Distributed L and C model of a transmission line

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Consider a uniform two-conductor transmission line.

Assuming that the electromagnetic wave propagates in a TEM mode, the voltage and current satisfies the equations:

where L and C are the inductance and capacitance per unit length along the transmission line.

We will derive the equations of distributed L and C model.

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We consider a uniform two-conductor transmission line and assume that the electromagnetic wave propagates in a TEM mode.

The voltage between conductor-1 and 2 is obtained by integrating ET ds along any path C from conductor-1 to 2 :

Therefore the gradient of voltage v(z,t) is proportional to the time derivative of current i(z,t), and the proportional coefficient is the inductance between conductor-1 and 2:

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The current of conductor-1 is obtained by integrating BT ds along any closed path C around conductor-1:

Therefore the gradient of current i(z,t) is proportional to the time derivative of voltage v(z,t), and the proportional coefficient is the capacitance between conductor-1 and 2:


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