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# Lecture 33 - 33 TL circuits with half and quarter-wave...

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33 TL circuits with half- and quarter-wave trans- formers Last lecture we established that phasor solutions of telegrapher’s equa- tions for TL’s in sinusoidal steady-state can be expressed as V ( d )= V + e jβd + V - e - jβd and I ( d )= V + e jβd - V - e - jβd Z o in a new coordinate system shown in the margin. l Input port Z o - l z 0 0 l d LOAD GENERATOR, Circuit Z L = R L + jX L I ( d ) V ( d ) + - By convention the load is located on the right at z =0= d , and the TL input connected to a generator or some source circuit is shown on the left at d = l . We have replaced the short termination of the previous lecture with an arbitrary load impedance Z L = R L + jX L . In this lecture we will discuss sinusoidal steady-state TL cir- cuit problems having arbitrary reactive loads but with line lengths l constrained to be integer multiples of λ 4 (at the op- eration frequency). The constraint will be lifted next lecture when we will de- velop the general analysis tools for sinusoidal steady-state TL circuits. 1

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In the TL circuit shown in the margin an arbitrary load Z L is connected to a TL of length l = λ 2 at the source frequency. Given that
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Lecture 33 - 33 TL circuits with half and quarter-wave...

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