After reading a number of articles by the late Walter Maxwell W2DU ARRL technical adviser, I was prompted to carry out some of my own experiments with mismatched loads.
I carried out a couple of similar experiments that Walter described in chapter 19A of his book “Reflections”.
My experiments were not as comprehensive as those that Walter described, however sufficient to convince me that his results were valid. The purpose of the experiments was to determine if all the reflected power from a mismatched load was necessarily lost. Many amateurs have the belief that reflected power is subtracted from the forward power to establish the radiated power.
Using a TS-830S Valve output transceiver as the RF source with the Pi output tuning and loading controls adjusted to deliver all of the available power into a 50 ohm dummy load. The measured impedance using an AUTEK RX vector analyst was found to be 50 +J0 ohms. Grid drive was adjusted to give 40 watts as indicated on a Bird 43 wattmeter with zero watts reflected.. I also had a 2.5 amp RF ammeter in circuit to measure the RF current into the load. With the 40 watts indicated on the wattmeter the RF ammeter indicated 0.9 amps P=I^2 R giving a power of 40.5 watts close enough to the 40 watts indicated by the Bird wattmeter.
Leaving the tuning and loading controls undisturbed the transceiver was powered down . As my Autek analyser will not measure impedances above 1000 ohms I had to resort to measuring the impedance using my HP 8405A vector voltmeter and a return loss bridge. The impedance was approximately 1400 ohms. I then connected a 1400 ohm non inductive resistor to the input of the Pi network and then measured the impedance looking back into the output of the network , (the antenna terminal of the transceiver). The impedance measured with the Autek analyzer was 52 ohms. Very close to the expected 50 ohms. Now comes the interesting part the dummy load was replaced with two 50 ohm terminations and a 100 ohm wire wound resistor in parallel. The measured impedance at the end of a short piece of coax was 21 +J5 ohms. The Autek analyst measured this as an SWR of 2.38:1.
The transmitter was powered up again and the plate and loading controls readjusted for maximum output poweras indicated on both the wattmeter and the RF ammeter. The ammeter now read 1.6 amps a quick calculation of power using P=I^2R into 21 ohm load was 53.76 watts the Bird wattmeter now read 54 watts forward power with reflected power of 14 watts. The plate voltage and current readings on the TS 830S were identical to those when the 50 ohm termination was used after the adjustment of the tuning and loading controls were adjusted for the mismatched load.
I again powered down the transceiver and placed the 1400 ohm resistor at the input of the Pi network. At first attempt I recorded a reading of 24 -j4 Ohms with repeat attempts I recorded a spread from 20 -j7 to 24 -j4. Using the wattmeter or the ammeter to indicate the peak in output was not accurate enough, I resorted to measuring the voltage across the termination with a HP 410C RF voltmeter and this resulted in being able to more accurately determine the peak when tuning the controls. The measured impedance was now measured to be 21 -J5 ohms the conjugate of the load impedance.
This is where we should look at the maximum power transfer theorem I shall quote Everitt (1)
The maximum power will be absorbed by one network from another joined to it at two terminals when the impedance of the receiving network is varied , if the impedances looking into the two networks are conjugates of each other.
Or put more simply if the delivery of power decreases when the receiving impedance is increased or decreased we have a conjugate match.
So what should be concluded from the above experiment? The forward power of 54 watts is actually the initial forward power of 40 watts plus the re reflected power of 14 watts. We are not getting something for nothing ; we are just adding the power that was reflected back to the incident wave.
The adjustment of the plate tuning and loading controls has matched the resistive part of the load and cancelled the reactance causing total re- reflection of the reverse power back down the line to the load. It has been a common misconception that a valve amplifier with an SWR such as this will get a little hot in the face but handle the mismatch.. however as can be seen from above the plate current and voltage readings are the same for both matched and mismatched condition. The output tubes are totally unaware of any mismatch due to the readjustment of the pi network.
The Pi network in the TS 830S has no trouble matching the 2.38:1 SWR. So within the constraints of the values used in the Pi network a large range of impedances can be accommodated. None of the reverse power returned to be dissipated in the tuning network or in the output tubes and all of the power returned to the load.
So where is the catch? If the transmission line has no loss, all of the power will be radiated regardless of the SWR , however if the power has to make return trips up and down a lossy line then there can be very significant loss.
Solid state transceivers don’t have the luxury of a Pi network output , an antenna tuner can do exactly the same job for your solid state rig and provide the conjugate match. The bottom line.. with reasonable lengths of good quality coax an SWR of 3:1 will in most cases for HF not be an issue.
Take yet another look at the graph from the ARRL handbook to see what will be additional loss due to the SWR .
Click on image to enlarge
1. The ARRL Antenna Book 19th edition pages 25-6
2. Everitt Communication Engineering 2nd edition McGraw Hill
3. Walter Maxwell Another look at Reflections