RF and Microwave Engineering: Fundamentals of Wireless Communications

3.2 Transient Signals on Transmission Lines

In Section 3.1 we considered sinusoidal signals . These continuous wave (CW) signals represent the steady state. Continuous wave signals are monofrequent and described by their complex amplitude U. In the case of periodic but non-sinusoidal signals we can develop the periodic signal in a series of sinusoidal signals (Fourier series). If the transient signal is non-periodic we apply the Fourier transform instead of the Fourier series. In the case of a linear system we can consider the individual sinusoidal components and use the principle of superposition to calculate the resulting signal.

An important class of signals are digital base band signals that represent symbols by rapidly switching between two logical states, for example 5 V for a logical ‘1’ and 0 V for a logical ‘0’. In order to understand the implications of reflection and propagation directly in the time domain, we can benefit from the results in Section 3.1 where we defined transmission line parameters and the reflection coefficient. The fundamental aspects can be derived by looking at step and rectangular pulse functions.

3.2.1 Step Function

Let us first look at the step function s(t)

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In a graphical representation we use a vertical line to indicate the voltage step. ...