![]() In each of the derivations below, we pick one of these three methods. And if we use the Laplace transform, we can derive the frequency response, step response, and impulse response with equal ease. ![]() But if we make use of the method of complex impedances, we can derive its frequency response far more quickly than by differential equations. We can always derive the behavior of a filter made of capacitors, inductors, and resistors using differential equations alone. If you are new to capacitors, inductors, and resistors, we introduce these components in the first three lectures of our Introduction to Electronics course. Transmission lines are a form of filter, but we discuss these separately and in detail in Transmission Line Analysis. In every case we restrict our discussion to circuits we have built and used ourselves. We discuss surface acoustic wave filters, which provide astounding performance in a small package. We consider matching networks, which are important at high frequencies for matching sources and loads. We study active implementations, which work well at low frequencies, and passive implementations, which work well at high frequencies. Our discussion begins with high-pass and low-pass filters. This guide attempts to teach the design and implementation of active and passive filter circuits through discussion of actual circuits built and used by BNDHEP and OSI. © 2004-2021 Kevan Hashemi, Brandeis University ![]()
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