61 from Ch 13 Filters - Making sense of EE 2nd ed Filters...

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Filters are circuits whose transfer function H = V output V input depends on the frequency. Frequency-dependent impedances belong to capacitors and inductors thus filters involve L and C. Quite often, filters are designed to suppress the noise and/or tune into the desired signal (your cell phone tunes into the better channel automatically; for your TV or radio you choose the channel yourself). Even more often, you may find that your circuit works as a filter though you did not want it to! Recall that any circuit has inductance & capacitance! Under sinusoidal steady-state conditions, in circuits with linear elements and sinusoidal input signals, we apply phasors to calculate voltages and currents. Thus phasors are used for analysis of filters. In the language of phasors, the input and output voltages are complex, thus the transfer function is complex; most often, we are interested in its magnitude H ( " ) . Using H ( " ) at the very low and very high frequencies, we classify filters into 4 types: Low-Pass, High-Pass, Band-Pass, and Band-Reject (also called Band-Stop or Notch). Here we consider passive filters that act as voltage dividers built of R , L , and C , and active filters based on Op Amps (inverting amplifiers). Passive filters do not have energy sources, while active filters do: recall that Op Amps cannot work without power supplies. The cutoff frequency is the borderline between the Pass-Band and the Stop-Band of a filter. According to the convention that we use, the power of output signal at the cutoff frequency equals 50% of the maximal output power with the same load.
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