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Attenuation for Transmission Lines

Lossy transmission lines exhibit a complex propagation constant which is defined as:

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where α and β are called the attenuation and phase factors. Attenuation factor, α, can be specified in Nepers/meter or dB/meter, both of which can be found from the other by the equation:

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If α = 0, the transmission line becomes ideal and lossless. In this case, propagation constant is purely imaginary and it is equal to jβ = j2πf. Then, the input impedance of a lossless transmission line of characteristic impedance Zo, length l, and terminated by a load impedance ZL can be stated as follows:

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