# BASIC ANTENNA THEORY

An antenna is a device that provides a transition between electric currents on a conductor and electromagnetic waves in space. A transmitting antenna transforms electric currents into radio waves and a receiving antenna transforms an electromagnetic field back into electric current.

There are several basic properties that are common to all antennas:

Reciprocity: an antenna’s electrical characteristics are the same whether it is used for transmitting or receiving. Because this is always true, throughout this lecture, we will consider antennas as transmitting antennas.

Polarization: polarization is the orientation of the electric field vector of the electromagnetic wave produced by the antenna. For most antennas, the orientation of the antenna conductor determines the polarization. Polarization may be vertical, horizontal or elliptical. The diagram above shows vertical and horizontal polarization. If the radio wave's electric field vector points in some other direction, it is said to be obliquely polarized.

If the electric field rotates in space, such that its tip follows an elliptical path, it is elliptically polarized.

Wavelength: this is the length of one RF wave. It can be computed by either of the following formulas, depending on the units required:

l(in m) = 300/f(in MHz) or l(in ft) = 984/f(in MHz) Gain (directivity): This is a measure of the degree to which an antenna focuses power in a given direction, relative to the power radiated by a reference antenna in the same direction. Units of measure are dBi (isotopic antenna reference) or dBd (half-wave dipole reference). The two gain measurements can be converted using the following formula:

dBi = dBd + 2.1

If the directivity of the transmitting and receiving antennas is known, it is possible to compute the power received by the receiving antenna using either of the formulas below:

When using dB: Antenna gain should be expressed in dBi, wavelength and distances in m and powers in dBm or dBW.

When using gain ratios and powers in W: Antenna gains should be expressed as a number, distances and wavelengths in m and powers in W.

Here is an example:

Two dipole antennas 100 km apart are aligned and one transmits a 1 kW signal. The frequency is 222 MHz. What is the received power?

Solution A using dB

Convert 1 kW to dbm PT = 10log(1kW/1mW) = 10 log(1,000,000) = 60 dBm

Find the wavelength: l = 300/f = 300/222 MHz = 1.35 m  This is the same as 9.4*10-10 W

Beamwidth: the angular separation between the half-point (-3dB) points in an antenna’s radiation pattern. In general, the beamwidth of the main lobe of the radiation pattern decreases as the directivity increases.

Near field (induction field): electromagnetic field created by an antenna that is only significant at distances of less than 2D/l from the antenna, where D is the longest dimension of the antenna.

Near field region: A spherical region of radius 2D/l centered on the antenna.

Far field (radiation field): electromagnetic field created by the antenna that extends throughout all space. At distances greater than 2D/l from the antenna, it is the only field. It is the field used for communications.

Far field region: The region outside the near field region, at distances greater than 2D/l.

Input Impedance: This is the impedance measured at the antenna input terminals. In general it is complex and has two real parts and one imaginary part:

Radiation resistance: - represents conversion of power into RF waves (real)

Loss resistance – represents conductor losses, ground losses, etc. (real)

reactance – represents power stored in the near field (imaginary)

Efficiency: this is the ratio of radiation resistance to total antenna input resistance: The loss resistances come from conductor losses and losses in the ground (the near field of the antenna can interact with the ground and other objects near the antenna). The efficiency of practical antennas varies from less than 1% for certain types of low frequency antennas to 99% for some types of wire antennas.

Electrical length. This came up in the section on transmission lines. It is the length or distance expressed in terms of wavelengths.

Bandwidth: generally the range of frequencies over which the antenna system’s SWR remains below a maximum value, typically 2.0

Azimuth and Elevation: These are angles used to describe a specific position in an antenna's radiation pattern. Azimuth is a horizontal angle, generally measured from true north. The elevation angle is a vertical angle, ranging from 0 degrees (horizon) to 90 degrees (zenith). # THE HALF WAVE DIPOLE (HERTZ ANTENNA)

The dipole antenna dates back to the early RF experiments of Heinrich Hertz in the late 19th century. It consists of a conductor that is broken in the center so that RF power can be applied to it. One can think of the half wave dipole as an open circuited transmission line that has been spread out, so that the transmission line can radiate a signal into space. A dipole can be any length, but it most commonly is just under 1/2 wavelength long. A dipole with this length, known as a resonant or half wave dipole, has an input impedance that is purely resistive and lies between 30 and 80 ohms, which provides a good match to commercially available 50 ohms coaxial cables as well as commercial transmitters and receivers, most of which have 50 ohm output and input impedances. The length of a dipole can be approximately determined from the following formula:

l = 468/f

where:

l is the length in feet and

f is the frequency in MHz.

