Nonrepetitive Stimuli

No stimulus is completely repetitive in the true sense of the word. Repetitive implies that the waveform has been exactly that way, since time immemorial, and remains so forever. But in the real world, there is a definite moment when we actually apply a given waveform (and another when we remove it). Even an applied sine wave, for example, is not repetitive at the moment it gets applied at the inputs of a network. Much later, the stimulus may be considered repetitive, provided sufficient time has elapsed from the moment of application that the initial transients have died out completely. This is, in fact, the implicit assumption we always make when we carry out steady state analysis of a circuit. 

But sometimes, we do want to know what happens at the moment of application of a stimulus — whether subsequently repetitive, steady, or otherwise. Like the case of the step voltage applied to our RC-network. If this were a power supply, for example, we would want to ensure that the output doesn t overshoot (or undershoot ) too much. 

To study any such nonrepetitive waveform, we can no longer decompose it into components with discrete frequencies as we do with repetitive waveforms. Now we require a spread (continuum) of frequencies. 

Further, to allow for waveforms (or frequency components) that can increase or decrease over time (disturbance changing), we need to introduce an additional (real) exponential term eCTt. So whereas, when doing steady state analysis, we represent a sine wave in the form eJojt, now it becomes e0 x ci jt = This is therefore a sine wave, but with an 

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Suppose we suddenly increase the load current of a converter from 4 A to 5 A. This is a step load and is essentially a nonrepetitive stimulus. But by writing all the transfer functions in terms of s rather than just as a function of jco, we have created the framework for analyzing the response to such disturbances too. We will need to map the stimulus into the s-plane with the help of the Laplace transform, multiply it by the appropriate transfer function, and that will give us the response in the s-plane. We then apply the inverse Laplace transform and get the response with respect to time. This was the procedure symbolically indicated in Figure 7-3, and that is what we need to follow here too. However, we will not perform the detailed analysis for arbitrary load transients here, but simply provide the key equations required to do so. 

This could be done in the lab, and/or on paper as we will soon see. In effect, what we are looking at closely is the response of the power supply to any frequency component of a repetitive or nonrepetitive impulse. But in doing so, we are in effect only dealing with a steady sine wave stimulus (swept). So we can put s = jco (i.e. a = 0). 

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