The transmission line will be analyzed in terms of voltage and current and also the relation between V and I of a line can be obtained by the simplest type of Transmission line.

i.e, a pair of parallel wires of uniform size which are spaced a small distance (S) apart in air.

Consider a short section of Transmission line of length (i.e an infinitesimal section with a very small length).

at – voltage is V and current is I and at voltage is and current is .

the voltage drop between and is

similarly, the current difference between and is

from EQNS (I) and(II)

and .

to neglect the transit time effect the condition to be applied is , then the two equations will become

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.

choose

differentiating the above equation w.r.to x

replacing in the above equation will result

.

, Let .

where is the propagation constant which is a complex number.

Similarly from

differentiating the above equation w.r.to x

replacing in the above equation will result

.

the solutions of Equations(1) and (2) are

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.

where A, B, C and D are arbitrary constants in which A and B have dimensions of voltage and C and D have current dimensions.

since is complex that is by replacing in the V and I equations

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.

the term represents waves travelling from source end to load end and are called as incident waves .

Similarly the term represents reflected waves when a transmission line is terminated with any load impedance at the output end.

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differentiating V w.r.to x

.

but

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since .

.

, where .

AS and .

this implies , .

by substituting and in the Voltage and current equations , V and I results to be

.

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at the input terminals , and , after substituting this condition in EQNs (1) and (2)

and .

then the EQNs (3) and (4)

.

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The above equations are known as general equations of a transmission line for voltage and current at any point which is located at x from the sending end.