The radiation pattern of a l/2 dipole in free space is shown below The 3-dimensional radiation pattern in free space is a fat doughnut with the dipole piercing its central hole. Notice that unlike an isotropic radiator that radiates equally well in all directions, the dipole radiates more RF in some directions than others. This means that the dipole has a gain or directivity over an isotropic radiator of approximately 2.1 dB. That means that the radiation from the dipole is 2.1 dB stronger in the direction of maximum radiation than the radiation from an isotropic radiator in the same direction, when both antennas are fed with the same amount of RF power..

As the dipole's electrical length changes, its radiation pattern changes. You can click on the link below to view an animation that shows how the dipole's radiation pattern varies with antenna length. The antenna is shown as a red line. When you are done, be cure to use your browser's BACK button to return to this web page.

The input impedance of a dipole antenna also depends on its electrical length. When the antenna is approximately an odd multiple of a half wavelength long, the input impedance is resistive and lies between 50 and 200 ohms. For antennas that are an even number of half wavelengths long, the input impedance is resistive and extremely high, between 1000 and 50,000 ohms.

The chart below shows the effect of ground on the input impedance of a dipole. As a horizontal antenna is brought closer to the surface of the earth, its input resistance decreases at first because the electric field is being shorted by the ground. As the antenna is brought closer, the input resistance will rise again because increases in ground loss resistance overwhelm the decrease due to shorting of the electric field. Over a good conductor such as sea water, the input resistance drops steadily as the antenna is lowered, reaching a value of zero when the antenna touches the water's surface.

As a horizontal dipole is raised above the ground, the input resistance increases until a maximum value of approximately 90 ohms is reached at a height of 3/8 l. As the antenna is raised even higher, the input resistance slowly oscillates around the free space value of 73 ohms. Most dipoles in actual installations show an input resistance of 50 to 75 ohms, depending on the location.

There is a variation of the l/2 dipole known as the folded dipole that is often used for FM and TV reception. A diagram of the folded dipole is shown below. The folded dipole is the same overall length as the l/2 dipole, but has a second conductor connected to the first only at the ends, and separated from it by approximately l/400. The input impedance of the folded dipole is approximately 300 ohms, which is a perfect match to TV twin lead and to the input of the TV set. The folded dipole also has a larger bandwidth than the regular dipole, which is important for proper TV reception.

# THE VERTICAL (MARCONI) ANTENNA

In the last unit, we discussed the ground wave, and the necessity that the ground wave have vertical polarization. A vertical antenna is used to launch a vertically polarized RF wave. Vertical antennas are most often used in two areas:

1. Low frequency communications – at frequencies below 2 MHz, it is difficult to use dipole antennas because of their length and the requirement that they be mounted at least a half wavelength above ground. For example: a 2 MHz dipole antenna is approximately 234 ft long and needs to be approximately 234 feet above ground. Also, most communications at frequencies below 2 MHz is via ground wave, which requires vertical polarization.

2. Mobile communications – it is difficult to mount a horizontally polarized dipole on a vehicle. A vertical antenna only has one mounting point and less wind resistance.

The most common vertical antenna is the Marconi antenna. It is a vertical conductor l/4 high, fed at the end near ground. It is essentially a vertical dipole, in which one side of the dipole is the RF image of the antenna in the ground. This may sound strange, but remember that ground reflects RF as a mirror reflects light Simple Marconi Antenna The image antenna formed in the ground under a Marconi antenna

This type of antenna, unlike the dipole, is an unbalanced antenna, and should be fed directly with coaxial cable. The shield of the coax is connected to the ground at the base of the antenna and the center lead of the coax is connected to the vertical radiator.

Because the ground under a vertical antenna is actually part of the antenna, it is necessary that ground losses be minimized. To minimize the losses, the electrical conductivity of the ground must be made as high as possible, or an artificial low loss ground must be provided.

