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I am taking some microwave engineering courses and was trying to explain the concept of reflection coefficients to my friend, but he asked me a question I am unable to answer....

So we know that given a transmission line with characteristic impedance [itex]Z_0[/itex] terminated with a load impedance [itex]Z_L[/itex], the voltage reflected is related to the incident voltage by the reflection coefficient, [itex]\Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0}[/itex].

Now what happens if we pick [itex]Z_L + Z_0 = 0[/itex]? This could happen if both [itex]Z_L[/itex] and [itex]Z_0[/itex] are purely imaginary, and one is the negative of the other (maybe some inductive and some capacitive reactances cancelling each other). Normally in our courses we considered [itex]Z_0[/itex] being a real number, usually 50 ohms. But if I assume it to be complex, then the reflection coefficient can become larger than 1, and even infinite like in that case.

So what's the physical meaning of an infinite reflection coefficient / reflection coefficient larger than 1? That seems to contradict conservation of power, because you get more power reflected than input power...

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# Transmission line and infinite reflection coefficient

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