# Antenna | Antenna Operation | Antenna Types | Radio Waves | Dipoles

Table of Contents

## Radio Waves

A radio signal is called an electromagnetic wave because it is made up of both electric and magnetic fields. Whenever voltage is applied to the antenna, an electric field is set up. At the same time, this voltage causes current to flow in the antenna, producing a magnetic field. The electric and magnetic fields are at right angles to each other. These electric and magnetic fields are emitted from the antenna and propagate through space over very long distances at the speed of light.

## Magnetic Fields

A magnetic field is an invisible force field created by a magnet. An antenna is a type of electromagnet. A magnetic field is generated around a conductor when a current flows through it. Fig. 14-1 shows the magnetic field, or flux, around a wire carrying a current. Although the magnetic field is a continuous force field, for calculation and measurement purposes it is represented as individual lines of force. This is how the magnetic field appears in most antennas. The strength and direction of the magnetic field depend upon the magnitude and direction of the current flow.

The strength of a magnetic field H produced by a wire antenna is expressed by

where I = current, A
d = distance from wire, m

The SI unit for magnetic field strength is ampere-turns per meter.

### Electric Field

An electric field is also an invisible force field produced by the presence of a potential difference between two conductors. A common example in electronics is the electric field produced between the plates of a charged capacitor (Fig. 14-2). Of course, an electric field exists between any two points across which a potential difference exists. The strength of an electric field E is expressed by

E = q/4πεd2

where q = charge between the two points, C
ε = permittivity
d = distance between conductors, m

The SI unit for electric field strength in volts per meter.

Permittivity is the dielectric constant of the material between the two conductors. The dielectric is usually air or free space, which has an ε value of approximately 8.85 x 10-12 εr, where εr is the dielectric constant of the medium.

## Magnetic and Electric Fields in a Transmission Line

Fig. 14-3(a) shows the electric and magnetic fields around a two-wire transmission line. Note that at any given time, the wires have opposite polarities. During the one-half cycle of the ac input, one
wire is positive and the other is negative. During the negative half-cycle, the polarity reverses. This means that the direction of the electric field between the wires reverses once per cycle. Fig. 14-3(b) is a detail of an electric field around conductors.

Note also that the direction of current flow in one wire is always opposite that in the other wire. Therefore, the magnetic fields combine, as shown in Fig. 14-3(c). The magnetic field lines aid one another directly between the conductors, but as the lines of force spread out, the direction of the magnetic field from one conductor is opposite that of the other conductor, so the fields tend to cancel one another. The cancellation is not complete, but the resulting magnetic field strength is extremely small. Although the magnetic and electric fields are shown separately in Fig. 14-3(b) and (c) for clarity, remember that they occur simultaneously and at right angles to one another.

A transmission line, like an antenna, is made up of a conductor or conductors. However, transmission lines, unlike antennas, do not radiate radio signals efficiently. The configuration of the conductors in a transmission line is such that the electric and magnetic fields are contained. The closeness of the conductors keeps the electric field primarily concentrated in the transmission line dielectric. The magnetic fields mostly cancel one another. The electric and magnetic fields do extend outward from the transmission line, but the small amount of radiation that does occur is extremely inefficient.

Fig. 14-4(a) shows the electric fields associated with a coaxial cable, and Fig. 14-4(b) shows the magnetic fields associated with a coaxial cable. The electric field lines are fully contained by the outer shield of the cable, so none are radiated. The direction of the electric field lines reverses once per cycle.

The magnetic field around the center conductor passes through the outer shield. However, note that the magnetic field produced by the outer conductor is in the opposite direction of the fields produced by the inner conductor. Since the amplitude of the current in both conductors is the same, the magnetic field strengths are equal. The inner and outer magnetic fields cancel one another, and so a coaxial cable does not radiate any electromagnetic energy. That is why coaxial cable is the preferred transmission line for most applications.

## Antenna Operation

As stated above, an antenna acts as the interface between a transmitter or receiver and free space. It either radiates or senses an electromagnetic field. But the question is, What exactly is an antenna, and what is the relationship between an antenna and a transmission line? Furthermore, how are the electric and magnetic fields produced?

### The Nature of an Antenna

If a parallel-wire transmission line is left open, the electric and magnetic fields escape from the end of the line and radiate into space [Fig. 14-5(a)]. This radiation, however, is inefficient and unsuitable for reliable transmission or reception.

The radiation from a transmission line can be greatly improved by bending the transmission line conductors so that they are at a right angle to the transmission line, as

shown in Fig. 14-5(b). The magnetic fields no longer cancel and, in fact, aid one another. The electric field spreads out from conductor to conductor (Fig. 14-6). The result is an antenna. Optimum radiation occurs if the segment of transmission wire converted to an antenna is one-quarter wavelength long at the operating frequency. This makes an antenna that is one-half wavelength long.

An antenna, then, is a conductor or pair of conductors to which is applied the ac voltage at the desired frequency. In Fig. 14-5, the antenna is connected to the transmitter by the transmission line that was used to form the antenna. In most practical applications, the antenna is remote from the transmitter and receiver, and a transmission line is used to transfer the energy between the antenna and transmitter or receiver. It is sometimes useful, however, to analyze an antenna as if the conductors were connected directly to the generator or transmitter, as in Fig. 14-7. The voltage creates an electric field and the current creates a magnetic field. Fig. 14-7(a) shows the magnetic field for one polarity of the generator, and Fig. 14-7(b) shows the accompanying electric field.

Fig. 14-7(c) and (d) show the magnetic and electric fields, respectively, for the opposite polarity of the generator.

The magnetic fields vary in accordance with the applied signal from the generator, which is usually a modulated sine wave carrier. The sinusoidal electric field changing over time is similar to a current that causes the generation of the sinusoidal magnetic field. A sinusoidally varying magnetic field produces an electric field. Thus the two fields support and sustain each other. The ratio of the electric field strength of a radiated wave to the magnetic field strength is a constant. It is called the impedance of space, or the wave impedance, and is 377 Ω. The resulting fields are radiated into space at the speed of light (3 x 108 m/s or 186,400 mi/s).

The antenna that is radiating electromagnetic energy appears to the generator as an ideally resistive electrical load so that the applied power is consumed as radiated energy. In addition to the resistive component, an antenna can have a reactive component. The resistive component is called the antenna radiation resistance. This resistance does not dissipate power in the form of heat, as in electronic circuits. Instead, the power is dissipated as radiated electromagnetic energy.

### The Electromagnetic Field

The electric and magnetic fields produced by the antenna are at right angles to each other, and both are perpendicular to the direction of propagation of the wave. This is illustrated in several ways in Fig. 14-8. Fig. 14-8(a) shows the basic right-angle relationship. Now, assume that you are looking at a small area of the space around an antenna and that the signal is moving either directly out of the page toward you or into the page away from you. Fig. 14-8(b) is a view of the field lines in Fig. 14-8(a), but the perspective is shifted 90° so that you are getting an edge view. Fig. 14-8(c) shows the variation in the strength of the electric and magnetic fields as they move outward from the antenna. Note that the amplitude and direction of the magnetic and electric fields vary in a sinusoidal manner depending upon the frequency of the signal being radiated.

### Near Field and Far Field

Antennas actually produce two sets of fields, the near field and the far-field. The near field describes the region directly around the antenna where the electric and magnetic fields are distinct. These fields are not radio waves, but they do indeed contain any information transmitted. These fields weaken with the distance from the antenna, approximately by the quadruple power of the distance. The near field is also referred to as the Fresnel zone.

The far-field that is approximately 10 wavelengths from the antenna is the radio wave with the composite electric and magnetic fields. For example, at 2.4 GHz, one wavelength is 984/2400 = 0.41 feet. The far-field is 10 times that, or 4.1 ft or beyond.