Ground conductivity can be improved by using ground radial wires. These are wires buried just under the earth’s surface or laid on the surface that provide a low resistance path for RF currents flowing in the ground. The ground currents are greatest in the vicinity of the feed point of a Marconi antenna, so the radials run out from the feed point, up to a distance of l/4 from the antenna, if possible. The ground radials do not have to be any specific length and the general rule is that a large number of short radials is preferable to a few long radials. The diagram below shows how current flows through the ground to the feed point of the Marconi antenna. The radials should be laid out in a pattern that follows the ground current, that is running radially out from the feed point of the antenna. The diagram below is a bird's eye view of typical ground radial layouts. Note that the radials do not all have to be the same length and that losses may be decreased by adding extra radials near the feed point. These extra radials can be as short as l/40 and still be effective. When a Marconi antenna cannot be mounted on the ground, an artificial ground system, called a counterpoise, is used. The counterpoise consists of l/4 wires emanating radially from the antenna feed point as shown below. The shield of the coax is connected to the counterpoise at the feed point. The counterpoise is not connected to ground. Ground losses affect the feed point impedance and antenna efficiency. A Marconi antenna mounted on a perfectly conducting ground would have an input impedance that is ½ the impedance of a dipole, or approximately 36 ohms. When mounted on a real ground, the input impedance can range from 38 ohms for a well designed AM broadcast antenna mounted over a specially prepared ground, to over 100 ohms for a Marconi mounted above poor, unprepared ground that has no radials.

Ground loss reduces the antenna's efficiency, because part of the power being delivered to the antenna is being dissipated in the ground rather than being radiated. The efficiency can be computed from the measured value of input resistance by using the following formula: The radiation pattern of the Marconi antenna is a half doughnut as shown in the figure below. There is no radiation straight up in the direction of the wire. The bulk of the radiation occurs at a low elevation angle, which is what is needed to launch a ground wave. # LOOP ANTENNAS

All antennas discussed so far have used radiating elements that were linear conductors. It is also possible to make antennas from conductors formed into closed loops. There are two broad categories of loop antennas:

1. Small loops, which contain no more than 0.085 wavelengths (~l/12) of wire

2. Large loops, which contain approximately 1 wavelength of wire.

SMALL LOOP ANTENNAS

A small loop antenna is one whose circumference contains no more than 0.085 wavelengths of wire. In such a short conductor, we may consider the current, at any moment in time to be constant. This is quite different from a dipole, whose current was a maximum at the feed point and zero at the ends of the antenna. The small loop antenna can consist of a single turn loop or a multi-turn loop as shown below: The radiation pattern of a small loop is very similar to a dipole. The figure below shows a 2-dimensional slice of the radiation pattern in a plane perpendicular to the plane of the loop. There is no radiation from a loop There is no radiation from a loop along the axis passing through the center of the loop, as shown below. When the loop is oriented vertically, the resulting radiation is vertically polarized and vice versa: The input impedance of a small loop antenna is inductive, which makes sense, because the small loop antenna is actually just a large inductor. The real part of the input impedance is very small, on the order of 1 ohm, most of which is loss resistance in the conductor making up the loop. The actual radiation resistance may be 0.5 ohms or less. Because the radiation resistance is small compared to the loss resistance, the small loop antenna is not an efficient antenna and cannot be used for transmitting unless care is taken in its design and manufacture.

While the small loop antenna is not necessarily a good antenna, it makes a good receiving antenna, especially for LF and VLF. At these low frequencies, dipole antennas are too large to be easily constructed (in the LF range, a dipole's length ranges from approximately 1600 to 16,000 feet, and VLF dipoles can be up to 30 miles long!) making the small loop a good option. The small loop responds to the magnetic field component of the electromagnetic wave and is deaf to most man-made interference, which has a strong electric field. Thus the loop, although it is not efficient, picks up very little noise and can provide a better SNR than a dipole. It is possible to amplify the loop's output to a level comparable to what one might receive from a dipole.

When a small loop is used for receiving, its immunity and sensitivity may be improved by paralleling a capacitor across its output whose capacitance will bring the small loop to resonance at the desired receive frequency. (see module A for a review of LC circuits). Antennas of this type are used in AM radios as well as in LF and VLF direction finding equipment used on aircraft and boats.

LARGE LOOP ANTENNAS

A large loop antenna consists of approximately 1 wavelength of wire. The loop may be square, circular, triangular or any other shape. Because the loop is relatively long, the current distribution along the antenna is no longer constant, as it was for the small loop. As a result, the behavior of the large loop is unlike its smaller cousin.

