# Impedance matching

We have all been taught that the load impedance must match the generator impedance in the case of non-DC voltages in order to obtain the most efficient transfer of power.

In DC work it seems that loads with an improper resistance fail to work because the supply voltage is too low, or else burn out because their resistance is too low for the applied voltage, and simple Ohm's law applies.

Figure 1. Two variations of an L network. Version A has a higher input impedance than the output. Version B has a higher output impedance than the input.

In RF work, the impedance of the load must match the generator impedance, otherwise standing waves develop, which can waste power, cause transmission line burnout, damage the generator, result in spurious radiation, damage matching components and ruin audio quality.

The problem is caused by the imaginary term in the expression for impedance:

Z = SQUARE ROOT OF (R2 + (XL - XC))2

Where Z = impedance

XL =inductive reactance

XC =capacitative reactance

Fortunately, AM and FM transmission systems have standardized on transmission line impedances of 50Ω, and it is only rarely that we encounter transmission line of a different value, regardless of whether the line is ¼ inch or 8 inches in diameter.

Figure 2. The T network provides a larger transformation than an L network.

It has been found that 50Ω provides a convenient impedance to keep line voltages and currents within reasonable limits. Higher line impedance results in higher operating voltage and lower line current, and lower impedance results in the opposite effect.

Load matching

Engineers sometimes lose sight of the fact that the networks we use to feed antennas are really transformers, although they do not have separate primary and secondary windings. Nevertheless, there are four terminal transmission networks even though one input and output terminal is grounded. We are transforming the impedance of the antenna to match that of the transmitter output circuit.

A network is tuned to a specific frequency and requires readjustment if the operating frequency is changed. It also has a distinct advantage in that it provides a simple transformation from a complex impedance to a purely resistive load. Although a transformer can work over a wider bandwidth in audio, it is very difficult to operate over a wide RF bandwidth.

When properly tuned, the network will present a load of 50Ω resistance with zero reactance, i.e. Z=50±j0, to the transmitter.

The simplest form of network is the L network shown in Figure 1. Notice the different signal flows.

These networks will work in either direction and transform inversely, provided the frequency is kept the same.

It is important to note several points. In both figures the output voltage will lag. The amount of phase shift is determined by the angle of impedance produced by the combination of load and reactance element closest to the output terminal. The transformation ratio is determined by the same components. This leads us to the conclusion that the phase shift and transformation ratio are not independent of each other.

This feature makes L networks suitable only for simple antenna matching requirements. Therefore, we have to look to the TEE network to provide independent phase and ratio values.

The TEE network in Figure 2, found in most phasors, is a useful and interesting network. Some foreign broadcast systems take advantage of transmission line length to obtain the desired phase shift, which is not allowed by the FCC. Such methods do not provide any control of phase shift, although they do work after a fashion.

Figure 3. A Pi network provides independent variation of phase shift and transformation ratio through the circuit.

In the case of a simple non-DA radiator, we are not usually concerned with the amount of phase shift in the network, so an L generally suffices. For a DA where all elements in the feeder system contribute to the achievement of the desired phase shifts, it is essential to use a TEE network.

Engineers need to be able to specify phase shift independently of the transformation ratio. This cannot be done in an L network. Theoretically, a TEE network can have any ratio from zero to infinity and a phase shift from zero to ±180 degrees. However, operational considerations limit this range. The TEE is noted for its easily obtained 90° phase shift and reasonable range.

The TEE may be considered as two L networks connected together with a common shunt leg, which has a higher impedance than either end. The overall phase shift is the total of the phase shifts of the two L networks. It also has good harmonic rejection.

When building an ATU, the total output leg reactance is that of the leg plus or minus the antenna reactance, which must be considered in the network circuit.

A combination of L and C is often found in the shunt, input and output legs of a TEE network. This has no circuit significance, but it is an easy way to obtain a desired capacitative (negative) reactance that has a non-standard value.

Coil taps are adjusted until the desired negative reactance is obtained. This is not the ideal method of obtaining the required reactance — it can effect signal quality. The preferred way is to use a variable vacuum capacitor.

In this discussion we have considered all components to be lumped, that is, as discrete units. Coils have capacitance that varies from turn to turn. Often this will antiresonate the coil at some odd frequency. Capacitors also have inductance associated with their leads, which can produce series resonance at some frequencies and cause capacitors to act like inductors at odd frequencies.

It used to be easy to obtain vacuum capacitors on the surplus market, but the supply seems to have dried up in recent years. However, in critical cases the extra expense is worthwhile.

The PI network is a natural follow on to the TEE and is shown in Figure 3. It resembles two L networks connected with a series reactor in lieu of a central shunt leg. The PI network is more commonly used in transmitter output circuits and is not often found in ATUs.

A point of interest while discussing transformation devices is that the familiar transmission line can transform impedances in a limited fashion. At low frequencies this effect is not normally perceived, but as frequency increases so that the line length is an appreciable part of a wavelength or more, we find that impedance transformation occurrs in the same way a TEE or similar network would work.

The line becomes a distributed, instead of a lumped, constant network. The voltage at the receiving end can be higher or lower than the sending end; this is not caused by I2R losses. Calculations of this nature call for calculus and differential equations, so we'll leave the subject purely as matter of interest because it currently has no general application in AM work.

E-mail John at batcom@bright.net.

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