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Alternating Current: Filters 

AC has some properties not shared by DC: frequency and the phase relationship between voltage and current. Sometimes we need to control one or both of these properties.
Realworld signals include multiple frequencies over a wide range. How will combinations of components affect the different frequencies that make up the total signal?
One thing we find ourselves dealing with throughout electronics and some other aspects of physics is the mathematical factor designated as π, which has a value of approximately 3.14159265. This factor inserts small errors at many places in our calculations, and the cumulative error can become significant. Can we find a way to do most of our calculations without invoking π?
In electronics, we deal with signal magnitudes and component values over a very wide range. Sometimes it's more convenient to deal with numbers in the range of a hundred or so, rather than 10¹² or more. Here's how to do that.
Remember what we said about using logarithms? Here's one place we need them. When we look at signal power gain or loss, we often have to calculate with values over several orders of magnitude. Using decibels makes such calculations much simpler.
Now that we have the mathematical tools we need to describe the behavior of signal filter circuits, we can examine the circuits themselves and their behavior. We start with a circuit that will pass low frequencies easily, but will increasingly attenuate signals at higher frequencies.
Just as we have circuits that can pass lower frequencies and attenuate higher frequencies, we can also turn them around and pass higher frequencies while attenuating lower frequencies.
We can also combine highpass and lowpass filters in such a way as to readily pass a certain range of frequencies but attenuate signals at either higher or lower frequencies.


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