Inside that 4.1 ft lies the near field. The combined fields actually detach themselves from the antenna and radiate into space as previously described. Its strength also diminishes with distance but only at the square of the distance. The far fi eld is also called the Fraunhofer zone.

Most wireless applications use the far-field wave. And any antenna radiation patterns are valid only if measurements are taken on the far-field. The near field is rarely used, but applications such as radio-frequency identification (RFID) and near-field communication (NFC) make use of the near field. Some cell phone manufacturers also build in a short-range near field radio for applications such as wireless building access, ticket purchases, or automotive functions.

### Polarization

Polarization refers to the orientation of magnetic and electric fields with respect to the earth. If an electric field is parallel to the earth, the electromagnetic wave is said to be horizontally polarized; if the electric field is perpendicular to the earth, the wave is vertically polarized. Antennas that are horizontal to the earth produce horizontal polarization, and antennas that are vertical to the earth produce vertical polarization.

Some antennas produce circular polarization, in which the electric and magnetic fields rotate as they leave the antenna. There can be right-hand circular polarization (RHCP) and left-hand circular polarization (LHCP); the type depends on the direction of rotation as the signal leaves the antenna. An electric fi eld can be visualized as rotating as if the antenna were connected to a large fan blade. The electric fi eld and the accompanying magnetic fi eld rotate at the frequency of the transmitter, with one full rotation occurring in one cycle of the wave. Looking from the transmitter to the distant receiver, RHCP gives a clockwise rotation to the electric field and LHCP gives a counterclockwise rotation.

For optimal transmission and reception, the transmitting and receiving antennas must both be of the same polarization. Theoretically, a vertically polarized wave will produce 0 V in a horizontal antenna and vice versa. But during transmission over long distances, the polarization of waves changes slightly because of the various propagation effects in free space. Thus even when the polarization of the transmitting and receiving antennas are not matched, a signal is usually received.

A vertical or horizontal antenna can receive circular polarized signals, but the signal strength is reduced. When circular polarization is used at both transmitter and receiver, both must use either left- or right-hand polarization if the signal is to be received.

### Antenna Reciprocity

The term antenna reciprocity means that the characteristics and performance of an antenna are the same whether the antenna is radiating or intercepting an electromagnetic signal. A transmitting antenna takes a voltage from the transmitter and converts it to an electromagnetic signal. A receiving antenna has a voltage induced into it by the electromagnetic signal that passes across it. The voltage is then connected to the receiver. In both cases, the properties of the antenna—gain, directivity, frequency of operation, etc.— are the same. However, an antenna used for transmitting high power, such as in a radio or TV broadcast station, must be constructed of materials that can withstand the high voltages and currents involved. A receiving antenna, no matter what the design, can be made of wire. But a transmitting antenna for high-power applications might, e.g., be designed in the same way but be made of larger, heavier material, such as metal tubing.

In most communication systems, the same antenna is used for both transmitting and receiving, and these events can occur at different times or can be simultaneous. An antenna can transmit and receive at the same time as long as some means is provided for keeping the transmitter energy out of the front end of the receiver. A device called a diplexer is used for this purpose.

### The Basic Antenna

An antenna can be a length of wire, a metal rod, or a piece of tubing. Many different sizes and shapes are used. The length of the conductor is dependent on the frequency of operation. Antennas radiate most effectively when their length is directly related to the wavelength of the transmitted signal. Most antennas have a length that is some fraction of a wavelength. One-half and one-quarter wavelengths are most common.

An important criterion for radiation is that the length of the conductor is approximately one-half or one-quarter wavelength of the ac signal. A 60-Hz sine wave signal has a wavelength of λ=300,000,000/60 5 5,000,000 m. Since 1 mi < 1609.34 m, one wavelength of a 60-Hz signal is about 5,000,000/1609.34 5 3106.86 mi. One-half wavelength is 1553.43 mi. Very little radiation of an electromagnetic field occurs if antenna wires are less than this length.

The same is true of wires carrying audio signals. A 3-kHz audio signal has a wavelength of 300,000,000/3000 5 100,000 m or 62.14 mi. This wavelength is so long compared to the length of the wire normally carrying such signals that little radiation occurs.

However, as frequency is increased, wavelength decreases. At frequencies from about 1 MHz up to 100 GHz, the wavelength is within the range of practical conductors and wires. It is within this range that long-distance radiation occurs. For example, a 300-MHz UHF signal has a wavelength of 1 m, a very practical length.

The other factor that determines how much energy is radiated is the arrangement of the conductors carrying the signal. If they are in the form of a cable such as a transmission line with a generator at one end and a load at the other, as shown in Fig. 14-3, very little radiation occurs at any frequency.

As seen in Figs. 14-5 and 14-6, an open transmission line can be made into an antenna simply by bending the conductors out at a right angle with the transmission line. This concept is illustrated again in Fig. 14-9. Such a line has a standing wave such that the voltage is maximum at the end of the line and the current is minimum. One-quarter wave back from the open end are a voltage minimum and a current maximum, as shown in the figure. By bending the conductors at a right angle to the transmission line at the quarter-wave point, an antenna is formed. The total length of the antenna is the one-half wavelength at the frequency of operation. Note the distribution of the voltage and current standing waves on the antenna. At the center, the voltage is minimum and the current is maximum.

## Common Antenna Types

All the most common types of antennas used in the communication industry are based on a basic dipole, and most are some modifi ed form of the one-half wavelength dipole discussed in the last section.

### The Dipole Antenna

One of the most widely used antenna types is the half-wave dipole shown in Fig. 14-10. This antenna is also formally known as the Hertz antenna after Heinrich Hertz, who first demonstrated the existence of electromagnetic waves. Also called a doublet, a dipole antenna is two pieces of wire, rod, or tubing that are one-quarter wavelength long at the operating resonant frequency. Wire dipoles are supported with glass, ceramic, or plastic insulators at the ends and middle, as shown in Fig. 14-11. Self-supporting dipoles are made from a stiff metal rod or tubing.

### Radiation Resistance

The transmission line is connected at the center. The dipole has an impedance of 73 Ω  at its center, which is the radiation resistance. At the resonant frequency, the antenna appears to be a pure resistance of 73 Ω . For maximum power transfer, it is important that the impedance of the transmission line match the load. A 73-V coaxial cable like RG-59/U is a perfect transmission line for a dipole antenna. RG-11/U coaxial cable with an impedance of 75 Ω  also provides an excellent match. When the radiation resistance of the antenna matches the characteristic impedance of the
transmission line, the SWR is minimum and maximum power reaches the antenna.

The radiation resistance of the dipole is ideally 73 Ω  when the conductor is infinitely thin and the antenna is in free space. Its actual impedance varies depending on the conductor thickness, the ratio of diameter to length, and the proximity of the dipole to other objects, especially the earth.

As the conductor thickness increases with respect to the length of the antenna, the radiation resistance decreases. A typical length-to-diameter ratio is about 10,000 for an ire antenna, for radiation resistance of about 65 Ω  instead of 73 Ω. The resistance drops gradually as the diameter increases. With a large tubing conductor, the resistance can drop to as low as 55Ω.

The graph in Fig. 14-12 shows how radiation resistance is affected by the height of a dipole above the ground. Curves for both horizontally and vertically mounted antennas are given. The resistance varies above and below an average of about 73 Ω , depending on height in wavelengths. The higher the antenna, the less effect the earth and surrounding objects have on it, and the closer the radiation resistance is to the theoretical ideal. Given that radiation resistance is affected by several factors, it often varies from 73 Ω . Nevertheless, a 75-Ω  coaxial cable provides a good match, as does 50-V cable at lower heights with thicker conductors.

