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An interesting property is that where a load is connected via an electrical half wavelength of lossless transmission line (of any characteristic impedance):
In fact V_{out}=V_{in}.
Taking the general case of the load, there is a mismatch at the load end of the line, and the complex reflection coefficient Γ' is the ratio of the reflected voltage wave to the forward voltage wave at the load. For more information on the meaning of Γ see Telegrapher's Equation.
V_{in}=V_{f}(1+Γ) where V_{f} is the forward wave voltage at the input to the line and Γ is the reflection coefficient at the input to the line.
Since the line is a lossless line an electrical half wave long, V_{f}'=V_{f}e^{jπ}=V_{f}∠180° and Γ'= Γ ,where V_{f}' is the forward wave voltage at the load end of the line and Γ' is the reflection coefficient at the load end of the line. So V_{out}=V_{f}'(1+Γ')=V_{f}∠180°(1+Γ).
V_{out}/V_{in} is (V_{f}∠180°(1+Γ))/(V_{f}(1+Γ))=1∠180°=1, or V_{out}=V_{in}.
Lossless lines do not exist in the real world, but short sections of low loss lines will deliver almost ideal results. For example, using TLLC to find Vo/Vi for a half wave of LMR400 with a load of 100+j0Ω at 144MHz we get Vo/Vi=9.975e1∠180.0°, less than 3% departure from ideal.
Version  Date  Description 
1.01  12/08/2012  Initial. 
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