(Solved): When a 32 V amplitude 1 microsecond pulse is applied to the transmission line shown in the figure, ...

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Solution .

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a) The voltage and current at the middle of the line with time can be found by using the equations for voltage and current on a transmission line:
V(z,t) = V0+ [Vf+ V0] / 2 * (1 + ?(z,t)) * cos(?t - ?z) I(z,t) = (Vf-V0) / [2Z0 * (1 + ?(z,t))] * cos(?t - ?z)
where V0 is the initial voltage on the line, Vf is the voltage at the end of the line, ?(z,t) is the reflection coefficient at a distance z from the source at time t, ? is the angular frequency of the signal, and ? is the propagation constant of the line.
In this case, V0 = Vf = 32 V, ? = 2?f = 2?/6?s, and ? = 2?/? = 2?/0.15m = 41.89 rad/m. The reflection coefficient can be found using the equation:
?(z,t) = [ZL - Z0] / [ZL + Z0] * e^(-2?z)
where ZL is the load impedance (which is equal to Z0 in this case), ? is the attenuation constant of the line, and e is the exponential function.
Using ZL = Z0 = 50 ? and ? = ? + j?, where ? is the attenuation coefficient of the line (which can be found using ? = ln(1/?) / d, where ? is the reflection coefficient at the load and d is the length of the line), we can calculate the reflection coefficient at the source end of the line:
?(z=0,t) = [ZL - Z0] / [ZL + Z0] = 0