Ford, Thomas
I quickly built and measured the situation you described. The transfomer
is conventional (separate primary and secondary windings), but tightly
inter-wound for k~1, with the right ferrite core for the frequency range.
Measurements wre made at 2 MHz.
With this 4:1 Z ratio transformer, a 200-ohm carbon resistor transformed
to 45 +j6 ohms. With an inductor added to create a 200 +j250 ohm
load, the transformed impedance was 46 +j62 ohms. Placing the right
capacitor in series with the low impedance winding could obtain a
45 +j0 impedance. I could not "zero out" the reactance using a
capacitor in series with the load, but it was certainly low enough to
be considered zero for practical purposes.
Conclusions? A good transformer simply changes the magnitude of
the vector representing the R +/-jX of the load without altering the
angle. This is what we want. There are many, many published RF
transformer designs that are OK at maybe 5 or 10 MHz but cannot do
this at 2 MHz.
I did not take the time to repeat the experiment with a transmission line
transformer.
Ford, with regard to your transmission line question -- The equations
are in Kraus, Jasik, Smith, Reference Data for Radio Engineers and
many other places. I just use the Smith chart...
73, Gary
K9AY
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