# Transmission line equations

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

.

.

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

.

.

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

.

.

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.

.

differentiating V w.r.to x

.

but

.

.

since .

.

,   where  .

AS      and .

this implies       ,    .

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

.

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

and  .

then the EQNs (3) and (4)

.

.

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.     (No Ratings Yet) Loading... ## Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.

Posted on Categories Electro Magnetic Theory