### Dipole Length

An antenna is a frequency-sensitive device. you learned that the formula λ = 984/f can be used to calculate one wavelength at a specific frequency, and λ = 492/f can thus be used to calculate one-half wavelength. For example, one-half wavelength at 122 MHz is 492/122= 4.033 ft.

As it turns out, to get the dipole to resonate at the frequency of operation, the physical length must be somewhat shorter than the one-half wavelength computed with the expression given above, since the actual length is related to the ratio of length to diameter, conductor shape, Q, the dielectric (when the material is other than air), and a condition known as end effect. The end effect is a phenomenon caused by any support insulators used at the ends of the wire antenna and has the effect of adding capacitance to the end of each wire. At frequencies up to about 30 MHz, the end effect shortens the antenna by about 5 percent. Thus the actual antenna length is only about 95 percent of the computed length. The formula must be modified as follows:

L = 492 x 0.95/f = 468/f

where L = length of a half-wave dipole antenna. For half-wave dipole wire antennas used below 30 MHz, the formula L =468/f provides a ballpark figure, so to speak. Minor adjustments in length can then be made to fine-tune the antenna to the center of the desired frequency range.

For example, an antenna for a frequency of 27 MHz would have a length of 468/27 = 17.333 ft. To create a half-wave dipole, two 8.666-ft lengths of wire would becut, probably 12- or 14-gauge copper wire. Physically, the antenna would be suspended between two points as high as possible off the ground (see Fig. 14-11). The wire conductors themselves would be connected to glass or ceramic insulators at each end and in the middle to provide good insulation between the antenna and its supports. The transmission line would be attached to the two conductors at the center insulator. The transmission line should leave the antenna at a right angle so that it does not interfere with the antenna’s radiation.

At frequencies above 30 MHz, the conductor is usually thicker because thicker rods or tubing, rather than wire, is used. Using thicker materials also shortens the length by a factor of about 2 or 3 percent. Assuming a shortening factor of 3 percent, one-half wavelength would be 492 x 0.97/f.

### Antenna Resonance

Because the antenna is the one-half wavelength at only one frequency, it acts as a resonant circuit. To the generator, the antenna looks like a series resonant circuit (see Fig. 14-13). The inductance represents the magnetic field, and the capacitance represents the electric field. The resistance is the radiation resistance. As always, this resistance varies depending on antenna conductor thickness and height. If the signal applied to the antenna is such that the antenna is exactly one-half wavelength long, the equivalent circuit will be resonant and the inductive reactance will cancel the capacitive reactance. Only the effect of the radiation resistance will be present, and the signal will radiate.

If the frequency of operation and the antenna length do not match, the equivalent circuit will not be resonant. Instead, like any resonant circuit, it will have a complex impedance made up of resistive and reactive components. If the frequency of operation is too low, the antenna will be too short and the equivalent impedance will be capacitive because the capacitive reactance is higher at the lower frequency. If the frequency of operation is too high, the antenna will be too long and the equivalent impedance will be inductive because the inductive reactance is higher at the higher frequency.

If the dipole is used at a frequency different from its design frequency, the antenna impedance no longer matches the transmission line impedance, so the SWR rises and power is lost. However, if the frequency of operation is close to that for which the antenna was designed, the mismatch will not be great and the antenna will work satisfactorily despite the higher SWR.

### Antenna Q and Bandwidth

The bandwidth of an antenna is determined by the frequency of operation and the Q of the antenna according to the familiar relationship BW=fr/Q. Although it is difficult to calculate the exact Q for an antenna, as the above relationship shows, the higher the Q, the narrower the bandwidth BW. Lowering Q widens bandwidth. In resonant circuits, a high Q (≥0) is usually desirable because it makes the circuit more selective. For an antenna, low Q, and hence wider bandwidth, is desirable so that the antenna can operate over a wider range of frequencies with reasonable SWR. As a rule of thumb, any SWR below 2;1 is considered good in practical antenna work. Modern communication transceivers rarely operate at just one frequency; typically they operate on a selected channel inside a broader band of frequencies. Furthermore, the transmitter is
modulated, so there are sidebands. If the antenna has too high a Q and its bandwidth is too narrow, the SWR will be higher than 2;1 and sideband clipping can occur.

The Q and thus the bandwidth of an antenna is determined primarily by the ratio of the length of the conductor to the diameter of the conductor. When the thin wire is used as the conductor, this ratio is very high, usually in the 10,000 to 30,000 range, resulting in high Q and narrow bandwidth. A length-to-diameter ratio of 25,000 results in a Q of about 14.

If the antenna conductors are made of larger-diameter wire or tubing, the length-to-diameter ratio and Q decrease, resulting in a wider bandwidth. A ratio of 1200 results in a Q of about 8.

When larger-diameter conductors are used to constructing an antenna, the larger plate area causes the inductance of the conductor to decrease and the capacitance to increase. The L/C ratio is reduced for a given resonant frequency. Lowering L lowers the inductive reactance, which directly affects Q. Since Q = XL/R and BW = fr/Q, lowering XL reduces Q and increases bandwidth.

At UHF and microwave frequencies, antennas are typically made of short, fat conductors, such as tubing. It is not uncommon to see conductors with diameters as large as 0.5 in. The result is wider bandwidth.

Bandwidth is sometimes expressed as a percentage of the resonant frequency of the antenna. A small percentage means a higher Q, and a narrower bandwidth means a lower percentage. A typical wire antenna has a bandwidth in the range of 3 to 6 percent of the resonant frequency. If thicker conductors are used, this percentage can be increased to the 7 to 10 percent range, which gives lower Q and wider bandwidth.

For example, if the bandwidth of a 24-MHz dipole antenna is given as 4 percent, the bandwidth can be calculated as 0.04 x 24= 0.96 MHz (960 kHz). The operating range of this antenna, then, is the 960-kHz bandwidth centered on 24 MHz. This gives upper and lower frequency limits of 24 MHz 6480 kHz or one-half the bandwidth. The operating range is 23.52 to 24.48 MHz, where the antenna is still close to resonance.

The Q and bandwidth of an antenna are also affected by other factors. In array-type antennas with many conductors, Q is affected by the number of conductors used and their spacing to the dipole. These antennas usually have high Q’s and, thus, narrow bandwidths, and so off-frequency operation produces greater changes in SWR than it does with lower-Q antennas.

### Conical Antennas

Another common way to increase bandwidth is to use a version of the dipole antenna known as the conical antenna [Fig. 14-14(a)]. Fig. 14-14(b) shows a flat, broadside view of a conical antenna. The overall length of the antenna is 0.73λ or 0.73(984)/f = 718.32/f. This is longer than the traditional one-half wavelength of a dipole antenna, but the physical shape changes the necessary dimensions for resonance. The cones are shaped such that the shaded area is equal to the unshaded area. When this is done, the distance between the boundaries marked by A and B in Fig. 14-14(b) is the one-half wavelength, less about 5 percent, or approximately 468/f, where f is in megahertz.

The center radiation resistance of a conical antenna is much higher than the 73 Ω  usually found when straight-wire or tubing conductors are used. This center impedance is given by Z = 120 ln (θ/2), where Z is the center radiation resistance at resonance and θ is the angle associated with the cone [see Fig. 14-14(b)]. For an angle of 30°, the center impedance is thus Z = 120 ln (30/2) = 120 ln 15 = 120(2.7) =325 Ω . This is a reasonably good match to the 300-Ω  twin-lead transmission line.

To use coaxial cable, which is usually desirable, some kind of impedance matching network is needed to transform the high center impedance to the 50 or 75 Ω characteristic of most coaxial cables.

