R1 + C1 + C2 inject RF with a phase shift of 90 degs. So the end of each winding will have two components to it :- say 0 degs + 90 degs, the other + 180 degs + 90 degs. Now if you balance the amplitudes so the C1 voltage equals the voltage at the end of the transformer when operating into a 50 ohm load, you will get one voltage at a phase of +45 degs, the other at -45 degrees with equal amplitudes, so when you detect them the + and - voltages cancel. As the reflected voltage increases, the voltages change in amplitude and phase so the outputs do not cancel so you can then calibrate the meter in VSWR units. Some where down the line you must calibrate for the actual power (operating into an open circuit ?).
Frank
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Just thinking about it a bit more. The circuit really compares the current and voltage PHASES on the line. With any line resistive impedance the Vtransformer plus Vline will be equal at both diodes, so equal cancelling DC outputs.
Frank