Steve <ve3tu@rac.ca> wrote:
>...I would like to know what a directional
>coupler would indicate if there was reactance and resistance on the load for
>example 35R with -35J . The vector sum is 50 ohms but just wondering what the
>coupler would show.
The VSWR is determined by the (complex) load impedance Zl and the
characteristic impedance of the transmission line Zo (which I'll take to be
resistive and equal to 50 ohms) as follows. Here, Gamma is the voltage
reflection coefficient, also complex. |Gamma| denotes the magnitude of
Gamma.
Gamma = (Zl-Zo)/(Zl+Zo)
VSWR = (1+|Gamma|)/(1-|Gamma|)
The only way that VSWR can be equal to 1 is for the magnitude of Gamma to
be zero. The only way for the magnitude of Gamma to be zero is for the
magnitudes of BOTH its real and imaginary parts to be zero. The only way
for the magnitudes of BOTH the real and the imaginary parts of Gamma to be
zero is for BOTH (1) the real part of Zl to be 50 ohms and (2) the
imaginary part of Zl to be zero.
I'll leave it as an exercise for the student to evaluate these formulas for
Zl = (35-35j) ohms.
A directional coupler with a wattmeter or two indicates (or is supposed to
indicate) forward power and reverse power. The ratio of the reverse power
to the forward power is the square of |Gamma|. As you see above, this
ratio will be zero if and only if BOTH (1) the real part of Zl is 50 ohms
and (2) the imaginary part of Zl is zero.
-Chuck W1HIS
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