Cones are difficult to make and expensive, and a popular and equally effective variation of the conical antenna is the bow-tie antenna. A two-dimensional cone is a triangle; therefore, an fl at the version of the conical antenna looks like two triangles or a bow tie. One bow tie version of the conical antenna in Fig. 14-14(b) would have the same shape and dimensions, but it would be made of flat aluminum. Bow tie antennas can also be made of a grillwork of conductors, instead of a flat plate, as shown in Fig. 14-14(c); this configuration reduces wind resistance. If the spacing between the conductors is made less than 0.1 wavelengths at the highest operating frequency, the antenna appears to be a solid conductor to the transmitter or receiver.

The primary advantage of conical antennas is their tremendous bandwidth: they can maintain a constant impedance and gain over a 4;1 frequency range. The length of the antenna is computed by using the center frequency of the range to be covered. For example, an antenna to cover the 4;1 range at 250 MHz to 1 GHz (1000 MHz) would be cut for a center frequency of (1000 + 250)/2 = 1250/2 = 625 MHz.

### Dipole Polarization

Most half-wave dipole antennas are mounted horizontally to the earth. This makes the electric field horizontal to the earth; therefore, the antenna is horizontally polarized. Horizontal mounting is preferred at the lower frequencies (<30 MHz) because the physical construction, mounting, and support are easier. This type of mounting also makes it easier to attach the transmission line and route it to the transmitter or receiver.

A dipole antenna can also be mounted vertically, in which case the electric field will be perpendicular to the earth, making the polarization vertical. Vertical mounting is common at the higher frequencies (VHF and UHF), where the antennas are shorter and made of self-supporting tubing.

### Radiation Pattern and Directivity

The radiation pattern of an antenna is the shape of the electromagnetic energy radiated from or received by that antenna. Most antennas have directional characteristics that cause them to radiate or receive energy in a specific direction. Typically that radiation is concentrated in a pattern that has a recognizable geometric shape.

The radiation pattern of a half-wave dipole has the shape of a doughnut. Fig. 14-15 shows the pattern with one-half the doughnut cut away. The dipole is at the center hole of the doughnut, and the doughnut itself represents the radiated energy. To an observer looking down on the top of the dipole, the radiation pattern would appear to be a figure 8, as shown in Fig. 14-16. This horizontal radiation pattern is plotted on a polar coordinate graph in the figure. The center of the antenna is assumed to be at the center of the graph. The dipole is assumed to be aligned with the 90° to 270° axis. As shown, the maximum amount of energy is radiated at right angles to the dipole, at 0° and 180°. For that reason, a dipole is what is known as a directional antenna. For optimum transmission and reception, the antenna should be aligned broadside to the signal destination or source. For optimal signal transmission, the transmitting and receiving antennas must be parallel to each other.

Whenever a dipole receiving antenna is pointed toward a transmitter or vice versa, it must be broadside to the direction of the transmitter. If the antenna is at some other angle, the maximum signal will not be received. As can be seen from the radiation pattern in Fig. 14-16, if the end of the receiving antenna is pointed directly at the transmitting antenna, no signal is received. As indicated earlier, this zero- signal condition could not occur in practice, because the radiated wave would undergo some shifts during propagation and, therefore, some minimal signal would be received from the ends of the antenna.

The measure of an antenna’s directivity is beam width, the angle of the radiation pattern over which a transmitter’s energy is directed or received. Beamwidth is measured on an antenna’s radiation pattern. The concentric circles extending outward from the pattern in Fig. 14-16 indicate the relative strength of the signal as it moves away from the antenna. The beamwidth is measured between the points on the radiation curve that are 3 dB down from the maximum amplitude of the curve. As stated previously, the maximum amplitude of the pattern occurs at 0° and 180°. The 3-dB down points are 70.7 percent of the maximum. The angle formed with two lines extending from the
center of the curve to these 3-dB points is the beam width. In this example, the beam width is 90°. The smaller the beam width angle, the more directional the antenna.

### Antenna Gain

The gain was previously defined as the output of an electronic circuit or device divided by the input. Obviously, passive devices such as antennas cannot have gain in this sense. The power radiated by an antenna can never be greater than the input power. However, a directional antenna can radiate more power in a given direction than a nondirectional antenna, and in this “favored” direction, it acts as if it had gain. Antenna gain of this type is expressed as the ratio of the effective radiated output power Pout to the input power Pin. Effective radiated power is the actual power that would have to be radiated by a reference antenna (usually a nondirectional or dipole antenna) to produce the same signal strength at the receiver as the actual antenna produces. Antenna gain is usually expressed in decibels:

dB= 10 log Pout/Pin

The power radiated by an antenna with directivity and therefore gain is called effective radiated power (ERP). The ERP is calculated by multiplying the transmitter power fed to the antenna Pt by the power gain Ap of the antenna:

ERP = ApPt

To calculate ERP, you must convert from decibels to the power ratio or gain.

The gain of an antenna is usually expressed in reference to either the dipole or an isotropic radiator. An anisotropic radiator is a theoretical point source of electromagnetic energy. The E and H fields radiate out in all directions from the point source, and at any given distance from the point source, the fields form a sphere. To visualize this, think of a lightbulb at the center of a large world globe and the light that illuminates the inside of the sphere as electromagnetic energy.

In what is known as the near field of the antenna, defined as the part of the field less than 10 wavelengths from the antenna at the operating frequency, a portion of the surface area on the sphere looks something like that shown in Fig. 14-17. In the far-field, 10 or more wavelengths distant from the source, the sphere is so large that a small area appears to be flat rather than curved, much as a small area of the earth appears flat. Most far-field analysis of antennas is done by assuming a flat surface area of radiation with the electric and magnetic fields at right angles to each other.

In reality, no practical antennas radiate isotropically; instead, the radiation is concentrated into a specific pattern, as seen in Figs. 14-15 and 14-16. This concentration of electromagnetic energy has the effect of increasing the radiation power over a surface area of a given size. In other words, antenna directivity gives the antenna gain over an isotropic radiator. The mathematics involved in determining the power gain of a dipole over an isotropic source is beyond the scope of this book. As it turns out, this power gain is 1.64; in decibels, 10 log 1.64 = 2.15 dB.

Most formulas for antenna gain are expressed in terms of gain in decibels over a dipole (dBd). If the antenna gain is said to be 4.5 dB, this means gain as compared to a dipole. To compute the gain of an antenna with respect to an isotropic radiator (dBi), add 2.15 dB to the gain over the dipole (dBi 5 dBd 1 2.15). In general, the more concentrated an antenna’s energy, the higher the gain. The effect is as if the transmitter power were actually increased by the antenna gain and applied to a dipole.

### Folded Dipoles

A popular variation of the half-wave dipole is the folded dipole, shown in Fig. 14-18(a). Like the standard dipole, it is one-half wavelength long. However, it consists of two parallel conductors connected at the ends with one side open at the center for connection to the transmission line. The impedance of this popular antenna is 300 Ω making it an excellent match for the widely available 300-Ω twin lead. The spacing between the two parallel conductors is not critical, although it is typically inversely proportional to the frequency. For very high-frequency antennas, the spacing is less than 1 in; for low-frequency antennas, the spacing may be 2 or 3 in.

The radiation pattern and gain of a folded dipole are the same as those of a standard dipole. However, folded dipoles usually offer greater bandwidth. The radiation resistance impedance can be changed by varying the size of the conductors and the spacing.

An easy way to make a folded dipole antenna is to construct it entirely of 300-Ω twin-lead cable. A piece of twin-lead cable is cut to a length of one-half wavelength, and the two ends are soldered together [Fig. 14-18(b)]. When the one-half wavelength is calculated, the velocity factor of the twin-lead cable (0.8) must be included in the formula. For example, the length of an antenna cut for 100 MHz (the approximate center of the FM broadcast band) is λ/2 = 492/f = 492/100 = 4.92 ft. By taking into account the velocity factor of twin-lead cables, the final length is 4.92 x 0.8=3.936 ft.

