# Calculation of Bandwidth

Author: Edmund A. Laport

The resistance and reactance curves of Figs. 2.15 and 2.16 can be used to compute bandwidth. It will be noted that the ratio G/D has a major influence on the reactance as the value of G changes with frequency.

To illustrate the prediction of antenna response, we shall consider a practical problem of computing the response of a 60-degree vertical radiator at 550 kilocycles to side frequencies of +10 and - 10 kilocycles. This radiator is 300 feet high and has a uniform triangular cross section with 5.2 feet per side. The periphery of this radiator is 15.6 feet, which we assume to be equivalent to a cylindrical section with the same periphery and thus having a diameter of 5 feet. Then the ratio of height to diameter G/D - 60. By plotting out the readable data for resistance and reactance from Figs. 2.15 and 2.16 so as to interpolate for small increments of G in the vicinity of G = 60 degrees and G/D = 60, we obtain the following information:

Variation of reactance - 6.8 ohms per degree change in G

Variation of G with frequency - 1.2 degrees per 10 kilocycles

At 550 kilocycles Z α = 9.8 - j118

At 540 kilocycles Z α = 9.2 - j126

At 560 kilocycles Z α = 10.4 - j110

If all reactance is tuned out at 550 kilocycles with an inductor of reactance j118, then at the two opposite side frequencies we find:

 Frequency (kilocycles) R X φ (degrees) Decibels 540 9.2 -j8 41.7 -2.52 550 9.8 0 0 0 560 10.4 +j8 40.5 -2.36

It is evident from this that the high-frequency-modulation response of a transmitter working into this particular antenna would be limited by the intrinsic bandwidth of the antenna. A further limitation may be imposed by the antenna coupling networks.

One should avoid drawing general conclusions from this single example, except possibly that the response characteristics of a radiator have to be studied whenever the reactance of an antenna is high and its resistance low and whenever the transmission bandwidth is more than 1 percent.

The response can be easily computed from measurements that have been made on a radiator already constructed. If it is found that the bandwidth of the antenna is inadequate for the quality of emission desired, the effective diameter of the radiator can usually be increased by means of vertical wires hung from an outrigger at the top or by booms attached to the tower a short distance from the top. The requisite number of wires and their distance from the tower to obtain the desired bandwidth can then be determined experimentally.

A suspended wire antenna has smaller intrinsic bandwidth because of its small diameter. To increase the bandwidth of a wire antenna, the system can be constructed as a large cage or several wires can be connected in parallel or as a fan in a common plane with considerable separation of the wires.

In the case of a directive array, the bandwidth of the complete radiator feeder system can be computed if one has the patience to undertake the labor involved. In some cases the effort is not justified. One should watch for the situation where mutual impedances may reduce the input resistance of one radiator to a very low value, with the reactance remaining high. The bandwidth of the one radiator can then be computed, using the expected values of resistance and reactance when the system is operating properly. If intolerable selectivity is found, other alternatives of design may have to be adopted, including, in some cases, a different kind of array configuration.

The response of a finished directive array can be determined by measuring the impedances at the common input to the system at the frequency limits of the desired transmission band and computing the response therefrom. The procedure is the same as that for a single elementary circuit.

Last Update: 2011-03-19