It is sometimes desirable to have circuits capable of selectively filtering one frequency or range of frequencies out of a mix of different frequencies in a circuit. A circuit designed to perform this frequency selection is called a filter circuit, or simply a filter. A common need for filter circuits is in highperformance stereo systems, where certain ranges of audio frequencies need to be amplified or suppressed for best sound quality and power efficiency. You may be familiar with equalizers, which allow the amplitudes of several frequency ranges to be adjusted to suit the listener's taste and acoustic properties of the listening area. You may also be familiar with crossover networks, which block certain ranges of frequencies from reaching speakers. A tweeter (highfrequency speaker) is inefficient at reproducing lowfrequency signals such as drum beats, so a crossover circuit is connected between the tweeter and the stereo's output terminals to block lowfrequency signals, only passing highfrequency signals to the speaker's connection terminals. This gives better audio system efficiency and thus better performance. Both equalizers and crossover networks are examples of filters, designed to accomplish filtering of certain frequencies.
Another practical application of filter circuits is in the “conditioning” of nonsinusoidal voltage waveforms in power circuits. Some electronic devices are sensitive to the presence of harmonics in the power supply voltage, and so require power conditioning for proper operation. If a distorted sinewave voltage behaves like a series of harmonic waveforms added to the fundamental frequency, then it should be possible to construct a filter circuit that only allows the fundamental waveform frequency to pass through, blocking all (higherfrequency) harmonics.
We will be studying the design of several elementary filter circuits in this lesson. To reduce the load of math on the reader, I will make extensive use of SPICE as an analysis tool, displaying Bode plots (amplitude versus frequency) for the various kinds of filters. Bear in mind, though, that these circuits can be analyzed over several points of frequency by repeated seriesparallel analysis, much like the previous example with two sources (60 and 90 Hz), if the student is willing to invest a lot of time working and reworking circuit calculations for each frequency.
 REVIEW:
 A filter is an AC circuit that separates some frequencies from others within mixedfrequency signals.
 Audio equalizers and crossover networks are two wellknown applications of filter circuits.
 A Bode plot is a graph plotting waveform amplitude or phase on one axis and frequency on the other.

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