The center of one conductor in the twin-lead cable is then cut open, and a 300-Ω twin-lead transmission line is soldered to the two wires. The result is an effective, lowcost antenna that can be used for both transmitting and receiving purposes. Note: Twinlead is no longer widely used for antennas or transmission lines.

## The Marconi or Ground-Plane Vertical Antenna

Another widely used antenna is the one-quarter wavelength vertical antenna, also called a Marconi antenna. It is similar in operation to a vertically mounted dipole antenna. However, it offers major advantages because it is one-half the length of a dipole antenna. Radiation Pattern. Most half-wave dipole antennas are mounted horizontally, but they can also be mounted vertically. The radiation pattern of a vertically polarized dipole antenna is still doughnut-shaped, but the radiation pattern, as seen from above the antenna, is a perfect circle. Such antennas, which transmit an equal amount of energy in the horizontal direction, are called omnidirectional antennas. Because of the doughnut shape, the vertical radiation is zero and the radiation at any angle from the horizontal is greatly diminished.

The same effect can be achieved with a one-quarter wavelength antenna. Fig. 14-19 shows a vertical dipole with the doughnut-shaped radiation pattern. One-half of the pattern is below the surface of the earth. This is called a vertical radiation pattern.

Vertical polarization and omnidirectional characteristics can also be achieved by using a one-quarter wavelength vertical radiator; see Fig. 14-20(a). This antenna is known as a Marconi or ground-plane antenna. It is usually fed with coaxial cable; the center conductor is connected to the vertical radiator, and the shield is connected to earth’s ground.

With this arrangement, the earth acts as a type of electrical “mirror,” effectively providing the other one-quarter wavelength of the antenna and making it the equivalent of a vertical dipole. The result is a vertically polarized omnidirectional antenna.

### Ground Plane, Radials, and Counterpoise

The effectiveness of a vertically polarized omnidirectional antenna depends on making good electrical contact with the earth. This can be tricky. Sometimes, a reasonable ground can be obtained by driving a copper rod 5 to 15 ft long into the earth. If the earth is dry and has high resistance because of its content, however, even a ground rod is insufficient. Once a good electrical connection to the earth has been made, the earth becomes what is known as a ground plane. If a good electrical connection (low resistance) cannot be made to the earth, then an artificial ground plane can be constructed of several one-quarter wavelength wires laid horizontally on the ground or buried in the earth [Fig. 14-20(b)]. Four wires are usually sufficient, but in some antenna systems, more are used. These horizontal wires at the base of the antenna are referred to as radials. The greater the number of radials, the better the ground and the better the radiation.

The entire ground-plane collection of radials is often referred to as a counterpoise.

At very high frequencies, when antennas are short, any large, flat metallic surface can serve as an effective ground plane. For example, vertical antennas are widely used on cars, trucks, boats, and other vehicles.The metallic roof of a car makes a superior ground plane for VHF and UHF antennas. In any case, the ground plane must be large enough that it has a radius of greater than the one-quarter wavelength at the lowest frequency of operation.

### Radiation Resistance

The impedance of a vertical ground-plane antenna is exactly one-half the impedance of the dipole, or approximately 36.5 Ω. Of course, this impedance varies depending on the height above ground, the length/diameter ratio of the conductor, and the presence of surrounding objects. The actual impedance can drop to less than 20 V for a thick conductor very close to the ground.

Since there is no such thing as 36.5-Ω coaxial cable, 50-Ω coaxial cable is commonly used to feed power to the ground-plane antenna. This represents a mismatch. However, the SWR of 50/36.5 =1.39 is relatively low and does not cause any significant power loss.

One way to adjust the antenna’s impedance is to use “drooping” radials, as shown in Fig. 14-21. At some angle depending upon the height of the antenna above the ground, the antenna’s impedance will be near 50 Ω, making it a nearly perfect match for most 50-Ω coaxial cable.

### Antenna Length

In addition to its vertical polarization and omnidirectional characteristics, another major benefit of the one-quarter wavelength vertical antenna is its length. It is one-half the length of a standard dipole, which represents a significant saving at lower radio frequencies. For example, a one-half wavelength antenna for a frequency of 2 MHz would have to be 468/f = 468/2 = 234 ft. Constructing a 234-ft vertical antenna would present a major structural problem, as it would require support at least that long. An alternative is to use a one-quarter wavelength vertical antenna, the length of which would only have to be 234/f = 117 ft. Most low-frequency transmitting antennas use the one-quarter wavelength of vertical configuration for this reason. AM broadcast stations in the 535- to 1635-kHz range use one-quarter wavelength vertical antennas because they are short, inexpensive, and not visually obtrusive. Additionally, they provide an equal amount of radiation in all directions, which is usually ideal for broadcasting.

For many applications, e.g., with portable or mobile equipment, it is not possible to make the antenna a full one-quarter wavelength long. A cordless telephone operating in the 46- to 49-MHz range would have a one-quarter wavelength of 234/f =234/46 = 5.1 ft. A 5-ft whip antenna, or even a 5-ft telescoping antenna, would be impractical for a device you have to hold up to your ear. And a one-quarter wavelength vertical antenna for a 27-MHz CB walkie-talkie would have to be an absurdly long 234/27= 8.7 ft!

To overcome this problem, much shorter antennas are used and lumped electrical components are added to compensate for the shortening. When a vertical antenna is made less than the one-quarter wavelength, the practical effect is a decreased inductance.

The antenna no longer resonates at the desired operating frequency, but at a higher frequency. To compensate for this, a series inductor, called a loading coil, is connected in series with the antenna coil (Fig. 14-22). The loading coil brings the antenna back into resonance at the desired frequency. The coil is sometimes mounted external to the equipment at the base of the antenna so that it can radiate along with the vertical rod. The coil can also be contained inside a handheld unit, as in a cordless telephone.

In some cases, the loading coil is placed at the center of the vertical conductor (see Fig. 14-23). CB antennas and cellular telephone antennas use this method. The CB antennas have a large coil usually enclosed inside a protective housing. The shorter cellular telephone antennas use a built-in self-supporting coil that looks like and serves the dual purpose of a flexible spring.

In both types of inductive vertical antennas, the inductor can be made variable, so that the antenna can be tuned; or the inductor can be made larger than needed and a capacitor connected in series to reduce the overall capacitance and tune the coil to resonance. Another approach to using a shortened antenna is to increase the effective capacitance represented by the antenna. One way to do this is to add conductors at the top of the antenna, as shown in Fig. 14-24. Sometimes referred to as a top hat, this structure increases the capacitance to surrounding items, bringing the antenna back into resonance. Obviously, such an arrangement is too top-heavy and inconvenient for portable and mobile antennas. However, it is sometimes used in larger fixed antennas at lower frequencies.

One of the most popular variations of the one-quarter wavelength vertical antenna is the 5⁄8λ vertical antenna (5λ/8, or 0.625λ). Like a one-quarter wavelength ground-plane antenna, the 5⁄8-wavelength vertical antenna is fed at the base with coaxial cable and has four or more one-quarter wavelength radials or the equivalent (i.e., the body of a car). A 5⁄8λ vertical antenna is one-eighth wavelength longer than the one-half wavelength.

This additional length gives such an antenna about a 3-dB gain over a basic dipole and one-quarter wavelength vertical antenna. The gain comes from concentrating the radiation into a narrower vertical radiation pattern at a lower angle to the horizon. Thus 5⁄8λ vertical antennas are ideal for long-distance communication.

