Transmitter Impedance

There is a misunderstanding among some Radio Amateurs that a transmitter is matched to its load, ie that the impedance looking into the transmitter output socket is 50Ω (This subject was touched upon in a previous article when observing that the power reflected by a mis-matched aerial was not necessarily absorbed by the transmitter; (see Standing Waves Part 2, Section on Multiple Reflections). In any case, why would you expect a transmitter to be matched to its load? After all, a nuclear power station is not matched to your 60 Watt bulb. It is not even matched to all the 60W bulbs, storage heaters, electric cookers etc in the domestic environment all connected in parallel. If it were so matched, only half the output power of the power station would be delivered to the whole load. The other half would be dissipated in the power station generator. The same principles apply to a radio transmitter, where a compromise must be made between maximising the output power and working at a reasonable efficiency with a reasonable internal heat dissipation.

However, there is a difference between the way a power station generates its 50Hz sine wave output and the way in which a radio transmitter generates its MHz sine waves. Whereas the alternator in a power station could, in principle, be 100% efficient if its windings were cooled superconductors, (giving the alternator zero internal resistance), a radio transmitter generates its output be varying the resistance in the path of a direct current through its power amplifier. Ie, to generate sine waves its output valves or transistors act as “variable efficiency modulators” of the DC supply. For CW transmission, where the output stages work “flat out”, something akin to 100% efficiency could be achieved by driving the power amplifier between fully conducting and fully cut off. This would result in square waves which could be “cleaning up” by using low pass filters between the PA and the aerial. However, driving the PA with variable width pulses in order to vary the output for those modes requiring the RF output power to be continuously variable, such as AM, SSB, PSK31, etc. presents considerable practical difficulties at high frequencies.

The following discussion revues the consequences of choosing a compromise between obtaining maximum power output and an acceptable efficiency. (Efficiency is here defined as the RF power output in Watts divided by DC input power in Watts). In this discussion a number of simplifying assumptions are made, the most important of which is:- any filter and/or impedance converting transformer between the power amplifier and the output socket of the transmitter takes care of the reactive components of the circuitry. This implies that the impedance looking into the output socket of the transmitter looks purely resistive. In general, this resistance will vary depending on the instantaneous carrier level, but it will be assumed that the design is optimised for maximum power, (which in the example below will be assumed to be 100Watts). Lesser power levels, from whatever cause, will be assumed to look after themselves in a linear manner with respect to the drive level. Such causes of lesser power levels arise from amplitude modulation inherent in such modes as SSB, PSK31 etc.

Transmitter Design
In designing a transmitter, the output impedance, (in our simplified model the internal resistance of the PA), is a compromise between the maximum possible power output which could be obtained from the circuit and components, and an acceptable efficiency. If, for example, the output impedance of the transmitter were made equal to the line impedance, the maximum efficiency, (in CW or RTTY modes or on SSB peaks), would be only 50% and half the DC input power to the PA would be dissipated in it. An efficiency of 50% is usually considered too low, and an efficiency nearer 75% is considered more acceptable. In our simplified model of a 100Watt transmitter with an efficiency of 75%, the PA acts as a “Voltage source” of 94.3 Volts (RMS) with an internal impedance of 16 2/3 Ω which drives RF power into a 50Ω load or transmission line. In practice, modern solid state transmitters are equipped with devices which monitor the outgoing and the reflected power to and from the 50Ω output socket. If either of these exceeds some internally set safety level, ‘an automatic level control’ is operated reducing the drive level and hence the output power to a safe level. However, in our simplified model, no such protection devices are assumed. With all these assumptions, the simple model of the generator with internal resistance, Ri, (equal to 16 2/3Ω), and load resistance RL, (equal to 50Ω) has the equivalent circuit shown in figure 1. Assuming the transmitter output impedance is purely resistive, the returning wave reflected by the aerial sees this rather low impedance of 16 2/3 Ω and therefore sees an SWR of 3:1. Assuming this design, what are the consequences in output power, internal dissipation and efficiency of changing the load impedance? These are illustrated in figure 2 for a typical 100Watt transmitter.

It can be seen that with a load impedance of 50Ω the output power is 100Watts, at an efficiency of 75%, and the power wasted, (or dissipated), in the PA is 33.3Watts, ie the intended design. However, more power could be squeezed out of this design, (although not safely), by lowering the load resistance. In the extreme, 133Watts could be output, but at an efficiency of only 50%, implying that another 133Watts would be dissipated in the PA. This represents the “matched condition”, where the output load is made equal to the internal resistance of the PA. Further reduction of the load resistance causes a reduction in output power but a huge increase in internal dissipation up to a maximum of 533.3Watts for a short circuit across the output socket corresponding to a zero Ohms load. Of course, in practice, the transistors in the PA would have melted or fused long before this, hence the need for protection circuitry.

People don’t normally put a short circuit on the output of their transmitters, but remember, an open circuit a quarter of a wavelength away has the same effect as a short circuit on the output. Also, you never know what the equivalent length of the Low Pass Filter and protection circuitry is between the PA and the output socket, so don’t even allow the output to be open circuited when the transmitter is running.


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