For a short-circuited transmission line if the length is exactly quarter wavelength, the transmission is equivalent to?

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When a transmission line is exactly a quarter wavelength long and is short-circuited at the load, it behaves in a specific manner that is crucial to understanding its equivalent circuit characteristics. In this configuration, the input impedance observed at the beginning of the line (the sending end) transforms into a parallel resonant circuit.

A quarter-wavelength transmission line essentially acts as an impedance inverter. The short-circuit at the load translates to a high impedance at the input because of the reflection and standing wave patterns established along the line. This behavior indicates that the line can resonate at certain frequencies.

In this case, the equivalent circuit seen at the input can effectively represent a parallel resonant circuit, where the reactive components oscillate between energy storage and release, similar to an LC circuit. This parallel resonant behavior is typical when considering the characteristic impedance and behavior of transmission lines at quarter wavelengths.

Understanding that the input impedance becomes very high due to the transformation properties of the transmission line at this specific length is key. Hence, this analysis confirms that the transmission line is indeed equivalent to a parallel resonant circuit in this scenario.

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