Transmission line responses

In order to understand the operation of transmission lines, we need to consider two cases:step-function response and the steady-state ac response. The step-function case involves a single event when a voltage at the input of the line snaps from zero(or a steady value) to a new (or nonzero) value, and remains there until all action dies out. This response tells us something of the behavior of pulses in the line, and infact is used to describe the response to a single-pulse stimulus. The steady-state ac response tells us something of the behavior of the line under stimulation by a sinusoidal RF signal. 

Step-function response of a transmission line 
Figure 3-3 shows a parallel transmission line with characteristic impedance Zo connected to a load impedance ZL. The generator at the input of the line consists of a voltage source Vin series with a source impedance Zs and a switch S1. Assume for the present that all impedances are pure resistances (i.e., R+j0). Also, assume that Zs=Zo.When the switch is closed at time To(Fig. 3-4A), the voltage at the input of theline (Vin) jumps to V/2. In Fig. 3-2, you may have noticed that the LC circuit resem-bles a delay line circuit. As might be expected, therefore, the voltage wave front propagates along the line at a velocity v of,

 where v is the velocity, in meters per second L is the inductance, in henrys C is the capacitance, in farads