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## [AMPS] High-SWR protection

 To: [AMPS] High-SWR protection ccc@space.mit.edu (Chuck Counselman) Tue, 31 Oct 2000 12:12:45 -0500
 ```Steve 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 -- FAQ on WWW: http://www.contesting.com/FAQ/amps Submissions: amps@contesting.com Administrative requests: amps-REQUEST@contesting.com Problems: owner-amps@contesting.com ```
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