Since a 5⁄8Ω antenna is not some integer multiple of a one-quarter wavelength, it appears too long to the transmission line; i.e., it looks like a capacitive circuit. To compensate for this, a series inductor is connected between the antenna and the transmission line, making the antenna a very close match to a 50-Ω coaxial transmission line. The arrangement is similar to that shown in Fig. 14-22.

The 5⁄8λ antenna is widely used in the VHF and UHF bands, where its length is not a problem. It is very useful in mobile radio installations, where omnidirectional antennas are necessary but additional gain is needed for reliable transmission over longer distances.

Example 14.1 Calculate the length of the following antennas and state their radiation resistance at
310 MHz: (a) dipole; (b) folded dipole (twin-lead; Z = 300 Ω, velocity factor = 0.8); (c) bow tie (θ=35°, 0.73λ); (d) ground plane (vertical).

### Directivity

In many types of communication systems, it is desirable to use antennas with omnidirectional characteristics, i.e., antennas that can send messages in any direction and receive them from any direction. In others, it is more advantageous to restrict the direction in which signals are sent or received. This requires an antenna with directivity.

Directivity refers to the ability of an antenna to send or receive signals over a narrow horizontal directional range. In other words, the physical orientation of the antenna gives it a highly directional response or directivity curve. A directional antenna eliminates interference from other signals being received from all directions other than the direction of the desired signal. A highly directional antenna acts as a type of filter to provide selectivity based on the direction of the signal. The receiving antenna is pointed directly at the station to be received, thereby effectively rejecting signals from transmitters in all other directions. Directional antennas provide greater efficiency of power transmission. With omnidirectional antennas, the transmitted power radiates out in all directions. Only a small portion of the power is received by the desired station; the rest is, in effect, wasted. When the antenna is made directional, the transmitter power can be focused into a narrow beam directed toward the station of interest.

The conventional half-wave dipole has some directivity in that it sends or receives signals in directions perpendicular to the line of the antenna. (This is illustrated in Fig. 14-16, which shows the figure-8 response curve of a half-wave dipole.) The half-wave dipole antenna is directional in that no signal is radiated from or picked up from its ends. Such an antenna is referred to as bidirectional since it receives signals best in two directions.

Antennas can also be designed to be unidirectional; unidirectional antennas send or receive signals in one direction only. Fig. 14-25(a) shows the directivity pattern of a highly directional antenna. The larger loop represents the main response curve for the antenna. Maximum radiation or reception is in the direction of 0°. The three smaller patterns or loops going off in different directions from the main larger pattern are called minor lobes. A three-dimensional version of the horizontal radiation pattern shown in Fig. 14-25(a) is given in Fig. 14-25(b).

Few antennas are perfectly unidirectional. Because of various imperfections, some power is radiated (or received) in other directions (the minor lobes). The goal is to eliminate or at least minimize the minor lobes through various antenna adjustments and enhancements designed to put more power into the main lobe.

The beamwidth on a standard half-wave dipole is approximately 90°. This is not a highly directional antenna. The narrower the beam width, of course, the better the directivity and the more highly focused the signal. The antenna whose pattern is shown in Fig. 14-25 has a beamwidth of 30°. At microwave frequencies, antennas with beam widths of less than 1° have been built; these provide pinpoint communication accuracy.

### Gain

When a highly directive antenna is used, all the transmitted power is focused in one direction. Because the power is concentrated into a small beam, the effect is as if the antenna had amplifi ed the transmitted signal. Directivity, because it focuses the power, causes the antenna to exhibit gain, which is one form of amplifi cation. An antenna cannot, of course, actually amplify a signal; however, because it can focus the energy in a single direction, the effect is as if the amount of radiated power were substantially higher than the power output of the transmitter. The antenna has power gain.

The power gain of an antenna can be expressed as the ratio of the power transmitted Ptrans to the input power of the antenna Pin. Usually, however, power gain is expressed in decibels:

dB= 10 logPtrans/Pin

The total amount of power radiated by the antenna, the ERP, is, as stated previously, the power applied to the antenna multiplied by the antenna gain. Power gains of 10 or more are easily achieved, especially at the higher RFs. This means that a 100-W transmitter can be made to perform as a 1000-W transmitter when applied to an antenna with gain.

### Relationship Between Directivity and Gain

The relationship between the gain and the directivity of an antenna is expressed mathematically by the formula

where B = beam width of antenna, deg
x = antenna power gain in decibels divided by 10 (x= dB/10)

The beamwidth is measured at the 3-dB down points on the radiation pattern. It assumes a symmetric major lobe.

For example, the beamwidth of an antenna with a gain of 15 dB over a dipole is calculated as follows (x= dB/10 = 15/10= 1.5):

It is possible to solve for the gain, given the beam width, by rearranging the formula and using logarithms:

The beamwidth of an antenna of unknown gain can be measured in the field, and then the gain can be calculated. Assume, e.g., a measured -3-dB beamwidth of 7°. The gain is

Since x = dB/10, dB = 10x. Therefore, the gain in decibels is 2.925 x 10= 29.25 dB.

To create an antenna with directivity and gain, two or more antenna elements are combined to form an array. Two basic types of antenna arrays are used to achieve gain and directivity: parasitic arrays and driven arrays.

## Parasitic Arrays

A parasitic array consists of a basic antenna connected to a transmission line plus one or more additional conductors that are not connected to the transmission line. These extra conductors are referred to as parasitic elements, and the antenna itself is referred to as the driven element. Typically the driven element is a half-wave dipole or some variation. The parasitic elements are slightly longer than and slightly less than one-half wavelength long.

These parasitic elements are placed in parallel with and near the driven elements. A common arrangement is illustrated in Fig. 14-26. The elements of the antenna are all mounted on a common boom. The boom does not have to be an insulator. Because there is a voltage null at the center of a one-half wavelength conductor at the resonant frequency, there is no potential difference between the elements and so they can all be connected to a conducting boom with no undesirable effect. In other words, the elements are not “shorted together.”

The reflector, a parasitic element that is typically about 5 percent longer than the half-wave dipole-driven element, is spaced from the driven element by a distance of 0.15l to 0.25λ. When the signal radiated from the dipole reaches the reflector, it induces a voltage into the reflector and the reflector produces some radiation of its own. Because of the spacing, the reflector’s radiation is mostly in phase with the radiation of the driven element. As a result, the reflected signal is added to the dipole signal, creating a stronger, more highly focused beam in the direction of the driven element. The reflector minimizes the radiation to the right of the driven element and reinforces the radiation to the left of the driven element (see Fig. 14-26).

Another kind of parasitic element is a director. A director is approximately 5 percent shorter than the half-wave dipole driven element and is mounted in front of the driven element. The directors are placed in front of the driven element and spaced by some distance between approximately one-tenth and two-tenths of a wavelength from the driven element. The signal from the driven element causes a voltage to be induced into the director. The signal radiated by the director then adds in phase to that from the driven element. The result is increased focusing of the signal, a narrower beamwidth, and a higher antenna gain in the direction of the director. The overall radiation pattern of the antenna in Fig. 14-16 is very similar to that shown in Fig. 14-25.

An antenna made up of a driven element and one or more parasitic elements is generally referred to as a Yagi antenna, after one of its inventors. The antenna elements are usually made of aluminum tubing and mounted on an aluminum cross member or boom.

Since the centers of the parasitic elements are neutral electrically, these elements can be connected directly to the boom. For the best lightning protection, the boom can then be connected to a metal mast and electrical ground. An antenna configured in this way is often referred to as a beam antenna because it is highly directional and has very high gain. Gains of 3 to 15 dB are possible with beam angles of 208 to 408. The three-element Yagi antenna shown in Fig. 14-26 has a gain of about 8 dB when compared to a half-wave dipole. The simplest Yagi is a driven element and a reflector with a gain of about 3 dB over a dipole. Most Yagis have a driven element, a reflector, and from 1 to 20 directors. The greater the number of directors, the higher the gain and the narrower the beam angle.

