether. NASA's Dryden Flight Research Center has demonstrated flight of a lightweight unmanned model plane powered by a laser beam. This proof-of-concept demonstrates the feasibility of periodic recharging using the Laser beam system and the lack of need to return to ground

Laser safety

Even the first laser was recognized as being potentially dangerous. Theodore Maiman characterized the first laser as having a power of one "Gillette" as it could burn through one Gillette razor blade. Today, it is accepted that even low-power lasers with only a few milliwatts of output power can be hazardous to human eyesight, when the beam from such a laser hits the eye directly or after reflection from a shiny surface. At wavelengths which the cornea and the lens can focus well, the coherence and low divergence of laser light means that it can be focused by the eye into an extremely small spot on the retina, resulting in localized burning and permanent damage in seconds or even less time.
Lasers are usually labeled with a safety class number, which identifies how dangerous the laser is:

  • Class 1 is inherently safe, usually because the light is contained in an enclosure, for example in CD players.

  • Class 2 is safe during normal use; the blink reflex of the eye will prevent damage. Usually up to 1 mW power, for example laser pointers.

  • Class 3A lasers are usually up to 5 mW and involve a small risk of eye damage within the time of the blink reflex. Staring into such a beam for several seconds is likely to cause (minor) eye damage.

  • Class 3B can cause immediate severe eye damage upon exposure. Usually lasers up to 500 mW, such as those in CD and DVD writers.

  • Class 4 lasers can burn skin, and in some cases, even scattered light can cause eye and/or skin damage. Many industrial and scientific lasers are in this class.

The indicated powers are for visible-light, continuous-wave lasers. For pulsed lasers and invisible wavelengths, other power limits apply. People working with class 3B and class 4 lasers can protect their eyes with safety goggles which are designed to absorb light of a particular wavelength.
Certain infrared lasers with wavelengths beyond about 1.4 micrometers are often referred to as being "eye-safe". This is because the intrinsic molecular vibrations of water molecules very strongly absorb light in this part of the spectrum, and thus a laser beam at these wavelengths is attenuated as completely as it passes through the eye's cornea that no light remains to be focused by the lens onto the retina. The label "eye-safe" can be misleading, however, as it only applies to relatively low power continuous wave beams and any high power or Q-switched laser at these wavelengths can burn the cornea, causing severe eye damage.
Advantages of laser Wireless Power Transfer

  1.  Collimated monochromatic wave front propagation allows narrow beam cross-section area for energy confinement over large ranges.

  2. Compact size of solid state lasers photo voltaic semiconductor diodes allows ease of integration into products with small form factors.

  3. Ability to operate with zero radio frequency interference to existing communication devices i.e. Wi-Fi and cell phones.

  4. Control of Wireless Energy Access, instead of unidirectional transfer where there can be no authentication before transferring energy.

Disadvantages of laser Wireless Power Transfer

  1.  Conversion to light, such as with a laser, is moderately inefficient (although quantum cascade lasers improve this)

  2. Conversion back into electricity is moderately inefficient, with photovoltaic cells achieving 40%-50% efficiency. (Note that conversion efficiency is rather higher with monochromatic light than with isolation of solar panels).

  3. Atmospheric absorption causes losses.

  4. As with microwave beaming, this method requires a direct line of sight with the target.

3.1.3    Evanescent wave coupling
Researchers at MIT believe they have rediscovered a way to wirelessly transfer power using non-radiative electromagnetic energy resonant tunneling. By sending electromagnetic waves around in a highly angular waveguide, evanescent waves are produced which carry no energy. Evanescent wave coupling is a process by which electromagnetic waves are transmitted from one medium to another by means of the evanescent (or decaying) electromagnetic field(s). This is usually accomplished by placing two or more waveguides close together so that the evanescent field does not decay much in the vicinity of the other waveguide. Assuming the receiving waveguide can support mode(s) of the appropriate frequency, the evanescent field gives rise to propagating wave mode(s), thereby connecting (or coupling) the wave from one waveguide to the next.  If a proper resonant waveguide is brought near the transmitter, the evanescent waves can allow the energy to tunnel (specifically evanescent wave coupling, the electromagnetic equivalent of tunneling) to the power drawing waveguide, where they can be rectified into DC power. Since the electromagnetic waves would tunnel, they would not propagate through the air to be absorbed or dissipated, and would not disrupt electronic devices or cause physical injury like microwave or radio wave transmission might. Researchers anticipate up to 5 meters of range for the initial device, and are currently working on a functional prototype. ("'Evanescent coupling' could power gadgets wirelessly", NewScientist.com)  Evanescent coupling is always associated with matter, i.e. with the induced currents and charges within a partially reflecting surface. This coupling is directly analogous to the nearfield, non-radiative coupling between the primary and secondary coils of a transformer, or between the two plates of a capacitor. Mathematically, the process is the same as that of quantum tunneling, except with electromagnetic waves instead of quantum-mechanical wave functions. Evanescent wave coupling is used to excite dielectric microsphere resonators among other things. A new application could be wireless energy transfer, useful, for instance, for charging electronic gadgets without wires.
If a proper resonant waveguide is brought near the transmitter, the evanescent waves can allow the energy to tunnel (specifically evanescent wave coupling, the electromagnetic equivalent of tunneling) to the power drawing waveguide, where they can be rectified into DC power. Since the electromagnetic waves would tunnel, they would not propagate through the air to be absorbed or dissipated, and would not disrupt electronic devices or cause physical injury like microwave or radio wave transmission might. Researchers anticipate up to 5 meters of range for the initial device, and are currently working on a functional prototype. Evanescent coupling is always associated with matter, i.e. with the induced currents and charges within a partially reflecting surface. This coupling is directly analogous to the nearfield, non-radiative coupling between the primary and secondary coils of a transformer, or between the two plates of a capacitor.
 Mathematically, the process is the same as that of quantum tunneling, except with electromagnetic waves instead of quantum-mechanical wave functions. Evanescent wave coupling is used to excite dielectric micro sphere resonators among other things. A new application could be wireless energy transfer, useful, for instance, for charging electronic gadgets without wires.

Break down of Evanescent wave coupling
This method of resonant inductive coupling has key implications in the solution of the two main problems associated with non-resonant inductive coupling and electromagnetic radiation, one of which is caused by the other; distance and efficiency. Electromagnetic induction works on the principle of a primary coil generating a predominantly magnetic field and a secondary coil being within that field so a current is induced within its coils. This causes the relatively short range due to the amount of power required to produce an electromagnetic field. Over greater distances the non-resonant induction method is inefficient and wastes much of the transmitted energy, just to increase range. This is where the resonance comes in and helps efficiency dramatically by "tunneling" the magnetic field to a receiver coil that resonates at the same frequency. Unlike the multiple-layer secondary of a non-resonant transformer, such receiving coils are single layer solenoids with closely spaced capacitor plates on each end, which, combined, allow the coil to be tuned into a certain frequency thereby eliminating the wide energy wasting wave problem and allowing the energy used to focus on a certain frequency increasing the range.
Here is a tuned circuit, out in the field with three incandescent lamps and a condenser. The energy is transmitted inductively, from the oscillator. In this case, I have the primary supply circuit, the energizing condenser circuit, the primary inducing circuit, and the secondary in the field as in the fourth circuit, all tuned—four circuits in resonance.
It is found that with the above circuits and under such conditions, about 1 mile communications should be possible. With circuits 1000 meters square, about 30 miles. From this, the inferiority of the induction method would appear to be immense as compared with disturbed charge of ground and air method.

Figure 3.5: Principle of evanescent wave fluorescence detection in polymer waveguides.


Evanescent wave coupling is commonly used in photonic and nanophotonic devices as waveguide sensors. Evanescent wave coupling is used to excite dielectric microsphere resonators among other things. A typical application is resonant energy transfer, useful, for instance, for charging electronic gadgets without wires. A particular implementation of this is WiTricity; the same idea is also used in some Tesla coils.
Evanescent coupling, as near field interaction, is one of the concerns in compatibility. Evanescent wave coupling plays a major role in the theoretical explanation of transmission. Sony wants to power flat TV sets (60 watt, 50 cm, and 60% efficiency over all)
 3.1.4    Electrical conduction
From experiments performed between 1888 and 1907 Nikola Tesla concluded that the earth is an excellent electrical conductor, and an electric current can be made to propagate undiminished for distances of thousands of miles. It was also found that the earth’s natural electrical charge can be made to oscillate, "by impressing upon it [very low frequency] current waves of certain lengths, definitely related to its diameter." .It was also discovered that the resistance of the earth is negligible due to its immense cross sectional area and relative shortness as compared to its diameter. A [conducting] sphere of the size of a little marble offers a greater impediment to the passage of a current than the whole earth. The resistance is only at the point where you get into the earth with current. In this system, the current actually flows from the transmitter through the ground to the receiver; it is stated distinctly: “It is to be noted that the phenomenon here involved in the transmission of electrical energy is one of true conduction and is not to be confounded with the phenomena of electrical radiation, etc." Tesla envisioned the development of a "world system" based upon these principles that would combine wireless telecommunications and electrical power transmission. The currents are proportionate to the potentials which are developed under otherwise equal conditions. The communications component was his initial goal. While electrical power transmission was viewed as being of greater importance, the attempt at its large-scale implementation would have taken place only after feasibility of the basic concept had been established. In 1901 work began on a prototype world wireless station known as Wardenclyffe, that would have been the first in a system of interconnected towers designed for this purpose. The second facility was planned for the southern coast of England. Wardenclyffe was not completed due to financial difficulties

fig. 3.6.a      The ground acts as the transmission line

fig. 3.6.b.   Charges vibrate, while energy flows sideways
 Conditions :
1. Used for low frequency
2.  Current waves of certain lengths.
3.  made to propagate undiminished for distances of thousands of miles .
3.2     Recent Technologies and Researches of Wireless Power Transmission – Beam Control, Target Detection, Propagation –

