By Robert E. Collin
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Extra info for Antennas and Radiowave Propagation (Mcgraw Hill Series in Electrical and Computer Engineering)
102) (actually some optimization was required due to the effects of line discontinuities, not accounted for by the model). 8 at 2fo. 14. The circuit simulation of the same line loaded with a shunt connected LC resonator with the reactive values given above is also included in the figure, for comparison purposes. The agreement is excellent up to 2fo, indicating that the semilumped approximation is valid in the considered frequency range. 14 can be considered to belong to this category (the bandwidth can be controlled by the inductance/capacitance ratio).
If the line length is l = λ/4 (βl = π/2), the input impedance is Zin = Zo2 ZL 1 32 which means that the input impedance is inversely proportional to the load impedance, and hence a λ/4 transmission line acts as an impedance inverter. This means that a reactive load with inductive/capacitive reactance is seen as capacitive/inductive reactance from the input port; in other words, the sign of the reactance is reversed in λ/4 lines. 32), it also follows that an open-circuit load is transformed to shortcircuit at the input port of a λ/4 line, and vice versa.
Partially reflected and absorbed power 10 FUNDAMENTALS OF PLANAR TRANSMISSION LINES occurs for resistive loads not matched to the line, or for complex loads. Notice also that for passive loads (ZL = R + jχ, with R > 0), the modulus of the reflection coefficient is |ρL| ≤ 1. 17) for passive loads. In microwave engineering, the reflection coefficient is typically expressed in dB and identified as the return loss: RL = − 20 log ρL 1 22 For infinitely long transmission lines or for transmission lines terminated with a matched load, constant amplitude travelling waves are present in the line.