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the RC low-pass

R in series, C to ground

One resistor, one capacitor. Slow changes pass; fast ones get smoothed away. It's the simplest filter there is and it's in almost everything.

H(s) = 1 / (1 + sRC)    fc = 1 / (2πRC)

With R = 1.6 kΩ and C = 100 nF: RC = 160 µs, and fc = 994.7 Hz. At that frequency the output is down 3 dB (to about 0.707 of the input) and the phase has slipped 45°.

Bode plot pole-zero

Bode plot (magnitude above, phase below; the orange line is fc) and the single pole at s = −1/RC = −6250 s−1. ngspice AC sweep finds the −3 dB point at 994.7 Hz. Agrees.

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updated 10/24/26