3.2.1   Recent Technologies of Retrodirective Beam Control
A microwave power transmission is suitable for a power transmission from/to moving transmitters targets.Therefore, accurate target detection and high efficient beam forming are important. Retrodirective system is always used for SPS. A corner reflector is most basic retrodirective systemThe corner reflectors consist of perpendicular metal sheets, which meet at an apex (Fig.3.7(a)). Incoming signals are reflected back in the direction of arrival through multiple reflections off the wall of the reflector. Van Atta array is also a basic technique of the retrodirective system. This array is made up of pairs of antennas spaced equidistant from the center of the array, and connected with equal length transmission lines (Fig.3.7(b)). The signal received by an antenna is re-radiated by its pair, thus the order of re-radiating elements are inverted with respect to the center of the array, achieving the proper phasing for retrodirectivity. Usual retrodirective system have phase conjugate circuits in each receiving/transmitting antenna, (Fig.3.7(c)) which play a same role as pairs of antennas spaced equidistant from the center of the array in Van Atta array. A signal transmitted from the target is received and re-radiated through the phase conjugate circuit to the direction of the target. The signal is called a pilot signal. We do not need any phase shifters for beam forming. The retrodirective system is usually used for satellite communication, wireless LAN, military, etc. There are many researches of the retrodirective system for these applications (Fig.3.8). They use the almost same frequency for the pilot signal and returned signal with a local oscillator (LO) signal at a frequency twice as high as the pilot signal frequency in the typical retrodirective systems (Fig.3.7(c)). Accuracy depends on stability of the frequency of the pilot signal and the LO signal. Prof. Itoh’s
group proposed the pilot signal instead of the LO signal.
Fig. 3.7 (a) two-sided corner reflector, (b) Van Atta Array, (c) retrodirective array with phase
conjugate circuits. 
There are other kinds of the phase conjugate circuits for the MPT applications. Kyoto University’s
group have developed a retrodirective system with asymmetric two pilot signals, ωt+Δω and ωt+2Δω,
and the LO signal of 2ωt. ωt indicate a frequency of a transmitter. They have also developed the
Fig.3.8 Various Retrodirective Array with Phase Conjugate Circuits Developed,
(a) 2.45GHz (b)  2.45GHz, (c) 62-66GHz, (d)  5.9GHz, (e) 6GHz, (f) 6GHz
other retrodirective system with 1/3 ωt pilot signal and without LO signal. The LO signal is generated from the pilot signals. The latter system solve a fluctuation problem of the LO and the pilot signal which cause phase errors because the fluctuations of the LO and the pilot signals are synchronous. They have used 2.45 GHz for ωt. Mitsubishi Electric Corporation in Japan have developed PLL-heterodyne type retrodirective system in which different frequencies for the pilot signal and the microwave power beam, 3.85 GHz and 5.77 GHz, respectively, have been used.The retrodirective system unifies target detection with beam forming by the phase conjugate circuits. There are some methods for target detecting with pilot signal which is separated to beam forming. We call the method “software retrodirective”. Computer is usually used for the software rectodirective with the phase data from a pilot signal and for the beam forming with calculation of the optimum phase and amplitude distribution on the array. In the software rectodirective, we can form microwave beam freely, for example, multi-beams. On contrary, we need phase shifters in all antennas.
After the target detection, we need accurate beam forming. For the optimum beam forming, there are some algorism, for instance, neural network, genetic algorithm, and multi-objective optimizationlearning. The “optimum” has multi-meanings, to suppress sidelobe level, to increase beam collection efficiency, and to make multiple power beams. We can select object of optimum and algorism freely with consideration of time of calculation.
A standard of the phase/frequency is very important to steer microwave power beam to a desired direction Both for beam forming with the software retrodirective and for retrodirective with the phase conjugate circuit. If the standard of the phase/frequency like the LO signal is different on one array, we cannot form the microwave beam to the desired direction. Although the best way is to use only one oscillator for the standard of the phase/frequency for one phased array of larger than km in size with more than billion elements, it is quite difficult. A better way is use of some oscillators on some group of sub-phased array and the oscillators are synchronous with each other. Some trials have been carried out. One is wireless synchronization of separated units. The present accuracy of wireless synchronization is below 0.6 ppm of the frequency and below 3.5 degree of phase error. The other is self-synchronization with some data sent from the target. In this method, a phase of a part of arrays is changed and a resultant change of the microwave beam intensity is measured in the rectenna site. The change gives us information on phase corrections.
3.2.2 Environmental Issues
Envernmental Issues are consider as
1. Interferences to Existent Wireless System
2 .Safety on Ground
3 .Interaction with Atmosphere
4. Interaction with Space Plasmas Interferences to Existent Wireless System
Most MPT system adopted 2.45 GHz or 5.8 GHz band which are allocated in the ITU-R Radio Regulations to a number of radio services and are also designated for ISM (Industry, Science and Medical) applications. Conversely speaking, there is no allowed frequency band for the MPT, therefore, we used the ISM band. The bandwidth of the microwave for the MPT do not need wide band and it is enough quite narrow since an essentially monochromatic wave is used without modulation because we use only carrier of the microwave as energy. Power density for the MPT is a few orders higher than that for the wireless communication. We have to consider and dissolve interferences between the MPT to the wireless communication systems. One calculation of the interferences between the MPT of the SPS, mainly 2.45 GHz, to the wireless communication systems was done in Japan. If the harmonics of the MPT frequencies are, however, regulated by the ITU (International Telecommunication Union) power flux density (PFD) limits, some modulation might be necessary. Carrier noises, harmonics, and spurious emissions of the MPT signal should be quite small to avoid interference to other radio services in operation around the world. Grating lobes and sidelobes of the MPT beam should be low enough in order to make the affected region as small as possible. Also, grating lobes should be mitigated because they are a direct loss of transmitter power. Safety on Ground
One of the characteristics of the MPT is to use more intense microwave than that in wireless
communication systems. Therefore, we have to consider MPT safety for human. In recent years there have been considerable discussions and concerns about the possible effect for human health by RF and MW radiation. Especially, there have been many research and discussions about effects at 50/60 Hz and over GHz (microwave). These two effects are different.
There is long history concerning the safety of the microwave. Contemporary RF/microwave
standards are based on the results of critical evaluations and interpretations of the relevant scientific literature. The SAR (specific absorption rate) threshold for the most sensitive effect considered
Potentially harmful to humans, regardless of the nature of the interaction mechanism, is used as the basis of the standard. The SAR is only heating problem. The scientific research results have indicated that the microwave effect to human health is only heating problem. This is different from the EMF research. Famous guidelines, the ICNIRP (International Commission on Non-Ionizing Radiation Protection) guidelines, are 50 or 10 W/m2 for occupationally exposed vs. the general public, at either frequency. The corresponding limits for IEEE standards for maximum permissible human exposure to microwave radiation, at 2.45 or 5.8 GHz, are 81.6 or 100 W/m2 as averaged over six min, and 16.3 or 38.7 W/m2 as averaged over 30 min, respectively, for controlled and uncontrolled environments. The controlled and uncontrolled situations are distinguished by whether the exposure takes place with or without knowledge of the exposed individual, and is normally interpreted to mean individuals who are occupationally exposed to the microwave radiation, as contrasted with the general public. In future MPT system, we have to keep the safety guideline outside of a rectenna site. Inside the rectenna site, there remains discussion concerning the keep out area, controlled or uncontrolled area. Interaction with Atmosphere
In general, effect of atmosphere to microwave is quite small. There are absorption and scatter by air, rain, and irregularity of air refraction ratio. In 2.45 GHz and 5.8 GHz, the absorption by water vapor and oxygen dominate the effect in the air. Especially, it is enough to consider only absorption by the oxygen in the microwave frequency. It is approximately 0.007 dB/km. In the SPS case, the amount of total absorption through the air from space is approximately 0.035 dB. When elevation is 47 degree in the middle latitude, for example, in Japan, the total absorption is approximately 0.05 dB. Attenuation factor by rain is shown in Fig.3.9 . The attenuation factor by rain whose intensity is 50 mm/h and 150 mm/h is 0.01 dB/km and 0.03 dB/km in 2.45 GHz and 0.3 dB/km and 1.2 dB/km in 5.8 GHz, respectively. In assumption that rain cell size is 5km at 50 mm/h and 3km at 150 mm/h, respectively, and that the elevation is 47 degree in the Japanese SPS case, we calculate the rain attenuation as follows; When rain intensity is 50 mm/h and 150 mm/h, the attenuation is 0.01 (dB/km) x 5 (km) x sec 47 (degree) = 0.07 (dB), 0.13 (dB) in 2.45 GHz, and 1.3 (dB) and 5.2 (dB) in 5.8 GHz, respectively. Scatter by irregularity of air refraction ratio is quite smaller than the absorption and scatter by air and rain. It was estimated below 0.0013 dB in the 2.45 Fig.3.9 Attenuation factor by rain 
GHz SPS. Total attenuation of the 2.45 GHz SPS is 0.05 + 0.13 + 0.0013 = 0.1813 dB. Total attenuation of the 5.8 GHz SPS is over 5 dB in hard rain circumstance. In the 2.45 GHz SPS, we can neglect the attenuation by air and rain. We have to consider a counter plan the attenuation by rain in the 5.8 GHz SPS.
3.2 .2.4 Interaction with Space Plasmas
When microwave from the SPS propagates through ionospheric plasmas, some interaction between the microwave and the ionospheric plasmas occurs. It is well known that refraction, Faraday rotation, scintillation, and absorption occur between weak microwave used for satellite communication and the plasmas. However, influence to the MPT system is negligible. For example, reflection through the ionosphere at 2.45 GHz and 5.8 GHz is only 0.67 m and 0.12 m, respectively, when they calculated theoretically with the Snell's law and total electron contents in the ionosphere.
However, there is no inference because diameter of rectenna site will be over km. Although plane of polarization will rotate in approximately 7 degree at 2.45 GHz by Faraday rotation, there is also no inference because we will use circular polarized microwave for the MPT of the SPS. It is nonlinear interaction between intense microwave and the space plasmas that we have to investigate before the commercial SPS. We theoretically predict that it has possibility to occur Ohmic heating of the plasmas, plasma hall effect by Ponderomotive force, thermal self-focusing effect of the microwave beam, and three-wave interactions and excitation of electrostatic waves in MHz bands. These interactions will not occur in existent satellite communication systems because the microwave power is very weak.
Perkins and Roble theoretically calculated the Ohmic heating by the microwave beam from the SPS in 1978.The absorption of the radio waves can be calculated from the electron density and electron-neutral collision frequency profile. The effect is largest in the lower ionosphere (D and E regions) where the collision frequency is highest. The NASA/DOE SPS was designed including the results of the reference and they decided that maximum microwave power density was 23 mW/cm2 at the center of the rectenna site. Concerning the three-wave interactions and excitation of electrostatic waves in MHz bands, Matsumoto predicted in 1982 that the microwaves may decay into forward traveling electron plasma waves (Raman scattering) or ion acoustic waves (Brillouin scattering) and a backward traveling Secondary microwave .The electron plasma waves could be Langmuir waves when the excitation is parallel to the geomagnetic field, or electron cyclotron waves for excitation perpendicular to the field. These frequencies are typically 2-10 MHz in the local ionospheric plasma. Matsumoto’s group carried out the first rocket MPT experiment called MINIX (Microwave Ionosphere Nonlinear Interaction experiment) in 1983 in order to observe the excitation of the plasma waves. It was found that the excited waves differed from the initial theoretical fig 3.10 expectations  in that the line spectrum expected from a simple three-wave coupling theory was in fact a broad spectrum, and the electron cyclotron harmonics were stronger than the Langmuir waves. Both these features could be successfully modeled using a more realistic computer simulationwhere the nonlinear feedback processes were fully incorporated. From these simulation results it was estimated that below 0.01 % of the microwave beam energy from the SPS would be converted to electrostatic waves.
Shklyar and Shinohara derived a equation of self-focusing effect of the microwave beam caused by the inhomogeneity of the microwave energy density in 1992. It occurs without the collisional plasma heating. They neglected collisions and based the analysis on kinetic equation in collision free plasma. Though the wave frequency is six orders of magnitude higher than the maximum collision

