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Roy Lewallen wrote:
Let's run a quick calculation as Tom has suggested several times. Consider a transmission line with Z0 = 50 - j10 ohms connected to a 50 + j0 ohm load. As I hope will be evident, it doesn't matter what's connected to the source end of the line or how long it is. We'll look at the voltage V and current I at a point within the cable, but very, very close to the load end. Conditions are steady state. When numerical V or I is required, assume it's RMS. I hope we can agree of the following. If not, it's a waste of time to read the rest of the analysis. 1. Vf / If = Z0, where Vf and If are the forward voltage and current respectively. 2. Vr / -Ir = Z0, where Vr and Ir are the reverse voltage and current respectively. The minus sign is due to my using the common definition of positive Ir being toward the load. (If this is too troublesome to anyone, let me know, and I'll rewrite the equations with positive Ir toward the source.) 3. Gv = Vr / Vf, where Gv is the voltage reflection coefficient. This is the usual definition. Likewise, 4. Gi = Ir / If 5. V = Vf + Vr 6. I = If + Ir Ok so far? I am looking at W.C. Johnson, pages 15 and 16, Equations 1.22 through 1.25, where he shows, very concisely and elegantly, that the reflection coefficient is zero only when the complex terminating impedance is identically equal to the the complex value of Z0. And not the complex conjugate of Z0. In other words (read carefully), the complex terminating impedance whose value is Z0 is equivalent to an *infinite extension* of the coax whose complex value is Z0. This is the "clincher". Observe also the the reflection coefficient for current is the negative of the reflection coefficient for voltage. Bill W0IYH |