Additional gain and directivity can be obtained by combining two or more Yagis to form an array. Two examples are shown in Fig. 14-27. In Fig. 14-27(a), two nine-element Yagis are stacked. The spacing determines overall gain and directivity. In Fig. 14-27(b), two nine-element Yagis are mounted side by side in the same plane. The gain and beam width depends on the spacing between the two arrays and on how the transmission line is connected.

The drive impedance of a Yagi varies widely with the number of elements and the spacing. The parasitic elements greatly lower the impedance of the driven element, making it less than 10 Ω in some arrangements. Typically, some kind of impedance-matching circuit or mechanism must be used to attain a reasonable match to 50-Ωcoaxial cable, which is the most commonly used feed line.

Despite the focusing action of the reflector and director in a Yagi, so that most power is radiated in the forward direction, a small amount is lost to the rear, making the Yagi a less than perfect directional antenna. Thus, in addition to the gain and beamwidth, another specification of a Yagi is the ratio of the power radiated in the forward direction to the power radiated in the backward direction, or the front-to-back (F/B) ratio:

where Pf = forward power
Pb =backward power

Relative values of forwarding and backward power are determined by estimating the sizes of the loops in the radiation pattern for the antenna of interest. When the radiation patterns are plotted in decibels rather than in terms of power, the F/B ratio is simply the difference between the maximum forward value and the maximum rearward value, in decibels.

By varying the number of parasitic elements and their spacing, it is possible to maximize the F/B ratio. Of course, varying the number of elements and their spacing also affects the forward gain. However, maximum gain does not occur with the same conditions required to achieve the maximum F/B ratio. Most Yagis are designed to maximize the F/B ratio rather than gain, thus minimizing the radiation and reception from the rear of the antenna. Yagis have widely used communication antennas because of their directivity and gain.

At one time, they were widely used for TV reception, but since they are tuned to only one frequency, they are not good for reception or transmission over a wide frequency range. Amateur radio operators are major users of beam antennas. And many other communication services use them because of their excellent performance and low cost.

Beam antennas such as Yagis are used mainly at VHF and UHF. For example, at a frequency of 450 MHz, the elements of a Yagi are only about 1 ft long, making the antenna relatively small and easy to handle. The lower the frequency, the larger the elements and the longer the boom. In general, such antennas are only practical above frequencies of about 15 MHz. At 15 MHz, the elements are in excess of 35 ft long. Although antennas this long are difficult to work with, they are still widely used in some communication services.

## Driven Arrays

The other major type of directional antenna is the driven array, an antenna that has two or more driven elements. Each element receives RF energy from the transmission line, and different arrangements of the elements produce different degrees of directivity and gain. The three basic types of driven arrays are the collinear, the broadside, and the end-fire. A fourth type is the wide-bandwidth log-periodic antenna.

### Collinear Antennas

Collinear antennas usually consist of two or more halfwave dipoles mounted end to end. (See Fig. 14-28.) The lengths of the transmission

lines connecting the various driven elements are carefully selected so that the energy reaching each antenna is in phase with all other antennas. With this configuration, the individual antenna signals combine, producing a more focused beam. Three different transmission line connections are shown in the figure. Like dipole antennas, collinear antennas have a bidirectional radiation pattern, but the two beam widths are much narrower, providing greater directivity and gain. With four or more halfwave elements, minor lobes begin to appear. A typical collinear pattern is shown in Fig. 14-29.

The collinear antennas in Fig. 14-28(b) and (c) use half-wave sections separated by shorted quarter-wave matching stubs, which ensure that the signals radiated by each half-wave section are in phase. The greater the number of half-wave sections used, the higher the gain and the narrower the beamwidth.

Collinear antennas are generally used only on VHF and UHF bands because their length becomes prohibitive at the lower frequencies. At high frequencies, collinear antennas are usually mounted vertically to provide an omnidirectional antenna with gain.

### Broadside Antennas

A broadside array is, essentially, a stacked collinear antenna consisting of half-wave dipoles spaced from one another by one-half wavelengths, as shown in Fig. 14-30. Two or more elements can be combined. Each is connected to the other and to the transmission line. The crossover transmission line ensures the correct signal phasing. The resulting antenna produces a highly directional radiation pattern, not in the line of the elements, as in a Yagi, but broadside or perpendicular to the plane of the array. Like the collinear antenna, the broadside is bidirectional in radiation, but the radiation pattern has a very narrow beam width and high gain. Its radiation pattern also resembles that of the collinear antenna, as shown in Fig. 14-29. The radiation pattern is at a right angle to the plane of the driven elements.

### End-Fire Antennas

The end-fire array, shown in Fig. 14-31(a), uses two half-wave dipoles spaced one-half wavelength apart. Both elements are driven by the transmission line. The antenna has a bidirectional radiation pattern, but with narrower beam widths and lower gain. The radiation is in the plane of the driven elements as in a Yagi. The end of the fire array in Fig. 14-31(b) uses five driven elements spaced some fraction of a wavelength D apart. By careful selection of the optimal number of elements with the appropriately related spacing, a highly unidirectional antenna is created. The spacing causes the lobe in one direction to be canceled so that it adds to the other lobe, creating high gain and directivity in one direction.

### Log-Periodic Antennas

A special type of driven array is the wide-bandwidth log-periodic antenna (see Fig. 14-32). The lengths of the driven elements vary from long to short and are related logarithmically. The longest element has a length of one-half wavelength at the lowest frequency to be covered, and the shortest element is one-half wavelength at the higher frequency. The spacing is also variable. Each element is fed with a special short transmission line segment to properly phase the signal. The transmission line is attached at the smallest element. The driving impedance ranges from about 200 to 800 Ω and depends on the length-to-diameter ratio of the driven element. The result is a highly directional antenna with excellent gain.

The great advantage of the log-periodic antenna over a Yagi or other array is its very wide bandwidth. Most Yagis and other driven arrays are designed for specific frequency or a narrow band of frequencies. The lengths of the elements set the operating frequency. When more than one frequency is to be used, of course, multiple antennas can be used. The log-periodic antenna can achieve a 4;1 frequency range, giving it a very wide bandwidth. The driving impedance remains constant over this range.

Some TV antennas in use today are of the log-periodic variety so that they can provide high gain and directivity on both VHF and UHF TV channels. Log- periodic antennas are also used in other two-way communication systems where wide bandwidth and multiple frequencies must be covered.

### Impedance Matching

One of the most critical aspects of any antenna system is to ensure maximum power transfer from the transmitter to the antenna. An important part of this, of course, is the transmission line itself. When the characteristic impedance of the transmission line matches the output impedance of the transmitter and the impedance of the antenna itself, the SWR will be 1 ; 1 and maximum power transfer will take place.

The best way to prevent a mismatch between antenna and transmission line is through correct design. In practice, when mismatches do occur, some corrections are possible. One solution is to tune the antenna, usually by adjusting its length to minimize the SWR. Another is to insert an impedance-matching circuit or antenna tuner between the transmitter and the transmission line, such as the balun or LC L, T, or π networks described previously. These circuits can make the impedances equal so that no mismatch occurs, or at least the mismatch is minimized. The ideal is an SWR of 1, but any SWR value below 2 is usually acceptable.

Today, most transmitters and receivers are designed to have an antenna impedance of 50 Ω. Receivers must see an antenna system including a transmission line that looks like a generator with a 50-Ω resistive impedance. Transmitters must see an antenna including transmission line with a 50-Ω resistive impedance over the desired operating frequency range if the SWR is to be close to 1 and maximum power is to be transferred to the antenna.

