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Everitt and Anner, "Communication Engineering," Third Edition, McGraw-Hill, 1956, provide a general method (pages 330-331) for examining a mismatch between a source and load, such as a transmission line feeding an antenna. They factor the source and the load into series networks, one element of which in each case is Zo, the desired impedance.
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They then use "Compensation Theorem A" from page 107, which states": "Any impedance in a network (either linear or nonlinear) may be replaced by a generator of zero internal impedance, whose generated voltage at every instant is equal to the instantaneous potential difference produced across the replaced impedance by the current flowing through it." Using this theorem, they replace the added network segments by voltage generators so that the resultant equivalent network consists of a matched source and load with added voltage generators to represent the voltages generated by the mismatch. I applied this to the special case of the complex conjugate load in "More Octave for Complex Zo," QEX, September/October, 2019. In that case, no modification of the source voltage or impedance is needed and the complex conjugate load is replaced by a matched load (image impedance) in series with a reactance of opposite sign that is twice the value of the reactance of the complex conjugate load's reactance. That "extra" reactance may then be replaced by a complex voltage source of zero internal impedance that will be seen to be generating a voltage that corresponds to the value of the reflected signal. 73, Maynard W6PAP On 6/26/23 23:01, Fran?ois wrote:
That's it, we have converged. In my application where I am looking for an equality between a value obtained by scanning and a target value, the distance between between the two points (in the complex plane) is a much better criterion for a good result than the ROS which only complicates by creating a non-monotonic function. |
