# Analog Filters Cheat Sheet by tenoooo

### Filters

 Passive filters The circuits built using RC, RL, or RLC circuits. Active filters The circuits that employ one or more op-amps in the design an addition to resistors and capacitors

### Active Filters

 Low-pass filters A low-pass filter is a filter that passes freque­ncies from 0Hz to critical frequency, fc and signif­icantly attenuates all other freque­ncies. The critical frequency of a low-pass RC filter occurs when Xc = R and can be calculated using the formula: fc=1/2πRC High-pass filters A band-pass filter passes all signals lying within a band between a lower-­fre­quency limit and upper-­fre­quency limit and essent­ially rejects all other freque­ncies that are outside this specified band band-pass filter A high-pass filter is a filter that signif­icantly attenuates or rejects all freque­ncies below fc and passes all freque­ncies above fc. The critical frequency of a high-pass RC filter occurs when Xc = R and can be calculated using the formula: fc=1/2πRC Bandpass The bandwidth (BW) is defined as the difference between the upper critical frequency (fc2) and the lower critical frequency (fc1). BW=Fc2-Fc1 Center Frequency The frequency about which the pass band is centered is called the center frequency , f o and defined as the geometric mean of the critical freque­ncies. f0= √Fc1fc2 Quality Factor The quality factor (Q) of a band-pass filter is the ratio of the center frequency to the bandwidth. Q = f0/BW Band-r­eject filters Band-stop filter is a filter which its operation is opposite to that of the band-pass filter because the freque­ncies within the bandwidth are rejected, and the freque­ncies above f c1 and f c2 are passed.

### Butter­worth Filter

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