Impedance-matching Techniques

Author: Edmund A. Laport

There are circumstances where a transmission line need not be terminated in its characteristic impedance. In such cases, the feeder, according to its length and characteristic impedance, transforms the load impedance to some different (and usually complex) value at the input terminals of the feeder. This input impedance can then be transformed by a coupling network to a value that will be accommodated by the connected equipment. When mismatched operation can be used, it is an extravagance and occasionally an operating inconvenience to use matched-impedance techniques.

Mismatched feeders may be employed when the feeder is electrically very short, say 10 degrees or less. With certain precautions, mismatched feeders may be desirable for feeding two identical loads with identical cophased currents, and where coupling networks would introduce the risk of dissymmetry of coupling-circuit adjustments. There are also occasional cases where half-wave and quarter-wave feeders may be used exactly as in very-high-frequency and ultrahigh-frequency techniques where a whole system may be mismatched except in a common input circuit. The admissibility of such practices depends upon the bandwidth to be transmitted, the magnitudes of mismatch at various points in the system, the magnitudes of potential and current at various points, the losses encountered, and the effect on cost, operating adjustments, and system stability.

Losses in feeders increase with the degree of mismatch, as shown in Fig. 4.1. Since loss is proportional to the feeder length, impedance matching on long feeders is used to obtain optimum efficiency.

For a given design of feeder, the losses also increase with frequency, and for this reason it is almost universal practice in the high-frequency band to use impedance matching.

There are several methods in use for impedance matching, the choice depending upon the circumstances. The commonest ones are:

1. To design the load and the feeder to have equal impedances so as to be self-matching.

2. To use coupling networks of lumped reactances.

3. To use tapped transmission lines beyond a short circuit.

4. To use a series section of transmission line of proper length and characteristic impedance as an impedance-matching transformer.

5. To use a stub section of line as a reactance in parallel with the feeder at a properly chosen point to make the impedance at this point equal to its characteristic impedance. Either open-circuited or short-circuited stubs may be used.

6. To use a lumped reactance of proper sign and value in place of the stub line and electrically equivalent to it.

7. To use a coupled section of line in parallel with the feeder and of proper length to reflect the correct amount of reactance into the main feeder at the correct point to effect an impedance match.

8. To use a tapered transmission line as an impedance-matching transformer.

The relative desirability of any of these methods depends upon many factors, among which are economics, potentials, currents, frequency, degree of initial mismatch, the amount of electrical and mechanical engineering involved in solving the problem, the available facilities for measurement and construction, the configuration of the feeder cross section and whether balanced or unbalanced, the available space, the ease of adjustment or switching to other working frequencies, the bandwidth to be transmitted (whether transmitting or receiving), the conditions of weather or other exposure to damage, etc. A method preferred for one application may be absurd in another. The choice is therefore made after an appraisal of the prevailing conditions.