Driving-Point Impedance of Periodic Antennas

The reason that the input impedance varies is evident from Fig. 12. From the theory of standing (stationary) waves, the input currents that voltages of different frequencies will produce will vary in both magnitude and phase, and hence the input, or driving-point, impedance will vary.

It is possible to predict the input impedance of antennas of various types from theoretical consideration,^3,44 but in practice, if the impedance must be known, bridge measurements are usually made on the actual antenna. As will be seen in the chapter that follows, the reactive component of the driving-point impedance is either ignored or canceled out with opposite reactance at the point where the antenna is driven.

Of interest is the antenna resistance, defined³⁴ as "the quotient of the power supplied to the entire antenna circuit by the square of the effective antenna current referred to a specified point." Antenna resistance includes³⁴ radiation resistance, ground resistance, radio frequency resistance of conductors in the antenna circuit, equivalent resistance due to corona, eddy currents, insulator leakage, and dielectric power loss.

In antenna design, of much importance is the radiation resistance, defined³⁴ as "the quotient of the power radiated by an antenna by the square of the effective antenna current referred to a specified point."

The radiation efficiency can be determined if the antenna resistance and radiation resistance are known. Radiation efficiency is defined³⁴ as "the ratio of the power radiated to the total power supplied to the antenna at a given frequency."

The theoretical radiation resistance of a half-wave antenna in free space and driven at center is 73 ohms. The radiation resistance of the horizontal half-wave antenna is affected by its position above the earth as indicated in Fig. 28.

Figure 28. The radiation resistance of a half-wave antenna in free space is about 73 ohms. When near the earth, the radiation resistance varies as indicated because of reflection.

The input impedance of a typical vertical antenna for amplitude-modulation broadcast service is shown in Fig. 29. This antenna has zero reactance and hence is said to be resonant at frequencies of 0.685, 1.070, and 1.715 megacycles. At 0,685 megacycles the resistance is about

Figure 29. Variations of driving-point input impedance for a vertical amplitude-modulation broadcast antenna. The tower is 350 feet high. The height of the mounting base arid base insulators is 14 feet. The antenna ground system consists of buried conductors extending radially. Impedance measurements made between tower and ground system. (Courtesy General Radio Co. and Radio Station WEEI.)

35 ohms. This is the natural frequency, defined³⁴ as the "lowest resonant frequency obtained without added inductance or capacitance."' At 0.685 megacycles, the antenna functions as a grounded quarter-wave antenna with voltage and current distribution as shown in Fig. 30(a). At 1.070 megacycles, the driving point input impedance is 310 ohms resistance, the antenna is operating in resonance as a half-wave antenna fed at the end, and the voltage and current distribution are as shown in Fig. 30(b). At 1.715 megacycles the antenna of Fig. 29 is resonant, operation is as a three-quarter wave antenna, and the impedance is 20 ohms resistance. The voltage and current are distributed as in Fig. 30(c). An antenna does not have to be driven at a resonant frequency; however, the frequency at which it is driven affects the shape of the radiation pattern.

Figure 30. Voltage and current distributions for a vertical antenna when driven at various frequencies so that it functions (a) as a quarter-wave antenna, (b) as a half-wave antenna, and (c) as a three-quarter wave antenna.