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# Deriving Telegraph Equations

Could you please show me how to derive the telegraph equations for a loss-less transmission line?

Also, please solve this problem with step-by-step calculations.

A loss-less transmission line of characteristic impedance Z0 is terminated by a resistive load R. Find an expression for the input impedance of a section of the line of length l. Show that this is (Z0^2)/R if l = lamba/4.

#### Solution Preview

Problem: Could you please show me how to derive the telegraph equations for a loss-less transmission line?

I will use the symbol "d/dx" for the first partial derivative with respective to x and "d^2/dx^2" for the second partial

derivative with respective to x.

Let Rp = Resistance in Ohms per Unit Length,
L = Inductance in Henry per Unit Length
C = Capacitance in Farads per Unit Length
G = Conductance in Siemens per Unit Length.

Then, the line voltage V(x) and the current ...

#### Solution Summary

The following posting provides 214 words to show how to derive a telegraph equation for a lossless transmission line. A detailed step-by-step solution is provided in the solution.

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