Wireless Power Transmission System

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Wireless Power Transmission System

Chapter -01


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 Solja?i?, 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 Transferand 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.



2.1 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 2.45 85
Circular Patch 2.45 81
Printed dual


5.6 78
Square patch 8.51 66

Table 2.2. Rectenna Efficiency for Various Diodes at Different Frequency











2.45 GaAs-W 92.5 90.5
5.8 Si 82 78.3
8.51 GaAs 62.5 66.2

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 sinb? / b? pattern shape is:

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<href=”#cite_note-0″> 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.

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, ?,?)








Consider for half wave dipole,


I= IocosßZ

Where, Io=Maximum value of the current

Now for transmitting antenna, the magnetic field intensity will be:-

^ -j?r ^

H= j/2?r (Io ? ) [cos (?/2cos?)/sin?] a?

j?/2 -j?r ^

= H? ? ? a? [where, H?=Io/2?r [cos (?/2cos?)/sin?]

-j (?r-?/2) ^

= H? ? a? ——————————– (i)

Again, for transmitting antenna the electric field intensity will be,

^ ^ -j(?r-?/2) ^

E = ? H? ? a?

-j?? -j(?r-?/2) ^

=???????????? H? ? a?

-j(?r-?/2-??) ^

=???????????H? ? a? —————————- (ii)

Consider the medium between the antennas have a conductivity of ?. Then the electric and magnetic field of the receiver end would be,

^ -?r -j(?r-?/2-??) ^

E=??????H? ? ? a?——————– (iii)

^ -?r -j(?r-?/2) ^

H = H? ? ? a? ———————– (iv)

So the power density of the receiving end will be,

^ ^

Sav= ½ Re (E x H)

-?r –j(?r-?/2) j?? -?r –j(?r-?/2) ^

=1/2 Re {??????H? ? ? ? x H? ? ? } ar

-2?r j?? ^

=1/2 Re {??????H?²? ? } ar

-2?r ^

=1/2??????H?²? cos?? ar

-2?r ^

= (1/2??????) (??????H?) ² ? cos?? ar

-2?r ^

= (1/2??????) Eo² ? cos?? ar ————————- (v)

[where (??????H?) =Eo]

Since the electric field makes an angle of (90º-?) with the axis of the receiver, then the voltage induced,


Vo=Eo ? .l sin? [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 ? sin²? ———————— (vi)

The radiation resistance of half wave dipole antenna,

Rrad= (1.219/2?) ??????cos??

Putting this value in (vi), then we have,


Pr = [2?/8(1.219) ??????cos??] Eo²l² ? sin²?

Now for a magnetic dipole antenna which radius is a. So the equation of the magnetic and electric field will be,

? ? -j?r ^

E?= (???/4?r) M sin?? a?

? ?

Where, M=?a²I is the magnetic dipole moment


and I= Io is the phasor equipment of i(t)=Io cos?t

? ? -j?r

and H?= – (???/4?r?) M sin? ?

Now the voltage induced in the antenna

? ? -?r

Et= E? sin? ?

Now, induced voltage at the receiving antenna,

Vo= Et.l


=?E? ?sin? l ?


=(???/4?r) ?M?sin?l?

So, the power delivered to the load,

Pr = 1/2??Vo/2Rrad??²Rrad

=1/8 (Vo²/Rrad)


=1/8 {(???/4?r) ?M?sin?l} ²? /Rrad

Where, Rrad=8/3?³? (?a²/?²) cos??

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 <href=”#Half-wave_dipole_or_dipole_.28lambda_over_2.29″ title=”Dipole antenna”>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 = h?, where E is the energy of the photon, h = 6.626 × 10-34 J·s is Planck’s constant, and ? 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 stages; DC-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 separat