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The SWR meter does not compare what it sees on it's input against it's output connector. It compares the ratio between the incident wave and reflected wave. About the only change you'll see if the output impedance of the device in front of the meter was off would be a reduction in the power transfer efficiency. Both on forward and reflected power. Maximum power transfer occurs when transmitter, coax, and antenna are at 50 ohms.


On the other hand I can see your point if the antenna system were generating reflected power. Then the output impedance of the amp may play some bearing on the true accuracy of the SWR reading because it's the load for reflected power. But that accuracy is compromised because of reflected power generated from the antenna system. It's not created by output impedance mismatch in the amp.


If the output transformer in the solid state amp is not converting the transistor collector impedance to the 50 ohm output, you could say there is a mismatch between these components but this in no way will show as a higher SWR on the output of the amp unless this mismatch pushes the amp into an unstable condition.


It's not combinations of resistance and reactance that provide the SWR match. It's when the antenna is tuned in such a way that the capacitive reactance and inductive reactance of the antenna system cancel each other out and appear as a theoretical purely resistive 50 ohm load at the resonant frequency.


What you refer to as a no tune output circuit in the solid state amp requires no tuning because it is a broadband matching transformer. It's matching impedance is controlled by the turns ratio and padder caps used. Solid state amps don't require tuned output circuits, they require individual filters with cutoff frequencies designed for each band.