Example 14.2 An antenna has a gain of 14 dB. It is fed by an RG-8/U transmission line 250 ft long
whose attenuation is 3.6 dB/100 ft at 220 MHz. The transmitter output is 50 W. Calculate (a) the transmission line loss and (b) the effective radiated power.

generator with a 50-Ω resistive impedance. Transmitters must see an antenna including a transmission line with a 50-Ω resistive impedance over the desired operating frequency range if the SWR is to be close to 1 and maximum power is to be transferred to the antenna.

For low-frequency applications (,30 MHz) using wire antennas high above the ground, the 50-Ω coaxial cable is a reasonable match to the antenna, and no further action needs to be taken. However, if other antenna designs are used, or if the feed point impedance is greatly different from that of a 50-Ωcoaxial cable, some means must be used to ensure that the impedances are matched. For example, most Yagis and other multiple-element antennas have an impedance that is not even close to 50 Ω. Furthermore, an antenna that is not the correct length for the desired frequency will have a large reactive component that can severely affect the SWR and power output.

In situations in which a perfect match between antenna, transmission line, and transmitter is not possible, special techniques collectively referred to as antenna tuning or antenna matching are used to maximize power output and input. Most of these techniques are aimed at impedance matching, i.e., making one impedance look like another through the use of tuned circuits or other devices. Several of the most popular methods are described in the following sections.

### Q Sections

A Q section, or matching stub, is a one-quarter wavelength of coaxial or balanced transmission line of a specific impedance that is connected between a load and a source for the purpose of matching impedances (see Fig. 14-33). A one-quarter wavelength transmission line can be used to make one impedance look like another according to the relationship

where ZQ = characteristic impedance of quarter-wave matching stub or Q section
Z0 = characteristic impedance of transmission line or transmitter at
input of Q section
ZL = impedance of load
Usually ZL is the antenna feed point impedance.

For example, suppose it is desired to use a Q section to match a standard 73- Ω coaxial transmission line to the 36.5- Ω impedance of a quarter-wave vertical antenna. Using the equation, we have

This tells us that a one-quarter wavelength section of 50-V coaxial cable will make the 73- Ω transmission line look like the 36.5- Ω antenna or vice versa. In this way, maximum power is transferred.

When open-wire balanced transmission lines are used, a special balanced line can be designed and built to achieve the desired impedance. If it is desirable to use standard coaxial cable, then standard available impedances must be used. This means that the Q section will have to be 50, 75, or 93  Ω, since these are the only three standard values commonly available.

In using Q section techniques, it is important to take into account the velocity factor of the cable used to make the Q section. For example, if a Q section of 93  Ω is needed, then RG-62/U coaxial cable can be used. If the operating frequency is 24 MHz, the length of a quarter-wave is 246/f = 246/24 = 10.25 ft. The velocity factor for this cable is 0.86, and so the correct length for the cable is 10.25 x 0.86= 8.815 ft.

Two or more Q sections can be used in series to achieve the desired match, with each section performing an impedance match between its input and output impedances.

### Baluns

Another commonly used impedance-matching technique makes use of a balun, a type of transformer used to match impedances. Most baluns are made of a ferrite core, either a toroid or rod, and windings of copper wire. Baluns have a very wide bandwidth and, therefore, are essentially independent of frequency. Baluns can be created for producing impedance-matching ratios of 4 ; 1, 9 ; 1, and 16 ; 1. Some baluns have a 1 ; 1 impedance ratio; the sole job of this type of balun is to convert between a balanced and unbalanced condition with no phase reversal.

Fig. 14-34 shows a 4 ; 1 balun made with bifilar windings on a toroid core. Bifilar windings, in which two parallel wires are wound together as one around the core, provide maximum coupling between wires and core. The connections of the wires are such as to provide a balanced-to-unbalanced transformation. A common example of such a balun is one that provides a 75- Ω unbalanced impedance on one end and a 300- Ωbalanced impedance on the other. Baluns are fully bidirectional; i.e., either end can be used as the input or the output. Such baluns have excellent broadband capabilities and work over a very wide frequency range.

Baluns can also be constructed from coaxial cable. A one-half wavelength coaxial cable is connected between the antenna and the feed line, shown in Fig. 14-35. When the length of the half-wave section for such a configuration is calculated, the velocity factor of the coaxial cable must be taken into account. Baluns of this type provide a 4 ; 1 impedance transformation. For example, they can easily convert a 300- Ω antenna to a 75- Ω load and vice versa.

### Antenna Tuners

When baluns and matching sections cannot do the job, antenna tuners are used. An antenna tuner is a variable inductor, one or more variable capacitors, or a combination of these components connected in various configurations. L, T, and π networks are all widely used. The inductor and capacitor values are adjusted until the SWR indicates that the impedances match.

It is important to mention that using an antenna tuner at the transmitter only “tricks” the transmitter into seeing a low SWR. In reality, the SWR on the line between the tuner and the antenna is still high.

One popular variation of the antenna tuner is a trans match circuit, which uses a coil and three capacitors to tune the antenna for optimal SWR (see Fig. 14-36). Capacitors C2 and C3 are ganged together and tuned simultaneously. Transmatch circuits can be made to work over a wide frequency range, typically from about 2 to 30 MHz. A similar circuit can be made by using lower values of inductance and capacitance for matching VHF antennas. At UHF and microwave frequencies, other forms of impedance matching are used.

To use this circuit, an SWR meter is usually connected in series with the antenna transmission line at the trans match output. Then L1 is adjusted for minimum SWR, with the transmitter feeding power to the antenna. Then C1 and C2–C3 are adjusted for minimum SWR. This procedure is repeated several times, alternately adjusting the coil and capacitors until the lowest SWR is reached.

A major development in antenna tuners is the automatic tuner. This may be an L, T,p, or other configuration that is self-adjusting. For example, the inductor in Fig. 14-36 would be provided with multiple taps along its length. By selecting the desired tap, the inductance could be changed. In place of each capacitor would be banks of parallel connected capacitors that could be switched in or out. All the inductor taps and capacitors are switched in or out by relay contacts. The relays in turn are operated by an embedded microcontroller.

The microcontroller gets its inputs from feedback provided by the outputs of an RF ower meter. Today’s power meters measure both forward and reflected power and provide a dc output proportional to those values. These dc values are converted to binary by an analog-to-digital converter and sent to the microcontroller. In the microcontroller resides a program that implements an algorithm that automatically adjusts the inductor and capacitors until the reflected power is reduced to zero or at least minimized. The modern antenna tuner can produce an excellent match in a few seconds or less.

Example 14.3 Calculate the length of the impedance-matching section needed for a Q section to
match a 50- Ω transmitter output to a Yagi with a feed impedance of 172  Ω. The operating frequency is 460 MHz.

Example 14.4 Calculate the length of the impedance-matching section needed for a λ/4 balun to convert 75  Ω to 300  Ω. The operating frequency is 460 MHz. RG-59 A/U coaxial cable is the line of choice; the velocity factor of RG-59 A/U cable is 0.66.

λ/4 =0.5347 x 0.66 = 0.353 ft (4.23 in)

### Watch Video

Smith Chart | Wavelength Scales | SWR Circle | Plotting and Reading ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Standing Waves | Matched Lines | Circuit Elements | Stripline | Microstrip ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Active Filters | Crystal Filters | Ceramic Filters | Surface Acoustic Wave ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Transmission Line | Cable | Connectors | Velocity Factor | Time Delay ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Network | Topologies | connectors | LAN | WAN | MAN | STAR | RING, BUS ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Ethernet LANs| Coaxial Cable | Twisted-Pair Cable | Advance Ethernet ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Click here to Learn More ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )

Click here to Learn ( Antenna | Antenna Operation | Antenna Types | Radio Waves | Fields | Dipoles )