Fig.3.10 Observed Wave Spectrum Concerning Three-wave Interactions and Excitation of
Electrostatic Waves by Microwave in MINIX Rocket Experiment 
3.3   Recent Technologies and Researches of Wireless Power Transmission – Receivers and
Rectifiers –
Point-to-point MPT system needs a large receiving area with a rectenna array because one
rectenna element receives and creates only a few W. Especially for the SPS, we need a
huge rectenna site and a power network connected to the existing power networks on
the ground. On contrary, there are some MPT applications with one small rectenna
element such as RF-ID.
3.3.1 Recent Technologies of Rectenna
The word “rectenna” is composed of “rectifying circuit” and “antenna”. The rectenna and its word
were invented by W. C. Brown in 1960’s. The rectenna can receive and rectify a microwave
power to DC. The rectenna is passive element with a rectifying diode, operated without any power source. There are many researches of the rectenna elements (Fig.3.11). Famous research groups of the rectenna are Texas A&M University in USA, NICT(National Institute of Information and Communications Technology, past CRL) in Japan, and Kyoto University in Japan. The antenna of rectenna can be any type such as dipole, Yagi-Uda antenna, microstrip antenna, monopole,loop antenna, coplanar patch, spiral antenna, or even parabolic antenna. The rectenna can also take any type of rectifying circuit such as single shunt full-wave rectifier, full-wave bridgerectifier, or other hybrid rectifiers.The circuit, especially diode, mainly determines the RF-DC conversion efficiency. Silicon Schottky barrier diodes were usually used for the previous rectennas. New diode devices like SiC and GaN are expected to increase the efficiency. The rectennas with FET or HEMT appear in recent years. The rectenna using the active devices is not passive element. The single shunt full-wave rectifier is always used for the rectenna. It consists of a diode inserted to the circuit in parallel, a λ/4 distributed line, and a capacitor inserted in parallel. In an ideal situation, 100% of the received microwave power should be converted into DC power. Its operation can be explained theoretically by the same way of a F-class microwave amplifier. The λ/4 distributed line and the capacitor allow only even harmonics to flow to the load. As a result, the wave form on the λ/4 distributed line has a π cycle, which means the wave form is a full-wave rectified sine form. The world record of the RF-DC conversion efficiency among developed rectennas is approximately 90% at 4W input of 2.45 GHz microwave. Other rectennas in the world have approximately 70 – 90 % at 2.45GHz or 5.8GHz microwave input. The RF-DC conversion efficiency of the rectenna with a diode depends on the microwave power input intensity and the connected load. It has the optimum microwave power input intensity and the optimum load to achieve maximum efficiency. When the power or load is not matched the optimum,
Fig.3.11  Various Rectennas (a) Brown’s Rectenna (2.45GHz) (b) Brown’s Thin-Film Rectenna
(2.45GHz) (c) Hokkaido University’s Rectenna (2.45GHz) (d) Kyoto University’s Rectenna (2.45GHz) (e) Texas A&M University’s Rectenna (35GHz)  (f) CRL’s Rectenna (5.8GHz)(g) Denso’s Rectenna for Microrobot (14-14.5GHz) (h) University of Colorado’s Rectenna (8.5-12.2GHz) the efficiency becomes quite low (Fig.3.11). The characteristic is determined by the characteristic of the diode. The diode has its own junction voltage and breakdown voltage. If the input voltage to the diode is lower than the junction voltage or is higher than the breakdown voltage, the diode does not show a rectifying characteristic. As a result, the RF-DC conversion efficiency drops with a lower or higher input than the optimum.
In recent years, major research topic in the rectenna is to research and develop new rectennas which are suitable for a weak-wave microwave, which can be used in experimental power satellites and RF-ID. The weak-wave means in the "micro-watt" range. The RF-ID is the first commercial MPT system in the world. The weak microwave will be transmitted from the experimental satelliteon LEO to the ground because microwave power and size of transmitting antenna on the experimental satellite will be limited by the capacity of the present launch rockets. We have two approaches to increase the efficiency at the weak microwave input. One is to increase an antenna aperture under a weak microwave density. There are two problems for this approach. It makes sharp directivity and it is only applied for the SPS satellite experiment and not for the RF-ID application. The other approach is to develop a new rectifying circuit to increase the efficiency at a weak microwave input. We can apply this type of the rectenna for the commercial RF-ID.
3.3.2 Recent Technologies of Rectenna Array
The rectenna will be used as an array for high power MPT because one rectenna element rectifies a few W only. For usual phased array antenna, mutual coupling and phase distribution are problems to solve. For the rectenna array, problem is different from that of the array antenna because the rectenna array is connected not in microwave phase but in DC phase. When we connect two rectennas in series or in parallel, they will not operate at their optimum power output and their combined power output will be less than that if operated independently. Thisis theoretical prediction[.It is caused by characteristic of the RF-DC c onversion efficiency of the rectenna elements shown in Fig. 3.11. It was experimentally and theoretically reported that the total power decrease with series connection is more than that with parallel connection. It was further confirmed with simulation and experiments that current equalization in series connection is worse than voltage equalization in parallel connection. There is the optimum connection of the
rectenna array
The SPS requires a rectenna array whose diameter of over km. Although there are many
researches of rectenna elements as shown in references  and more , only a few rectenna
arrays were developed and used for experiments (Fig.3.12). The maximum rectenna array in the world
Fig. 3.12 Large Rectenna Array Used for (a) G-to-G Experiment in Goldstone in 1975 , (b)
G-to-G Experiment in Japan in 1994-95 , (c) fuel-free airship experiment in 1995
, (d) Experimental Equipment in Kyoto University
is that used for a ground to ground experiment in Goldstone by JPL, USA, in 1975 as shown in the section of MPT history. The size was 3.4 m x 7.2 m = 24.5 m2. A rectenna array that had 2,304 elements and whose size was 3.54 m x 3.2 m was developed for a ground to ground experiment conducted by Kyoto University, Kobe University, and Kansai Electric Corporation in 1994. Kyoto University has several types of rectenna arrays at 2.45 GHz and 5.8 GHz. These sizes are approximately 1mφ. Another rectenna array with the size of 2.7 m x 3.4 m was developed for MPT to fuel-free airship experiment with conducted by CRL (Communication Research Laboratory, NICT in present) in Japan and Kobe University in 1995. There is a large gap between these arrays of a few meters in size and the SPS array of kilometers in diameter. Research of larger scale rectenna arrays is required.
3.3.3 Recent Technologies of Cyclotron Wave Converter
If we would like to use a parabolic antenna as a MPT receiver, we have to use Cyclotron Wave Converter (CWC) instead of the rectenna. The CWC is a microwave tube to rectify high power microwave directly into DC. The most studied cyclotron wave converter (CWC) comprises an electron gun, a microwave cavity with uniform transverse electric field in the gap of interaction, a region with symmetrically reversed (or decreasing to zero) static magnetic field and a collector with depressed potential as shown in Fig.3.12 Microwave power of an external source is converted by this coupler into the energy of the electron beam rotation, the latter is transformed into additional energy of the longitudinal motion of the electron beam by reversed static magnetic field; then extracted by decelerating electric field of the collector and appeared at the load-resistance of this collector.
3.3.4 Rectenna Site Issue
It is widely assumed that a commercially feasible SPS will be on the order of GW. It delivers
significant electric power, and can contribute to any national power grid. The technology for
connection to the grid already exists, although the output of the SPS is a direct current. The output of thermal or nuclear power plant is an AC, because they must first drive a kind of
The SPS will be steady state base power system without CO2 emission. Its output is predictable. We have no problems economically and technologically with connecting the SPS to an existent power grid. Moreover, a GW class power plant is similar to a nuclear power plant or large hydropower plant. Most of the grid connection issues, therefore, are the same.
In Japan, some simulations concerning the connection with the rectennas and the existent power grid are carried out. When The SPS connect to existent power grid, it has possibility that accidents can occur at either the SPS side or the grid side. The grid is designed to take up the slack if the SPS dropouts without warning. In some cases the output of the rectenna may lapse. However, the DC power converter may be able to handle these lapses in most cases — within a certain specified range of lapses. If the lapse or power failure is too large, then output may cease. If connected to a large existent grid, then the grid should be able to take up the slack, somehow. If an accident occurs on the grid side, there is potential for trouble for the rectenna (power source to the grid). The grid CWCs Developed in Russia may be hit by electrical storms (thunder storms), but the power failure duration should be very short, short enough for the SPS to manage with such hits to the grid. However, a major accident at another power source (resulting output failure for hours or days), may be difficult for the SPS to cope with. More careful studies are needed on this matter. 
3.4    Wireless power transmission system for a Micro Aerial Vehicle
Wireless power transmission system for a Micro Aerial Vehicle using a microwave beam has been developed. This system has been intensively studied as the technology for the Solar Power Satellite (SPS) system, in which microwave is transmitted from a satellite to the ground .The concept of this system is following. A MAV working over the area struck by disaster, for example, comes to the power station when its battery becomes low. The battery is charged by receiving the microwave beam transmitted from a phased array transmitter while it is circling above the power station and goes back to the working area without landing and take-off. Figure 1 shows the system developed in our laboratory. It consists of three sub-systems; a transmitter system, a rectenna system, and a tracking system.

