# The system wide conjugate match stuff crashes out again

Walt Maxwell (W2DU) made much of conjugate matching in antenna systems, he wrote of his volume in the preface to (Maxwell 2001 24.5):

It explains in great detail how the antenna tuner at the input terminals of the feed line provides a conjugate match at the antenna terminals, and tunes a non-resonant antenna to resonance while also providing an impedance match for the output of the transceiver.

Walt Maxwell made much of conjugate matching, and wrote often of it as though at some optimal adjustment of an ATU there was a system wide state of conjugate match conferred, that at each and every point in an antenna system the impedance looking towards the source was the conjugate of the impedance looking towards the load.

This was recently cited in a discussion about techniques to measure high impedances with a VNA:

WHEN the L and C's of the tuner are set to produce a high performance return loss as measured by the vna, then in essence, if the tuner were terminated (where the vna was positioned) with 50 ohms and we were to look into the TUNER where the antenna was connected, we would see the ANTENNA Z CONJUGATE. Wow, that's a mouth full. The best was to see this is to do an example problem and a simulator like LT Spice is a nice tool to learn. Or there are other SMITH GRAPHIC programs that are quite helpful to assist in this process. Standby and I will see what I can assemble.

The example subsequently described set about demonstrating the effect. The example characterised a certain antenna as having an equivalent circuit of 500Ω resistance in series with 4.19µH of inductance and 120pF of capacitance (@ 7.1MHz, Z=500-j0.119, not quite resonant, but very close). A lossless L network (where do you get them?) was then found that gave a near perfect match to 50+j0Ω. The proposition is that if you now look into the L network from the load end, that you see the complex conjugate of the antenna, Z=500+j0.119.

I asked where do you get a lossless L network? Only in the imagination, they are not a thing of the real world.

So lets replicate the scenario matched with an L network where the inductor has a Q of 100, no other loss elements. (Quality real capacitor losses are very small, and the behavior will not change much, the inductor loss dominates.)

Above is a model in Simsmith where I have adjusted the lossy L network for a near perfect match. I have used a facility in Simsmith to calculate the impedance looking back from L1, often known as the source impedance at a node but in Simsmith speak the calculated L1_revZ on the form, (ie back into the L network)  from the equivalent load.

The impedance looking back is 471.3-j0.1274Ω. The resistance element is quite different to the proposed 500Ω. The L network in this scenario lacks reciprocity.

Although the L network is conjugate matched at its input, it is not conjugate matched at its output.

This example is yet another that disproves Walt Maxwell's simultaneous system wide conjugate matching nonsense.

None of this should be taken to suggest that when an ATU or other matching network is adjusted for an input VSWR50 that it is conjugate matched to the source, much less that a typical ham transmitter is well represented by a Thevenin equivalent circuit or that the Jacobi Maximum Power Transfer Theorem applies.

## References

Duffy, O. Mar 2013. The failure of lossless line analysis in the real world. https://owenduffy.net/transmissionline/folla/index.htm.
• Everitt, W L. 1937 Communications Engineering, 2nd ed. New York: McGraw-Hill Book Co.
• Everitt, W L, and Anner, G E. 1956 Communications Engineering, 3rd ed. New York: McGraw-Hill Book Co.
• Maxwell, Walter M. 2001. Reflections II. Sacramento: Worldradio books.