Transmission Line - Input Impedance of Lossless Transmission Line

Input Impedance of Lossless Transmission Line

The characteristic impedance of a transmission line is the ratio of the amplitude of a single voltage wave to its current wave. Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line.

For a lossless transmission line, it can be shown that the impedance measured at a given position from the load impedance is

Z_mathrm{in} (l)=Z_0 frac{Z_L + jZ_0tan(beta l)}{Z_0 + jZ_Ltan(beta l)}

where is the wavenumber.

In calculating, the wavelength is generally different inside the transmission line to what it would be in free-space and the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation.

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Other articles related to "input impedance of lossless transmission line, transmission line, impedance, input impedance":

Input Impedance of Lossless Transmission Line - Stepped Transmission Line
... A stepped transmission line is used for broad range impedance matching ... It can be considered as multiple transmission line segments connected in series, with the characteristic impedance of each individual element to be Z0,i ... The input impedance can be obtained from the successive application of the chain relation where is the wave number of the ith transmission line segment and li is the length of this segment, and Zi ...

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