# Is Zs of a HF ham tx typically 50+j0?

It is often assumed that a ham transmitters designed for a nominal 50+j0Ω load can be accurately represented generally by a Thevenin equivalent circuit with a source impedance of 50+j0Ω. This assumption may then be used for instance to infer the reduction in power delivered to an antenna of certain VSWR using the concept of Mismatch Loss.

Thevenin’s theorem for linear networks states that any combination of voltage sources, current sources and resistors with two terminals can be represented by an electrically equivalent circuit of a single voltage source Vs and a single series resistance Rs. In the frequency domain, the theorem can also be applied to impedance, not just resistance. A Thevenin equivalent circuit can be used to determine how much power would be developed in a load of any given impedance.

An interesting property of a Thevenin source (constant Vs and with Zs=50+j0Ω) is that the ‘forward power’ indicated by a quality directional wattmeter calibrated for 50+j0Ω will be independent of load impedance.

The following shows that Vf=Vs/2, ie Vf is independent of Zl, and therefore ‘forward power’ (Vf2/Z0) is independent of Zl. The proof starts by calculating the voltage V at the terminals of load Zl where Vs is the Thevenin equivalent source voltage and the Thevenin equivalent source impedance (Zs) in matched system is taken to be Z0 , Γ is the complex reflection coefficient due to Zl. (Hint: to simplify the second last expression, multiply top and bottom of the right hand expression by Zl+Z0.)

A simple and easily performed test for practical hams therefore is to connect a transmitter via a directional wattmeter to an ATU and dummy load. If one can vary the ATU settings to vary the load impedance seen by the transmitter within VSWR(50) limits of say 1.5:1, the indicated ‘forward power’ should not vary. (If you swing the load VSWR too far, you may trigger some further non-linear effects like VSWR protection, power control, voltage or current saturation of the PA, which are further reasons why the assumed Zs may be invalid.)

Try the experiment at different frequencies, different power levels, you are likely to find that the results are frequency dependent and power level dependent.

Of course, nothing is perfect so an acceptable tolerance for depending on the assumed Zs=50+j0Ω for Mismatch Loss calculations might be that ‘forward power’ doesn’t vary by more than 10% of the ‘reflected power’ at any point. The worst case ‘reflected power’ for the experiment as described is 4%, so a variation of ‘forward power’ by more than 0.4% (ie 0.4W in 100W) at any point would indicate significant error in any Mismatch calculations based on an assumed Zs=50+j0Ω.

Now, it is very hard to discern such a small variation in ‘forward power’, but for most transmitters that I have ever tested, the variation is more like 5% and readily seen on a meter.

If you perform this test on a range of transmitters, at a range of frequencies, you will probably be convinced that whilst it is possible that Zs=50+j0Ω, it is not always, or even often the case, and that calculations such as Mismatch Loss that depend on that assumption are in error.

# Changes

 Version Date Description 1.01 20/06/2010 Initial. 1.02 1.03