Figure 3.13. System of microwave power supply to MAV.
In the transmitter system, a microwave beam of 5.8GHz is formed and steered using a phased array antenna. In the rectenna system, the microwave power received by an antenna is converted to DC power by an in-house rectifier and used to drive an electric motor on a MAV model. In the tracking system, the position of the MAV is detected using a software-retro-directive mechanism. The microwave beam from the transmitter system is pointed to the MAV using the information of its position analyzed in the tracking system and the MAV flies by the electric motor on it using the power received by the rectenna system
Transmitter System
Pointing and steering of a 5.8GHz microwave beam was achieved by controlling the phase of microwaves emitted from the five-element antenna called the phased array system, not by mechanical control of the antenna’s attitude. Figures 3.14 and 3.15 show the picture of the microwave circuits and geometry of the antenna, respectively. Five horn antennas were used for the antenna elements. Each horn antenna transmits 0.7W power and each phase of microwaves was controlled by the phase shifter connecting a PC. The beam divergence was about 9deg, which corresponds to the beam quality factor M2=1.6. The beam steering angle was from -9deg to +9deg. The specifications are listed in Table 1.
Fig. 3.14. The picture of the antenna array system.           Fig. 315. Geometry of the five arrayed antenna elements.
Table 1. Specifications of the five-element phased array antenna.



microwave frequency     
wavelength, λ 
 total transmission power,
array pitch, d   
   diameter of the array , D                    

330 mm

Rectenna System
The rectenna system consists of a receiver antenna on the front side and a rectifier circuit on the back side
(Fig.5). The patch antenna for circular polarization was used as a receiver antenna for constant power conversion at various MAV’s yaw angle with respect to the polarization axis of the transmitted wave
Fig. 3.16A leaf pattern patch antenna (left) and rectifier circuit (right).
To obtain electric power enough to drive an electric motor on an MAV, eight rectennas was connected in parallel in Fig.3.16. Figure 3.17 shows the rectifying characteristic of single and eight-rectenna arrays at 80cm from transmission antenna. The measured output voltage of eight-element array was slightly lower than the predicted. As a result, the electric motor driving was demonstrated at the altitude of 80cm from the transmitter emitting 3.5W power in total.

Fig. 3.17. Eight-rectenna array.
Tracking System
In the tracking system, the software retro-directive function is under development. This system receives the pilot signal of microwave sent from the MAV and analyzes its current position using the phase difference.

Fig. 3.18. The block diagram of tracking system.
As a receiver, two patch antennas were aligned with the pitch of λ. An analog phase shifter was inserted in one line to make π/2 of phase difference to each other. Divided and coupled microwave signals are rectified using a commercially available detectors. Finally three DC outputs V0, Vcom, V1 are read in the PC. The incident angle of a pilot signal α is computed by a LabVIEW program.For tracking a MAV while it is circling, two units of antenna system were set in the rectangular coordinates. The incident angles αx and αy are analyzed in a PC. Leaf pattern antennas same is employed to detect the linearly-polarized wave despite the MAV yaw angle.
In the transmitter system the microwave beam from five horn antennas was formed using phased array system. The beam divergence was about 9deg and the steering angle was also 9 deg. In the rectenna system, eight rectennas were arrayed and connected in parallel minimizing the array pitch to drive an electric motor. And an electric motor was driven by eight-rectenna array at 80cm from the transmitter. In the tracking system, two units of antenna system with a leaf pattern patch were set in the rectangular coordinates to track a circling MAV
Observation of Lunar Wireless Power Transfer Feasibility
This study examines the feasibility of a multi-kilowatt wireless radio frequency (RF) power system to transfer power between lunar base facilities. Initial analyses, we show that wireless power transfer (WPT) systems can be more efficient and less expensive than traditional wired approaches for certain lunar and terrestrial applications. The possible operational parameters, and a baseline design approach for a system that could be used in the near future to power remote facilities at a lunar base.  In our experiment, we includes state-of-the-art photo-voltaics (PVs), high-efficiency microwave transmitters, low-mass large-aperture high-power transmit antennas, high-efficiency large-area rectenna receiving arrays, and reconfigurable DC combining circuitry.
Traditional power transfer methods for this type of off-site extraction mission would utilize cables, estimated to have a mass of about 7,500kg for five load stations. These transmission lines must traverse large distances, are sensitive to temperature, will be expensive to transport from Earth to the moon, may be a safety hazard for lunar operations, are susceptible to solar flare induced transient effects, have large diameters due to high voltages and power levels, have a large mass, and are difficult to manage due to residual cable stresses. In addition, once the cables are set up, they would be difficult to move in the event that a different facility needs to be powered. Since multi-kilowatt power requirements are envisioned for these work sites, new methods of power transfer must be explored. For comparison purposes, a top-level system design for a traditional transmission line approach was developed. A transmission voltage of 480 V was selected based upon minimum cable sizes 2 and voltage ranges available directly from series/parallel combined solar cells. Higher voltages are possible but conversion losses, insulation requirements, and other inefficiencies become driving factors. For five 10 kW load stations located 2 km away from two generation stations, the following power transmission link system parameters are calculated and compared to corresponding parameters for a traditional transmission line approach (Table 4.1).
Table 4.1. Traditional transmission line system parameters compared to WPT system parameters.

Power System




Transmission Line

480 Volts


User voltage less losses will be down converted to 120 V

Transmission Line
Voltage Drop

80 Volts


Stranded AL Cable with connection losses at nominal 20 degrees C .

Temperature Related
Voltage Drop

33 Volts


Lunar Temp = 121 degrees C

Current between Load
and Generation Station

21 Amps



System mass

7500 kg
500 kg (IC)

4200 kg
50 kg (SA)

Four generation stations with three load stations each, No. 2 Duplex
(Plus and Return) cables, Added 25% for packaging and
deployment hardware. Additional 500Kg for
Cable interconnecting (IC) hardware.

