## Calculate active Low & High Pass Filter

One simple electrical circuit that will serve as a low-pass filter consists of a resistor in series with a load, and a capacitor in parallel with the load.

The capacitor exhibits reactance, and blocks low-frequency signals, causing them to go through the load instead. At higher frequencies the reactance drops, and the capacitor effectively functions as a short circuit. The combination of resistance and capacitance gives you the time constant of the filter \tau = RC (represented by the Greek letter tau).

The break frequency, also called the turnover frequency or cutoff frequency (in hertz), is determined by the time constant:

fc = 1 / (2 * 3,141592 ) * R * C

One way to understand this circuit is to focus on the time the capacitor takes to charge. It takes time to charge or discharge the capacitor through that resistor:
• At low frequencies, there is plenty of time for the capacitor to charge up to practically the same voltage as the input voltage.
• At high frequencies, the capacitor only has time to charge up a small amount before the input switches direction. The output goes up and down only a small fraction of the amount the input goes up and down. At double the frequency, there's only time for it to charge up half the amount.

Another way to understand this circuit is with the idea of reactance at a particular frequency:
• Since DC cannot flow through the capacitor, DC input must "flow out" the path marked V_\mathrm{out} (analogous to removing the capacitor).
• Since AC flows very well through the capacitor - almost as well as it flows through solid wire - AC input "flows out" through the capacitor, effectively short circuiting to ground (analogous to replacing the capacitor with just a wire).
The capacitor is not an "on/off" object. The capacitor will variably act between these two extremes. It is the Bode plot and frequency response that show this variability.

### 2 Pole Active Low Pass Filter

Input Calculated Values
 Filter Type Butterworth Chebyshev 0.1 dB Bessel Resistors kOhms 3dB Cutoff Freq Hz
 R1, R2 kOhms C1 uF C2 uF

### 2 Pole Active High Pass Filter

Input calculated Values
 Filter Type Butterworth Chebyshev 0.1 dB Bessel Capacitors uF 3dB Cutoff Freq Hz
 C1,C2 uF R1 kOhms R2 kOhms

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