The current distribution and radiation pattern of a large loop can be derived by folding two half wave dipoles and connecting them as shown in the diagrams below:

We begin with two l/2 dipoles separated by l/4. RF is fed into the center of each dipole. The resulting current distribution is shown below as a pink line. Note that the current is zero at the dipoles' ends, Now each dipole is folded in towards the other in a "U" shape as shown below. The current distribution has not changed - the antenna current is still zero at the ends. Since the current at the ends is zero, it would be OK to connect the ends to make a loop as shown below. We have now created a square loop of wire whose circumference is 1 wavelength. From an electrical point of view, we have just shown that the large loop is equivalent to two bent dipole antennas.

The radiation pattern of a loop antenna is shown below: A horizontal slice of the radiation pattern in the XY plane is highlighted in red. It is similar to the figure-8 pattern of a dipole.

It is possible to create either horizontally or vertically polarized radiation with a large loop antenna. The polarization is determined by the location of the feed point as shown below. If the feed point is in a horizontal side of the loop, the polarization is horizontal. If the feed point is in a vertical side of the loop, the polarization is vertical. So far we have looked at square loop antennas. One of the interesting things about the large loop antenna is that the shape is not important. As long as the perimeter of the antenna is approximately 1 wavelength, the loop antenna will produce a radiation pattern very similar to the one shown above. The shape of the loop may be circular, square, triangular, rectangular, or any other polygonal shape. While the shape of the radiation pattern is not dependent on the shape of the loop, the gain of the loop does depend on the shape. In particular, the gain of the loop is dependent on the area enclosed by the wire. The greater the enclosed area, the greater the gain. The circular loop has the largest gain and the triangular loop has the least. The actual difference between the gain of the circular loop and triangular loop is less than 1 dB, and is usually unimportant.

Loop antennas may be combined to form arrays in the same manner as dipoles. Arrays of loop antennas are called "quad arrays" because the loops are most often square. The most common type of quad array is a Yagi-Uda array using loops rather than dipoles as elements. This type of array is very useful at high elevations, where the combination of high voltage at the element tips of the dipoles in a standard Yagi array and the lower air pressure lead to corona discharge and erosion of the element . In fact, the first use of a quad array was by a broadcaster located in Quito, Ecuador (in the Andes Mountains) in the 1930's.

The input impedance of a loop depends on its shape. It ranges from approximately 100 ohms for a triangular loop to 130 ohms for a circular loop. Unlike the dipole, whose input impedance presents a good match to common 50 or 75 ohm transmission lines, the input impedance of a loop is not a good match and must be transformed to the appropriate impedance. Impedance matching will be the topic of the next unit.

# ANTENNA ARRAYS

An antenna array is an antenna that is composed of more than one conductor. There are two types of antenna arrays:

Driven arrays – all elements in the antenna are fed RF from the transmitter

Parasitic arrays – only one element is connected to the transmitter. The other elements are coupled to the driven element through the electric fields and magnetic fields that exist in the near field region of the driven element

There are many types of driven arrays. The four most common types are:

Collinear array

Log Periodic Array

Yagi-Uda Array

COLLINEAR ARRAY

The collinear array consists of l/2 dipoles oriented end-to-end. The center dipole is fed by the transmitter and sections of shorted transmission line known as phasing lines connect the ends of the dipoles as shown below. The length of the phasing lines are adjusted so that the currents in all the dipole sections are in phase, as shown below. The input impedance of a collinear array is approximately 300 ohms. The directivity of a collinear array slowly increases as the number of collinear sections is increased.

A broadside array consists of an array of dipoles mounted one above another as shown below. Each dipole has its own feed line and the lengths of all feed lines are equal so that the currents in all the dipoles are in phase.

Rows of broadside arrays can be combined to form a two dimensional array as shown below:

The two-dimensional array is used in high performance radar systems. The amplitude and phase of each input current is adjusted so that the antenna radiates its RF in a narrow beam. By making changes to the input phase and amplitude, the beam can be made to scan over a wide range of angles. Electronic scanning is much faster than mechanical scanning (which uses a rotating antenna) and permits rapid tracking of large numbers of targets.

A special type of phased array consisting of 2 or more vertical antennas is widely used in AM broadcasting. Consider an AM transmitter located in a coastal city such as Charleston, SC. It would make no sense to radiate a signal in all directions; there is only water to the east of city. Two or more antennas could be used to produce a directional pattern that would radiate most of the signal to the west.

The design and analysis of phased arrays is quite difficult and will not be covered further in this unit.