Voltage Down

500 kg

500 kg

Mass Est., five Load Stations

Power Transfer Tower


400 kg

Mass Est., Four generation stations
Est. $100K per tower

Power Transfer

~60 %

~45 %


Power Transmission

2,400 W

5,500 W

38.8 m2 (33 kg ) of additional solar array (SA) area required for WPT system, Additional cost = $3.9M

Power Transfer
System Cost

$50 K
$5 M

$13 M
$4 M (SA)
$0.5 K ( PT

Estimated costs for four generation stations with three load stations$50 K Commercial Cable Cost
$5 M Space qualified cable

Launch Costs

$850 M

$520 M

$100 K / kg – To Moons Surface

Total Cost

$860 M

$540 M


         Wireless Power System Requirements
The four key parameters identified for the wireless power transfer system design of interest are:
• Power must be beamed from four solar power generation stations to five fixed load
• Power received at each facility must be at least 10 kW;
• Load stations must receive power from minimum of two generation stations;
• Distance between transmitters and receiver ranges from 0.5 km to 2 km.
The beaming frequency, transmit and receive apertures sizes, and overall architecture are
parameters varied in this study to show trends and the potential optimization. This study considers the following system aspects of a wireless beaming system with respect tothe specifications given above:
1. Top level system architecture – this includes a discussion of the distribution of power from 4 solar power generation stations to 5 load stations, as well as a high-level system block diagram.
2. Solar power generation – overviews the state of the art in PV arrays and discusses requirements in terms of size and mass for the required 50kW of received power at the five sites.
3. Power management and distribution – describes how the output of the PV arrays is managed and distributed to microwave transmitters.
4. System grounding on the lunar surface – electrostatic and other means are discussed.
5. Energy storage – describes alternatives and strategies for storage at the transmitter and
site ends.
6. RF wireless power transmission – consists of a discussion of choice of frequency, transmitter technology, transmit aperture for given distance, towers for line-of-sight transmission, rectenna array size and DC reconfiguration. This is the central part of the  study, but it cannot be considered properly without the other parts of the system.
7. System considerations including potential harm to astronauts and thermal issues are
outlined for future more detailed study.
8. Mass and cost of the system is estimated. This is a very rough estimate since there is
significant new work, and detailed analyses and design have not been performed.
The overall architecture for the lunar Wireless Power Transfer (WPT) system is shown in Figure 4.1. Four transmission towers power a total of five load stations, such that each facility may be powered by at least two towers, and each tower can power up to three facilities. Each tower can send power in up to three directions using three separate microwave transmitting antennas. Each arrow represents a directional microwave beam.

Figure 4.1. Top-level diagram of lunar Wireless Power Transfer (WPT) system provides 10
kW to multiple load stations at distances between 0.5 and 2.0 km. Each arrow represents a directional microwave beam. The length of the arrow is an indicator of the aperture size of that particular transmitantenna – the larger the beaming distance, the larger the aperture for a given beaming efficiency.
The distances between the transmitters and rectenna arrays are between 0.5 and 2km, meaning that the farthest facility will be four times further with sixteen times more power attenuation than the closest facility (assuming identical aperture sizes). The farthest facility 5, is powered by four beams in this scenario, which enables all transmitters to have the same total output power. Table 4.2. Alternatively, Transmitters 1 and 4 could produce more power than Transmitters 2 and 3, eliminating the beams shown in dashed lines in Figure 4.2. The numbers corresponding to this scenario are shown in parentheses in Table 4.2. The last row in the table includes beaming efficiencies, which are discussed in more detail in Section II. A modular transmitter approach would be advantageous since it allows tailoring of the transmitter size to the expected load
Table 4.2. Transmitter power levels contained in different beams for two scenarios shown in Figure 4.1. In one case, all transmitters produce equal total power levels, each with three beams. In the second case, Transmitters 1 and 4 have three beams and produce more power than Transmitters 2 and 3, each with 2 beams (shown in parenthesis). For optimal efficiency, all apertures would be of different sizes.







Facility 1   






Facility 2






Facility 3






Facility 4






Facility 5

2.5kW (5kW)

2.5kW (0)

2.5kW (5kW)

2.5kW (0)



η1 12.5kW
(η’1 15kW)

η2 12.5kW
(η’2 10kW)

η3 12.5kW
(η’3 10kW)

η4 12.5kW
(η’4 15kW)

η 50kW

The most relevant parameter for comparing WPT with a traditional cable power transmission
system is the overall efficiency and mass, with cost following. Figure 4.2 shows an overall
system block diagram, with the relevant efficiency budget given for the box with dashed lines, which shows the portion of the system most appropriate to compare to a traditional power transfer system.The total WPT efficiency for a single channel can be defined as
η = ηT . PCE .ηBeam  ηRect.ηPM  = P DC in / PDC out
Table 4.3 describes the efficiencies that can be separated out and characterized separately.

Figure 4.2. Overall power transfer system block diagram for a single powering beam (powering channel).
The dashed shaded block outlines the portion of the wireless power beaming system that should be compared to traditional power transmission lines.
Table 4.3. Efficiency budget.



 Max Demonstrated


Total microwave transmitter DC-RF conversion efficiency, where PRF, is the RF power delivered to the transmitting antenna.

70-80% power and
frequency dependent


Power-combining efficiency of the transmitter (nosingle RF source provides the required multiple kW)

80-90%, combiner type

ηBeam = P RF Trans / P RF  Rec

 Beaming efficiency between the transmit and receive apertures, including the free-space propagation loss

About 80% for farfield

ηRect = PDc,Rectified / PRF,Rect

Rectification efficiency of the rectenna, where the input is the received RF power at the aperture, and the output the non-regulated DC power



Rectenna power management efficiency required to produce given fixed output voltage

85-90% dependent on rectenna number and power

The third column shows best reported results for efficiencies, which are not at consistent
frequencies, power levels, etc. Thus, these numbers show an upper limit on the overall efficiency of WPT of around 45%. A relevant comparison needs to take into account grounding, mass, cost/ease of deployment and reconfigurability, in addition to the efficiency (loss). The WPT approach has the potential to have advantages in terms of grounding, reconfigurability, mass and cost.
The envisioned lunar WPT system consists of several wireless powering channels, each one
depicted in some detail schematically in Figure 4.3. A channel consists of an advanced solar
arrays, power system based on the International Space Station (ISS) architecture (energy storage, Sequential Shunt Unit (SSU) & Battery Charge/Discharge Units (BCDU), Main Bus Switching Unit (MBSU), Remote Power Distribution Assemblies (RPDAs), Secondary Power Distribution Assemblies (SPDAs)), solar array control, power management and distribution (PMAD), high efficiency RF transmitters, high-directivity transmit antennas, and large-area rectenna arrays with associated DC combining and regulation. The system architecture also addresses the need for a transmission tower structure, grounding, energy storage, static dissipation, and thermal management.
The blocks shaded in blue in Figure 4.3 are directly related to the wireless power beaming
system. Some of the components in the dashed boxes containing the RF transmitters and rectennas would need to be specifically designed for WPT. Some subsystems would likely be the same no matter what power distribution method were to be chosen, including cables.
As shown in Figure 4.3, the solar power generation and power management and storage will not differ significantly between a WPT system and other power transmission systems. Nevertheless, it is important to briefly overview some possibilities and challenges in these areas, as well as the issue of grounding.
The solar power photovoltaic (PV) generation facility is one of the most mature technologies employed in the WPT system. A typical photovoltaic system has planar solar arrays for power generation and chemical batteries to store excess solar array energy during periods of sunlight and provide power during periods when the load station is in shadow. It is expected that the batteries will only provide survival power during eclipse.
For a future lunar power system, one should consider using a new technology known as a
Stretched Lens Arrays (SLA). This solar array technology uses a Fresnel lens and high efficiency multi-junction cells to provide superior PV performance. The Fresnel lens (concentrates the Sun, 8 to 1), is light weight, scalable with a capacity of 100’s of kW’s, provides outstanding radiation resistance, has a built in passive thermal management (radiator), has a high specific power (~300 W/kg) and can operate at high voltages (300 – 600 V).
A single SLA is shown in Figure 4.4.

Fig.4.3   Block diagram of WPT channel. Several such channels power a single remote facility. The top figure shows the transmitter system block diagram, starting from solar array to a transmitter antenna or array. The bottom figure shows the receiver, starting from a rectenna array with reconfigurable DC summing, to the remote site loads.

Figure 4.4. Single cell stretched lens array enables low Mass high efficiency power
For a lunar power generation station, developed a modular 2.5 m X 5 m 4 kW SLA square rigger (SLASR) array as shown in Figure 4.5. This modular SLASR is highly compactable and is expected to be easily mass produced. Future SLA concepts are expected to have specific power levels in excess of 1000 W/kg.

