Rob Roschewsk wrote:

Roy, how did you come up with "1275 ohms in *parallel* with 319 ohms "
equatating to "75 ohms resistance in series with 300 ohms of capacitive
reactance" ??? Just wondering.

I got it from a routine I keep on my HP48GX calculator, which comes from
the following series-parallel transformations:

Let:

Rs = resistance of series equivalent circuit
Xs = reactance of series equivalent circuit
Rp = resistance of parallel equivalent circuit
Xp = reactance of parallel equivalent circuit

To convert a series circuit to a parallel circuit which has an identical
impedance:

Rp = (Rs^2 + Xs^2) / Rs
Xp = (Rs^2 + Xs^2) / Xs

To convert a parallel circuit to a series circuit which has an identical
impedance:

Rs = (Rp * Xp^2) / (Rp^2 + Xp^2)
Xs = (Rp^2 * Xp) / (Rp^2 + Xp^2)

These aren't very difficult to derive if you're comfortable with complex
arithmetic. They should be in the toolkit of everyone who works with
electrical circuits.

Important things to keep in mind when using these transformations:

1. Although frequency isn't explicitly involved in the conversions, when
you make an equivalent circuit from a resistor and inductor or
capacitor, Xp and Xs will change with frequency. Therefore a transformed
circuit will have the same impedance as the original only at one
frequency. If the frequency changes, new values of resistance and
capacitance or inductance have to be calculated for the equivalent circuit.

2. Because point 1, one circuit or the other will usually be better for
modeling a real circuit over a range of frequencies, because the
impedance of the real circuit will change with frequency more like one
or the other of the two equivalent circuits.

In the example, where the feedpoint Z = 75 - j300:

Rs = 75
Xs = 300

so

Rp = (75^2 + (-300)^2) / 75 = 1275
Xp = (75^2 + (-300)^2) / (-300) = -318.75

You can check this if you'd like. You'll find that the parallel
combination of 1275 and -j318.75 ohms is 75 - j300.

Roy Lewallen, W7EL