LOG PERIODIC DIPOLE ARRAY

The log periodic dipole array (LPDA) is one antenna that almost everyone over 40 years old has seen. They were used for years as TV antennas. The chief advantage of an LPDA is that it is frequency-independent. Its input impedance and gain remain more or less constant over its operating bandwidth, which can be very large. Practical designs can have a bandwidth of an octave or more.

Although an LPDA contains a large number of dipole elements, only 2 or 3 are active at any given frequency in the operating range. The electromagnetic fields produced by these active elements add up to produce a unidirectional radiation pattern, in which maximum radiation is off the small end of the array. The radiation in the opposite direction is typically 15 - 20 dB below the maximum. The ratio of maximum forward to minimum rearward radiation is called the Front-to-Back (FB) ratio and is normally measured in dB.

Log-Periodic Dipole Array

The log periodic antenna is characterized by three interrelated parameters, a,s, and t.as well as the minimum and maximum operating frequencies, fMIN and fMAX. The diagram below shows the relationship between these parameters.

Unlike many antenna arrays, the design equations for the LPDA are relatively simple to work with. If you would like to experiment with LPDA designs, click on the link below. It will open an EXCEL spreadsheet that does LPDA design.

YAGI-UDA ARRAY (YAGI)

The Yagi-Uda array, named after the two Japanese physicists who invented it, is the most common antenna array in use today. In contrast to the other antenna arrays that we have already looked at, the Yagi has only a single element that is connected to the transmitter, called the driver or driven element. The remaining elements are coupled to the driven element through its electromagnetic field . The other elements absorb some of the electromagnetic energy radiated by the driver and re-radiate it. The fields of the driver and the remaining elements sum up to produce a unidirectional pattern. The diagram below shows the layout of elements in a typical Yagi. Behind the driven element is a single element that is approximately 5% longer. This is the reflector. It prevents radiation off the back of the array. In front of the director are a series of elements that are shorter than the driven element. These are the directors. They help focus the radiation in the forward direction. Together the reflector and directors can reduce the radiation off the back of the antenna to 25 - 30 dB below the forward radiation. As more directors are added, the forward gain increases.

The table contains hyperlinks to manufacturers of Yagi antennas. You may want to check some of these links out to get a look at typical Yagi antennas.

The design and analysis of Yagi antennas is very involved and is best done using antenna modeling software. However, to get insight into the basic operation of theYagis, we will examine one with only three elements: a reflector, driver, and director. Simple 3 Element Yagi-Uda Array

The reflector is 5% longer than the driver, and the director is 5% shorter. The spacing is the same between all three elements. The plots below show the radiation pattern of the Yagi in two perpendicular planes. Notice that the pattern is unidirectional, and somewhat wider in the plane perpendicular to the elements. This is true in general for Yagis, regardless of the number of directors used. However, as more directors are added, the forward gain will increase, and the beamwidth will become narrower in both planes.

You may wonder what would happen if additional reflectors are added. The answer is that nothing happens. The first reflector reduces the power radiated rearward to approximately 1% of the forward value. The additional directors cannot couple strongly to the driver because the radiated field passing by them is so small. Only 1 reflector is necessary to reduce rearward radiation.

The operating bandwidth (the range of frequencies over which the gain and FB ratio stay within design criteria) for a Yagi is generally quite narrow and can be altered to some extent through careful adjustment of the length and spacing of the elements. The chart below shows how the gain and FB ratio of the 3 element Yagi depend on frequency. Notice that the maximum gain and FB ratio do not occur at the same frequency. This is true in general for 3 element designs. By making the Yagi longer (adding more elements) and controlling the length and spacing of each new element, it is possible to bring the frequency of maximum gain and FB ratio closer together.

The operating bandwidth of a Yagi is often defined as the range of frequencies over which the FB ratio is greater than 20 dB. In the chart above, the range of frequencies over which the FB ratio is greater than 20 dB is 0.985 f0 to 1.01f0 or 2.5% of the design frequency. This is a typical bandwidth for a Yagi array. It is possible to widen the operating bandwidth by lengthening the array and adding elements, although this improvement normally comes at the expense of forward gain.

There are many variations on these basic designs, but our examination of array antennas will end here.