Figure 4.5. Single Cell Stretched Lens Array enables low mass high efficiency power generation
The power management and distribution (PMAD) system for WPT is very similar to the
ISS PMAD System. Since the ISS PMAD system is modular, much of the hardware can be used with little or no modification for the lunar WPT system. A single PMAD channel or “set” of ISS PMAD hardware can supply the required fault protection, redundancy, and power for one lunar load station exceeding 10kW. A multiple set of modular ISS PMAD channels can supply the required fault protection, redundancy and power for one lunar solar power generation station exceeding 80KW. The main modifications that would be required to a baseline ISS PMAD channel are as follows:
– New concentrator solar arrays will be used instead of conventional planar solar arrays
– New technology Lithium Ion batteries will be used instead of conventional Nickel Hydrogen batteries
– Software modification to support new technology Li Ion batteries and new concentrator Solar Arrays will be required in the form of current and voltage regulation set points and battery charging algorithms.
– The Solar Array “Sequential Shunt Unit” (SSU) would require modification for load current      and number of channels in order to adapt to the new concentrator solar arrays
– The “Battery Charge/Discharge Unit” (BCDU) would require modification to support the
  new Li Ion Batteries.
– The DC Switching Unit (DCSU) would require modification for fault protection software
  and potentially hardware modifications as well.
– Quantities of Main Bus Switching Units, DC-DC Converters and Remote Power
  Controller Modules will be fewer than the ISS requires.
– Modification of hardware to replace obsolete components will also be required in some
Grounding – The lunar environment presents difficult problems in the grounding of electrical
systems. Since the lunar regolith is in general a good insulator, terrestrial concepts such as single
point grounds connected to simple buried rods are not viable on the moon. Additionally, the
surface of the moon is highly charged due to interaction with the local plasma environment and solar radiation-induced photoemission of electrons. Such surface static charging is periodic over both short and long timescales. During the lunar day, the surface typically charges positively, while at night the surface charges negatively. Due to orbital variations, the moon has periods of time where interaction with the geomagnetic plasma sheet of the earth creates an enhanced charging environment. During these cycles, which peak approximately every 18 years, the lunar surface becomes even more charged. It is believed that the static potential of the lunar surface may vary daily between +10 and -600 volts  and possibly to several kilovolts  Lunar surface charging is not fully understood and has only been observed indirectly. During theApollo and Surveyor missions a glowing haze was observed above the limb of the moon which is believed to have been caused by charged dust particles lofted high above the surface . Note however that the Apollo and Surveyor missions occurred during a low point in the 18-year cycle, so these effects are likely to be more pronounced during a cycle peak.
Grounding can be defined as the electrical connection of the primary reference of the electrical device to a large enough conductive mass such that charges transferred to the mass do not result in a significant increase in the overall charge of the mass. Thus the reference maintains a charge that is stable during the operation of the device. Such a stable reference is useful for reducing electrical noise, and preventing a build-up of charge that could cause arcing to other areas or present a danger to operators or other systems.
Note that power beaming has significant grounding advantages when compared to transmission via cables. Since there is no physical connection between the transmitting station and the receiving station, different ground potentials for each will not be an issue. For cables, variations in static charging environments between the two sites (due for example to being in shade and sun) could cause large return currents to flow. This can drive the need for additional circuitry to handle such currents and also result in stations becoming highly charged with respect to their local environment if the capability of the ground is limited.
Various approaches to lunar grounding have been proposed, some of which could properly be
characterized as charge management rather than traditional grounding. Each of the approaches described below will require further study to determine which are truly viable:
– Use of grounding rods with the injection of conductive materials into the lunar regolith.
– Use of ion/electron guns to expel positively or negatively charged ions.
– Ion Proportional Surface Emission Cathode (MIT)
– Field Effect Emitters (Space Systems/Loral)
The main sub-system for a single wireless powering channel are discussed here, with references to state-of-the art results. Section II presents more detailed discussion of the WPT channel.
Microwave Transmitter – The transmitter takes DC input and converts it to a radiated RF
output. It consists of a DC-RF conversion oscillator, which is typically low-power and followed by a gain stage and finally a power amplifier (PA). The following considerations are relevant in this case:
– Since the DC input is 128V, some DC-DC conversion is needed to supply the required
voltage needed for microwave devices (typically 8 to 48V range). This DC-DC
conversion circuitry can be very efficient (98% is relatively easy to demonstrate).
– The main contributor to the loss is the Power Added Efficiency (PAE) of the output stage
PA. A number of new wide band gap semiconductor technologies are showing excellent
efficiencies and power levels in the lower microwave range (commercially available) .
– Both the device and circuit are important for the efficiency budget, and since no linearity
or noise requirements exist in this case, a ultra-high efficiency saturated switched-mode
PA will give the best efficiency.
– Power combining will be necessary, and there are several options at the circuit level or
upon radiation.
Transmitter Antenna – The size of the antenna is determined by several factors: beaming
Efficiency for a given range, transmitted power per unit area, ease of fabrication and deployment, etc. For optimal efficiency with a large aperture, spatial power combining is a good choice, e.g. Power combining efficiencies of great than 80% have been demonstrated in spatial combiners. An array of narrowband planar printed antennas, e.g. patches, is a good candidate for this approach. In the next section some possible power levels and array sizes are given at several frequencies. Ultimately, they will be driven by transistor technology and $/watt of power.

Figure 4.6. ATK’s FAST Mast enables rapid deployment of the RF transmission tower .
Beaming – the beaming efficiency can be high for line-of-sight links. On the lunar surface, line of sight for a 2-km range requires towers for the transmitters. We also envision towers for the rectenna receivers in order to provide safety of personnel at the load stations. As an example, ATK’s Folding Articulated Square Truss (FAST) Mast technology, installed on the
International Space Station in2006, allows for compact stowage length less than eight feet when fully retracted and more than 115 feet when fully deployed . The FAST shown in Figure 4.6 is attractive not only for its ISS heritage, but also because it utilizes the following:
– A motor driven, internally-threaded canister shell to extrude the boom
– Stowed and transitioning portions of boom are fully contained within canister
– Near full stiffness and strength throughout deployment
– Large deployment push force capability
– Remotely retractable and deployable
– No rotation during deployment
– Typical applications include solar array deployment
Rectification – The transmitted power density is focused on an array of rectennas in the far field of the transmitter. An integrated antenna and rectifier is usually referred to as a rectenna, as shown in Figure 4.7a. Rectification of microwave signals for supplying dc power by high power beaming has been researched for several decades, and a good review of earlier work is given in power beaming, the antennas have well-defined polarization, and high rectification efficiency is enabled by single-frequency high microwave power densities incident on an array of antennas and rectifying circuits. Applications for this type of power transfer have been proposed for helicopter powering, solar-powered satellite-to-ground power transmission, inter satellite power transmission including utility power satellites, mechanical actuators for space based telescopes, small dc motor driving and short range wireless power transfer. Linear, dual-linear and circular polarization of the receiving antennas were used for demonstrations of efficiencies ranging from around 85-90% at lower microwave frequencies to around 60% at X-band and around 40% at Ka-band. For most rectennas and arrays reported to date, the antenna is matched to the diode around one frequency at a well-defined polarization and assuming relatively high incident power levels. For example, the rectenna shown in Figure 4.7b is linearly-polarized and designed to operate at 5.8GHz with an incident power of 50mW corresponding to an incident power density of around 3.2mW/cm2, assuming a dipole effective area of λ2/8. In this case, the incident wave carries enough power to turn on the diode and rectification efficiency can be very high (>80%).

Figure 4.7. (a) Schematic of a rectenna and associated power management circuit. The incident wave is received by the antenna, coupled to the rectifying device, and the low-pass filter (LPF) ensures that no RF is input to the power management circuit. A controller provides input to the power management circuit, which enables storage of the received energy over time, and delivery of DC power at the level and time when it is needed. (b) An example of a dipole rectenna for 5.8GHz narrowband operation.

