Question

Derive (9.5), the expression for $Z_{\mathrm{L}}$ given $Z_{\text {in }}$.

    Derive (9.5), the expression for $Z_{\mathrm{L}}$ given $Z_{\text {in }}$.

Small Antenna Design (Communications Engineering Series)

Small Antenna Design (Communications Engineering Series)

Douglas B. Miron 1st Edition

Chapter 9, Problem 9

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Step 1

The input impedance at a distance $l$ from the load is given by: $$Z_{in} = Z_0 \frac{Z_L + jZ_0\tan(\beta l)}{Z_0 + jZ_L\tan(\beta l)}$$ where $Z_0$ is the characteristic impedance of the line and $\beta$ is the phase constant. Show more…

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Derive (9.5), the expression for $Z_{\mathrm{L}}$ given $Z_{\text {in }}$.

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