Antenna Feeder Systems and Impedance-Matching Networks

Mismatched, or Resonant, Feeders. Assume, for the moment, that a 500-ohm open-wire line is to drive a horizontal half-wave antenna at the center where the input impedance is approximately 73 ohms. If the line is directly connected to the antenna it will be mismatched and standing waves will exist on the line. At the transmitter the impedance of the line (with the antenna connected) must be matched to the output circuit of the transmitter so that power will flow into line and antenna. The input impedance of the line terminated with the antenna will depend on the frequency, physical length of the line, characteristic impedance of the line, and the impedance of the antenna. Two common coupling circuits are shown in Fig. 5. These impedance-transforming circuits can be designed in accordance with the theory in Chapter 3. There are advantages to operating with a mismatch at the antenna. If a radio system operates at several frequencies that are changed frequently and if the line is mismatched at the antenna, then adjustments can be made at the transmitter and no changes need be made in antenna matching networks. On the other hand, radiation from the feeders is slightly greater, and the overall efficiency is lower; furthermore, the voltage is higher at certain points on the feeder, but usually this causes no insulation problems.

Figure 5. Circuits sometimes used in connecting mismatched, or resonant, antenna feeders to the output circuit of a radio transmitter, so that the output power amplifier will be loaded correctly and power will flow from the transmitter to the feeder.

Matched, or Non-resonant, Feeders. If a radio transmission system is to operate at one frequency and maximum performance is desired, then an impedance transforming, or matching, network is often placed between the antenna and the feeder, and between the feeder and the transmitter.

The so-called delta-matching transformer of Fig. 6 (a) is commonly used for connecting a half-wave antenna to a balanced transmission line. The dimensions

are used.⁶ The values of E and C are in feet, f is in megacycles, and the constants apply for a 600-ohm feeder line composed of two No. 12 A.W.G. copper wires 6 inches apart. The theory of this matching arrangement can be explained by referring to Fig. 6(b). If a half-wave antenna is "folded" into a quarter-wave line (to illustrate the theory), the current and voltage distribution will be as indicated. By moving the point of contact of the transmission line along the folded antenna, various ratios of voltage to current, and hence various impedances, are available. This partly explains the "C" portion of Fig. 6(a). The other factor is that the "E" portion approximates an exponential transmission line (page 229) which has impedance-transforming properties.

Figure 6. In (a) is shown a method of matching the impedance of a half-wave antenna to an open-wire transmission line. The dotted lines between the wires of the transmission line, or feeder, represent the positions of ceramic insulating spreaders. In (b) is shown a sketch indicating how different impedances are obtained by connecting at different points.

What is known as stub matching is often used to match an antenna to a transmission line, particularly at very high and ultrahigh frequencies.⁷ There are several ways of accomplishing this, one of which is shown in Fig. 7. The impedance of the stub is in parallel with the impedance of the feeder and antenna to the right of the stub. Such a combination w^rill have impedance-transforming properties,⁸ and, by the proper length and location of the stub, an impedance match is obtained, and no standing waves will exist on the feeder between the stub and the transmitter. The location and the length of the stub can be found from Fig. 8. The standing-wave ratio indicated on Fig. 8 is the ratio of voltage maximums to voltage minimums, or current maximums to current mini-mums, before the stub is attached. These can be measured in several ways, simple methods being as follows: For measuring voltage ratios, attach a low-impedance thermomilliammeter to the end of a quarter-wave section of transmission line.

Figure 7. A stub is often used to match an antenna to a transmission line, or feeder, so that standing waves do not exist between the stub and the transmitter.

The input impedance of this combination will be very high, and it can be moved along the line as a voltmeter, the indications of the thermomilliammeter being an indication of the voltages along the line. For measuring current ratios, attach two short sturdy wire hooks directly to the thermomilliammeter so that it can be hung from one wire. As the thermomil-liammeter is moved along the wire, the indication will be a measure of the current in the wire. The instrument used should read effective values, or the readings must be corrected.

Figure 8. Curves for determining the length and the location of stubs for matching an antenna to a transmission line, or feeder. The distant end of the stub may be open or shorted. The "location" curve gives the location on the line from a voltage maximum toward the transmitter if a shorted stub is used, and from a voltage maximum toward the antenna if an open stub is used. The two other curves give the proper stub length, all dimensions being in terms of the wavelength, λ. The characteristic impedance of the stub is assumed to equal that of the line.

What is known as a reentrant network⁹ is also used for impedance matching. With this arrangement a short loop of wire extends as a loop from one point on each feeder wire to another point on the same feeder wire.

Figure 9. Two large wires or tubes placed close together can be used to match an antenna to a transmission line, or feeder.

Another matching device is the quarter-wave matching section of Fig. 9. Note that the two large wires or tubes are exactly λ/4 in length. This is because the input impedance of a half-wave antenna (with which this system is used) is 73-ohms resistance, and the characteristic impedance of radio-frequency transmission-line feeders also is pure resistance. The characteristic impedance Z_0S of the quarter-wave matching section to be used is¹⁰

where Z_OL is the characteristic impedance of the transmission line and Z_A is the driving-point, or input, antenna impedance; all values being in ohms. The size and spacing of the conductors for the quarter-wave matching section can be determined as explained in Chapter 6.

Two circuits for connecting matched or non-resonant transmission-line feeders to a radio transmitter are shown in Fig. 10. These can be designed in accordance with discussions in Chapter 3.

Figure 10. Networks for connecting matched, or non-resonant, lines to radio transmitters.

For coaxial cables feeding broadcast antennas the two impedance-matching circuits of Fig. 11 are used. In (a), the antenna is an ungrounded vertical tower with a base insulator and a ground system composed of buried radial wires. This matching circuit can be designed as explained in Chapter 3. In (b), the antenna is a grounded vertical tower, the ground being buried radial wires as before. This impedance-matching circuit, and in fact the entire arrangement, will be recognized as one half of the circuit of Fig. 6. In the final adjustments a radio-frequency impedance bridge, instead of the coaxial cable, is connected to the end of the sloping feed wire, and the wire is moved up and down the tower until a resistance value equal to the characteristic impedance of the coaxial (usually 77 or 52 ohms) is found. Ordinarily, some inductive reactance is also measured, and this is neutralized with the capacitor of Fig. 11(b). At the transmitter, the coaxial cable would be connected to the last power output stage through an impedance-matching network such that the power output tube (or tubes) operates into the proper load impedance. In broadcast installations, phase-shifting networks¹¹ are used at the transmitter if directional antennas are employed. These networks produce the proper current ratios and phase shifts to give the desired directional patterns (page 473).

Figure 11. Methods of connecting coaxial cables to radio-broadcast antennas. Diagram (a) is for a base-insulated antenna, and (b) is for a grounded antenna.