Figure 4.8.
Measured power flux from parabolic transmitter at receiving rectenna. The power exhibits radial symmetry, with peak power flux occurring in the center.
For the proposed beaming study, the following needs to be considered:
– The rectenna arrays will be very large, planar and deployable.
– The beam from each transmitter will non-uniformly illuminate the rectenna array aperture. An example of a measured beam specifically used in wireless power transfer is shown in Figure 4.8 . The exact beam pattern would off course depend on transmitter antenna design.
– This implies that not all rectennas will be receiving the same power, and thus might not be operating at optimal efficiency. A solution is to design the rectenna to be modular, i.e. that a subarray of rectennas is connected to a local powering circuit which presents an optimal load at the particular power level that the rectenna elements are receiving on average.
– The powering beam needs to be maximally absorbed by the rectenna aperture, implying direct integration of antenna elements with rectifying elements. The rectenna in Figure
4.7(b), for example, does not meet this requirement as the filtering and matching circuit takes up too much real-estate at the expense of absorbing area. The design of the integrated rectenna element requires a specific procedure which is not well established in the field, although a good methodology for low power is described in .The procedure involves a load-pull measurement that provides an empirical nonlinear device model. The diode impedance can then be determined for a given power, and the antenna impedance designed to directly match this optimal diode impedance.
– When several transmitters are beaming power to a rectenna aperture, the combined incident field will change as compared to that of a single transmitter case. The differences among elements will be even larger, and thus the modular approach is essential if efficiency is to be optimized.
Some additional system considerations are summarized in the below.
System level considerations for the lunar WPT system.
Astronaut Considerations              • Safety issues for astronauts walking through the beams
                                                          • Uncontrolled pointing of the RF transmitter
                                                          • Human capabilities analysis and plan
                                                          • Antenna side lobe and reflected power safety issues
Transmission Tower                        • Deployment in 0.6g
                                                           • Testing in 1g
System Design                                     • Packaging for launch /storage
                                                              • Transportation to final location on lunar surface
                                                              • Deployment at landing site – Automatic vs. manual
                                                              • Assembly Process (Cable management)
                                                              • Antenna alignment / point away approach
                                                              • Grounding of the various system elements
                                                              • Voltage regulation approach
RF WPT Operations                   • RF Transmitter / Rectenna Pointing
                                                      • Assembly Process
                                                      • Maintenance
System Efficiency                      • Best common voltage for the system
                                                    • Load shedding and management approach
Thermal Control System         
                                                     • Array and transmitter thermal management
                                                     • Electronics thermal management
Others                                          • Dust mitigation in the presence of large static fields
                                                      • Power harvesting of the side lobes
                                                      • Energy storage sizing and selected battery technology
                                                      • RF and sub-RF EMI mitigation
                                                      • Control of the system via WiFi or other means
In this section, some estimates are given for the transmitter and transmitting antenna efficiencies, beaming efficiency and receiving rectenna efficiency, assuming a single powering channel.
Beaming efficiency is discussed first, since this consideration determines the relationship
between the transmitting and receiving aperture sizes for a given frequency (wavelength), then range (beaming distance).
Assuming a beaming frequency f at which the free-space wavelength is λ, the required beam
diameter d for a power beaming range R can be determined using the antenna theorem A/ D = λ2 / 4π , where A is the effective area of the antenna and D the directivity. Assuming a 100% aperture efficiency, the half-power beam-width of a symmetrical-beam antenna can be calculated approximately to be, in degrees from D ≈ 32,000 /θ 2 . For different power beaming ranges, the aperture size can now be estimated using tan θ-3db / =  d/R   or,  2d =aperture The following simple estimate can be used for beaming efficiency and determining the required aperture size. If the transmit and receive antennas are in each other’s far field, one can define (from the Friis formula) a beaming efficiency as  ηbeam =  P RF Trans/P RF , Rec = A Trans.A Rec/ λ^2. R^2   where the effective areas of the antennas are assumed to be equal to their geometric areas for this estimate. The distance R needs to be in the far field for this to be valid. For a distance (range) of 2km, assuming 2GHz, 5GHz and 10GHz beaming frequencies, and a 80% beaming efficiency,
Table 4.4  shows possible resulting aperture sizes.
These specific frequencies were chosen as examples in order to illustrate scaling: from a
beaming standpoint, the higher frequencies (smaller wavelengths) are clearly better. However, the transmitters and rectennas are less efficient at the higher frequencies. In fact, at X-band the best rectenna efficiencies were about 60% and it would be difficult to get more than 60% efficiency from a power amplifier with a few watts at this frequency.
The following is noted for the calculations in Table 4.4:
– For each frequency, the beaming efficiency is set to 80%, i.e. AT. AR= 0.8 λ^2 (2km) ^2
– The first row for each of the three frequencies is the case of equal transmitting and rectenna (receiving) apertures;
– The estimate the number of antenna elements, assuming both apertures are arrays, an element spacing of one half of a free space wavelength is assumed both at transmitter and rectenna apertures;
– The directivity is calculated from A/ D = λ2 / 4π assuming that the effective area of the transmitting antenna is equal to its geometric area;
– The far field condition FF~4A/λ is calculated w.r.t. the transmitting aperture, since therectenna elements have individual detectors, and RF-wise they are not in an array (only
the DC adds);
– The far field condition is not met for all cases when apertures are of equal size. This implies that the estimates used here are not valid (Fresnel zone equations should be used);
– The half-power beamwidths are calculated fromD ≈ 32,000 /θ 2 , which is an assumption. A more precise beamwidth can be calculated once the transmitting antenna architecture is determined;
– Based on the 2-km range and the half-power beamwidth, the spot size of the transmitting beam on the rectenna surface is calculated. A system design would have an increased
rectenna size, in order to capture as much power as possible of the beam, thus increasing the beaming efficiency. Note also that the beam power density across the rectenna aperture will vary according to a sinc2 function.
Table 4.4   For an 80% beaming efficiency, and three beaming frequencies, several transmit and receive apertures can be considered. The borderline far field at the 5GHz frequency is the baseline configuration used for mass and cost estimates provided .



No. of el. N
Directivity D

Far Field

No. elements N


2GHz / 15cm

72,000 m4
Not in far
field at all
far field

16m x 16m
N=106 x 106
10m x 10m
N=133 x 133
5m x 5m
N= 67 x 67


16m x 16m
N=106 x 106
27m x 27m
N=360 x 360
54m x 54m
N=720 x 720

d=55m 1

5GHz / 6 cm

Not in far
far field

10m x 10m
N=333 x 333
5m x 5m
N= 150 x 150
3m x 3m
N=100 x 100



10m x 10m
N=333 x 333
21m x 21m
N=700 x 700
36m x 36m
N=1200 x 1200


10GHz / 3cm

2,880 m4
Not in far
field at all

7.3m x 7.3m
N=485 x 485
3m x 3m
N=200 x 200


7.3m x 7.3m
N=485 x 485
 18m x 18m
N=1200 x 1200


The main considerations in the transmitter are power amplifier device technology, efficiency and cost; power amplifier circuit architecture and efficiency; and power combining efficiencies, as discussed below.
Power devices for high-power microwave sources can be either tubes, solid-state or solid-state driven traveling wave tubes (TWTs). The mass, reliability, efficiency and continuous improvements in solid-state device technologies, along with considerations in Table 2, points to the use of transistor amplifiers in active antenna arrays. Standard transistors with tens to hundreds of watts of output power at lower microwave frequencies are LDMOS (cell-phone base stations) or GaAs FETs (tens of watts at X-band in class AB). The LDMOS devices cannot operate efficiently above about 2GHz, while GaAs FETs are expensive and limited in power. On the other hand, wide-bandgap semiconductors such as GaN and SiC have better intrinsic material properties than standard Si LDMOS transistors, i.e. larger energy gap (support higher internal electric fields before breakdown), lower relative permittivity (lower capacitive loading), higher thermal conductivity (higher heat handling), and higher critical electric fields (higher RF power). High voltage operation and high power density with low parasitic reactance translate into robust devices that can withstand high-stress conditions typically associated with switched-mode operation. For example, in ultra-efficient Class–E mode, the peak voltage across the device can be more than 3.56 times higher than the supply voltage. The supply voltage must then be limited by this factor (VDSS/3.56 were VDSS is the absolute maximum drain-to-source voltage). Therefore, devices with high breakdown voltage are ideal for efficient modes of operation.
A brief overview of some available devices is given in Table 4.5, although it should be noted that the cost quoted here is for small quantities.
Table 4.5.  Comparison of transistor power levels, frequencies, voltages, and costs


Power Levels





30, 60, 100W,

<2GHz in high
eff. Mode



GaN on Si

25W, 50W,

To about 4GHz

28V and


GaN on SiC

10W, 30W,
60W, 100W

To about





Claim to 8GHz





Up to X-band



A number of other defense contractor companies produce GaN devices at higher frequencies
(there is a successful DARPA Wide-bandgap program). For example, BAE Systems has broadband GaN devices with around 10W up to 20GHz, while Northrop Grumman Space Technologies (formerly TRW) have produced GaN on SiC devices with close to 20W as high as 30GHz. TriQuint also produces GaN on Si targeting X-band. These are still in the development stage, but improvements have been happening very fast. GaN may not be space qualified yet, but Northrop Grumman will certainly have that focus. GaAs is still an option, with higher cost per watt of power. The remainder of the transmitters consist of VCOs (low-cost components from, e.g MiniCircuits), and some gain and driver stages. These only contribute to the efficiency minimally, since they are low power, and their cost is low compared to the power amplifier.
Power Amplifiers
The highest efficiency power amplifiers demonstrated to date operate in switched mode (classes E, D etc.). These are highly saturated nonlinear amplifiers with high additive phase noise. For powering applications, linearity and noise are not relevant, and the high efficiency of class E and tolerances to small differences in circuit parasitic parameters give this mode an advantage, e.g. In class E operation, the transistor is either on or off, with a minimal amount of time during a period where the product of voltage and current through the device is non-zero. Unlike in class C, the maximum output power of the device only needs to be sacrificed by 0.5dB or so. The disadvantage of class-E mode of operation for this particular application is that the high efficiency is achieved at the expense of operating at about 3 to 5 times below the specified device maximal frequency of operation. For example, a device that is normally operated in class AB mode at 2GHz will perform well in high-efficiency switched mode anywhere between 0.5 and 1 GHz. With current device trends, it is likely that 5GHz will be an appropriate frequency for high efficiency with tens of watts per device in a few years, and 10GHz is not out of the question.
Mass: Northrop Grumman Space Technologies has produced 3-D stacked power amplifiers
which are only a few tens of grams in mass.This is achieved with a new packaging technology, and similar approaches can be adapted to the power beaming transmitters.
Antennas and Active Arrays With Spatial Power Combining
Given the numbers in Table 4, a high-level transmitter and antenna design is now discussed.
– Consider the middle frequency of Table 2 (5GHz) with 150×150 elements (a 5-meter square aperture) at a half-wavelength spacing for the array elements.
– For a single powering beam that delivers 5kW of power to a facility, and accounting for 80% beaming efficiency and 80% rectification efficiency, the transmitted power needs to be about 7.8kW.
– If every array element contained a high-efficiency amplifier, this would imply only 350mW per element.
– This is however not a practical approach, since it would require feeding 150×150 elements.
– We thus consider an array of modules. Assuming one can implement a low-loss 1:16 divider .the transmit array antenna would consist of 1400 modules.
– Each module will then need to radiate 5.6W of power. This is a very reasonable task, but still implies a large number of feeds. A more extensive trade study, including the type of antenna element, how it would be deployed, etc., is required. Table 4.6 provides a few estimates in terms of subarray size, number and power, for a total of 150 x 150 elements at 5GHz, assuming a beaming efficiency of 80% and a rectifier efficiency of 80%, with 5kW of power per beam. This assumes a 100% power combining efficiency for the modules in the array.
Table 4.6. Estimates of sub-array quantities and transmitted power.

