Multiple reflection in terminated coupled-lines

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Two coupled-lines are identically terminated.

The voltage and current at the source end are:

The voltage and current at the termination end are:

where is the propagation delay and S,T are the reflection coefficients.

We will derive a special solution for identically terminated coupled-lines.

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We assume the boundary condition at the source and termination end as:

Because the terminations of two lines are identical, it is convenient to use even and odd mode.

Laplace transformed boundary conditions are:

Reminding that these conditions and the general solutions (General solution of coupled transmission-line equations)

are the same form in the case of a single line (Multiple reflection in a terminated line) ,we obtain the solutions:

where is the propagation time from x=0 to x=l and S,T are the reflection coefficients.

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The voltages of line-1 and 2 are obtained from those of even and odd mode:


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