# ANTENNA MATCHING

An antenna may have an input impedance as low as 15 ohms or as high as 1000 ohms. However, most transmitters have an output impedance of 50 or 75 ohms and transmission lines are only available in a limited number of characteristic impedances, so it is necessary to transform the antenna input impedance to the same value as the transmission line characteristic impedance. This process is called matching. There are a variety of matching techniques for antennas:

Delta match

Quarter-wave transformer

LC network match

Transformer match

DELTA MATCH

The delta match uses a section of 2-wire transmission line with gradually increasing separation to match a 2-wire line to an antenna. Two advantages of the delta match is the simplicity of its construction and its ability to match a wide range of impedances. Two major disadvantages are: generally, the length and amount of separation increase must be determined experimentally for a specific antenna and feed line, and the delta match section radiates some RF, changing the radiation pattern of the antenna. A variation of the delta match that is widely used for VHF/UHF Yagi antennas is the T-match: The T-match, unlike the delta match, does not radiate, but this advantage is offset by the need to adjust the overall length of the antenna slightly, as well as the T-match separation and length, to get a proper match. In general, lengths A, B and C must be determined by experiment.

QUARTER WAVE TRANSFORMER

The quarter wave transformer is a quarter wavelength section of transmission line whose characteristic impedance is selected to provide a match between the antenna and the main transmission line. We explored the properties of quarter wave sections of transmission line in the earlier section on transmission lines, and you may want to click here to review that information.

The quarter wave transformer can theoretically be used to match any antenna impedance to any feed line impedance, although it is difficult to construct quarter wave line sections to match two low values of impedance. The impedance, ZQ of the quarter wave line necessary to match an antenna of impedance ZA to a feed line of impedance Z0 is given by:  The advantages of the quarter wave transformer are that it is very easy to construct, and it can be used to transform a wide range of impedances. The disadvantages are that it is only useful over a narrow bandwidth and that a transmission line of proper characteristic impedance may not be available.

The narrow bandwidth of the match is the result of the requirement that the matching section be one quarter wavelength long. As we move the operating frequency away from the design frequency, the electrical length of the line changes and the matching section is no longer the proper length.

Transmission lines are commercially available in a limited number of characteristic impedances: 50, 75, 95, 135, 300, and 450 ohms. If a different impedance is required for the matching section, the matching section must hand made. Depending on the impedance required, it may not be possible to construct a line with the proper impedance.

LC NETWORK MATCH

The LC network match consists of a network of capacitors and inductors that are used to transform the antenna impedance into the feed line impedance. There are three types of LC matching networks in wide use:

L-network

T-network

p-network The advantages of this type of matching are that any two values of impedance may be matched and there are formulas available that permit computation of all component values necessary to achieve a match. The major disadvantage is that the network is will only match the impedances over a relatively narrow bandwidth.

We will examine only the equations for the L-Match because the mathematics for the other two networks is considerably more complicated. Consider the diagram below. It shows an L-network that is matching two purely resistive impedances, Rp and Rs. The two circuit elements, Xp and Xs may be either capacitors or inductors at the discretion of the circuit designer, but if one, say Xp is chosen to be inductive, the other should be capacitive. Here is an example of L-network design:

We wish to match an antenna whose impedance is 250 ohms to a 50 ohm coaxial cable. The first step is to compute the network Q: Next we compute the series and parallel reactances, Xs and Xp: Now we are finished. Depending on which component is chosen to be a capacitor, there are two possible matching networks: Both networks will make the required match. Normally, the network that yields the smallest component values is chosen. To see how this works, let us make the operating frequency for this network 2.4 MHz. We can then use the formulas for capacitive and inductive reactance to determine the component values. If you do not remember the formulas for converting between reactance and component values, click here to return to Module A for a review.

For the network with the series inductance: For the network with the parallel inductance: In this case, the network with the parallel inductance has the smaller component values, so it would be the best choice in most circumstances.

It is possible to combine L, T or p networks together to make matching networks with almost any desired band pass response and input and output impedance. The analysis of these networks is quite complex and will not be covered in this course.

TRANSFORMER MATCHING

Transformer matching uses a specially designed RF transformer to match the antenna to the transmission line.. Its chief advantage is that it is a broadband matching device. Its chief disadvantage is that it does not work well with extremely large impedances ( > 600 ohms) The RF transformer works very much like its low frequency counterpart. The relationship between the number of turns in each winding and the impedance ratio is given by: Because they work over a wide frequency range, RF transformers are often used for impedance matching. The turns may be wound over a hollow core or may be wound onto a toroid made from powdered iron or a ferrite.