Number Of
Sub arrays

Number Of Elements
Per Sub array

Power Transmitted Per
Sub array



22 W (28 W)



45 W (56 W)



60 W (75 W)

The power from each module from the table above is radiated and combined with the radiated power from the other modules via spatial power combining. It has been shown, e.g. , that power combining efficiency degrades with the number of stages for circuit combiners and remains roughly constant for spatial combiners, with combining efficiencies demonstrated in the 80% range. This implies that the power levels in the above table need to be increased to the numbers in parentheses.
In a load station’s power receiving array, the number of elements can be very large, since there is no RF combining network that can introduce loss. Instead, the rectified DC is combined. The modular approach for this design would be as follows:
– Assume an aperture size for the rectenna. For example, take a 20m x 20m rectenna aperture (Table 2, 5GHz, middle case).
– Knowing that 5kW (times the rectification efficiency) of power is incident over the aperture, the resulting incident power density assuming uniform illumination (which is not the case, but gives an average value) is calculated. In this case, it will be on the order of 5mW/cm2.
– Calculate the power density per rectenna array element. In the given example, the 5mW/cm2 power density results in about 45mW per array element assuming halfwavelength
– This amount of power is sufficiently high to drive a rectifier diode operating point into a region of high rectification efficiency. This will off course depend on the antenna element in the rectenna, choice of rectifying device (most likely zero-bias Schottky diode), impedance match and DC load.
– Now assume an array with element spacing of half wavelength (λ/2 period), implying narrowband beaming.
– Find number of elements in a module of that size (in the example here, it is 700 x 700 elements).
– Next, assume illumination profile of main beam (varies between modules, assume constant per module). This can be obtained by simulation or measurement and is transmitter-dependent.
– For V=28V nominal output voltage, assuming 0.5-0.7V per element based on previous work, find how many elements are needed in a subarray of each module (maybe no subarrays are needed, but rather parallel connections to boost the power).
Rectenna Element
An example patch rectenna with two rectifiers (one for each linear polarization) in the unlicenced ISM band around 2.4GHz is shown in Figure 4.9. The rectenna is a 19mm x 19mm square patch, with a 6cm x 6cm square ground plane on a Rogers Duroid 6010 substrate (εr=10.2, thickness=50mil) chosen to reduce the antenna size. A Schottky diode is connected at each of the two centers of the two orthogonally-polarized patch radiating edges. A via isolated from the patch ground plane terminates each diode to RF/DC ground, and the DC output is taken from the RF short in the center of the patch. This rectenna operates with incident power levels as low as 10μW/cm2 and is capable of powering a low-power wireless sensor, but very similar planar antennas with different diodes can be designed for higher power levels

Fig 4.9  A broadband
rectenna array on a flexible substrate (no ground plane, bidirectional). Remaining design issues are:
– type of substrate that is best for this application;
– type of metallization for the antenna;
– most appropriate way to attach diodes;
– is a ground plane needed on the back of the substrate, or would a reflector that is
separated from the array by a half-wavelength vacuum layer be appropriate? This would
imply that we do not need to work with patch antennas, but can use dipoles etc.
– how do we design the DC collection lines so that they do not couple to the RF. A patch
antenna is a good choice, since the RF voltage null can be used for the DC.
Rectenna Modules
The rectenna arrays at the load stations will necessarily have large areas .The diodes in individual rectenna elements can rectify only a limited amount of power and also produce a small voltage, so series/parallel combinations of many elements must inevitably be made. For V=28V nominal output voltage, assuming 0.5-0.7V per element based on previous work, about 56 elements need to be combined in series to produce the required voltage, which  implies over 8000 modules of this size for the entire rectenna array. With this requirement come several issues of electrical element interconnection within the array. Distributed power management is designed and integrated at the subarray level to create integrated power modules that cover a range of power (e.g. 10-50W). The power management circuitry achieves two primary functions:
(1) peak power tracking of the rectenna subarray by matching the input impedance of the converter cell to the rectenna subarray low frequency output impedance and
(2) charge control for battery protection and long life charging.
The first function of impedance matching is required to achieve high overall system efficiency in the presence of wide variations in incident power density over the entire receiver aperture. A
single power converter and management unit is used for both functions to achieve maximum
system efficiency and to avoid the need to passively dissipate excess energy from the rectenna subarray in the case of battery overcharge. As a battery overcharge condition is approached, charge control is achieved by forcing a mismatch between the rectenna output and converter input impedance, causing the received input power to decrease to match the battery requirements. This removes the need for shunt dissipation elements and associated thermal dissipation considerations.
A trade-off study needs to be performed to determine the optimal series-parallel configuration
and physical layout for each sub-array and the converter topology for maximum system efficiency.
The overall WPT system efficiency is given by
η = ηT.PCE.ηBEAM.ηRect.ηPM = PDC in/PDC out
where the individual efficiencies were discussed above. The expected efficiency budget is given in the  Table 4.7.
The study so far has focused on a single wireless powering channel, i.e. beam. Referring to
Figure 1.1, there will be multiple (at least 2) beams powering a single facility. The remaining
study that needs to be performed is the effect of multiple transmitted beams incident on the same
receiving rectenna aperture. There has been limited work on effect of simultaneous beams incident on rectenna arrays, with two beams at two different power levels and frequencies .
The results show that in each of 10,000 random trials, the efficiency increased, while the beam angles, frequencies and powers were varied. The increase was more pronounced for lower incident power levels. This implies that the overall rectification efficiency at the rectenna aperture in the presented case will increase with multiple beams, since the modules that are not capturing the peak power density of the beam with increase in efficiency.
It is interested to note that the rectenna array images the incident beam power profile. When
elements are a half wavelength apart, the sampling of the incident beam is according to Nyquist and the beam profile can be recovered fully. This direct mapping of the incident beam at the rectenna aperture has the potential to simplify dramatically the beam pointing of the transmitter Table 4.7. Expected efficiency budget for the lunar WPT system. Details used for the conclusions can be found in Tables 1-6 above. η =…. = PDC in/PDC out


Discussion of upper and lower



ηT= PRF,antennas/ PDC in

– upper bound is for lower microwave frequencies where the size increases
– currently over 85% is achievable below 1GHz, but above 5GHz to get that same efficiency will require improvements in device technology


efficiency higher at lower frequencies, but arrays very large
– cost lower at lower
frequencies at expense of size


– depends on array architecture
-for upper bound, which is Achievable  for narrowband case, all
elements need to be designed for relatively broader bandwidth


– high efficiency implies large number of elements, and the trade will be in the size of the
module vs. number of


– for upper bound, it is borderline far field condition. This means that the incident field on rectenna aperture might differ from far-field approximation.
– imaging beam pattern in situ can help achieve possibly higher beaming efficiencies where near
field conditions might exist

for farfield

– large range requires large apertures.
– large rectenna aperture that captures most of the beam power for high efficiency implies larger mass and cost

ηRect = PDC Recified/PRF REC

– rectifiers need to all be in largesignal
mode for upper bound.
– for upper bound (optimal diodes
and dense element packing), direct
antenna-diode integration is needed


– dense element packing gives higher efficiency at expense of complexity and cost.


– upper bound has been shown for lower power levels, and it should be
possible to get higher efficiencies for higher power levels
– high efficiency will require highquality
component selection, which will increase the cost and might
increase the mass.


-reconfigurable parallel series combining can
optimize in-situ efficiency, at expense of complexity.
– higher power at module
level gives better module
efficiency, but possibly lower overall array efficiency due to increased size of subarray

η (total)

– difficult to predict upper and lower
bounds without further experimental
and theoretical study


– all of the above with
additional parameters that require more study

4.8.      MASS AND COST
The cost and mass of a traditional cable-based system and a wireless powering system are
estimated using the 5-GHz beaming architecture for the case of a 5m x 5m transmitter aperture and a 20m x 20m receiving rectenna aperture. A 480-V transmission line cable system was used for comparison since it is optimal in terms of loss. More details of the analysis are shown in Appendix D, and a summary is shown below in Table 4.8. The loss of the cable is increased due to temperature variations, as detailed in Appendix D. The mass of the cable is calculated for the case of bare cable. In reality, the cable comes with one line insulated with a thin PVC type insulation. The best solution might be to trench the cables, in order to suffer less voltage drop due to temperature changes, as well as enable operation at 220V.
The associated loss is corresponds to an efficiency of ~60% . The lunar surface is composed of lunar regolith which has been shown to be a very good insulator, similar to exceptionally dry micron-fine silica sand. With a transmission line system, the source and the load are electrically connected and a return path to the source must be provided or current will not flow. The lunar surface is an insulator and will provide such a path. Conventional terrestrial transmission line systems ground at multiple locations, but do not use "Earth ground" for a current return path. Return lines are used exclusively for a current return path. In a WPT system, the source and the load are not electrically connected and rely on their respective "local" grounds.
Table 4.8. Summary of estimated mass and cost comparison between a conventional cable-based power transfer system and a wireless transfer power system






Traditional Transmission Line


5.05 M

800 M


– Four Transmission Stations (Transmission Array)
– Five Load Facilities (Rectenna Arrays


17 M

513 M


In this thesis, we try to show the basic elements of WPT system and its details.
From our observation of experiment, we showed that, 10 k watt power can transmit in 2 km by wirelessly. It’s a huge development for WPT system.
We hope, Day by day WPT theory and projects could be developed and we can apply this for our power transmission system.