Basic Electronics

RC Filters and the Cutoff Frequency

Think of a capacitor as a frequency-sensitive gate: it shuts the gate on slowly changing (low-frequency) signals and swings it wide open for fast ones. Mathematically, its impedance is inversely proportional to frequency: Zc = 1/(2πfC).

Combine this gate with a resistor and a filter is born: take the output across the capacitor and the high frequencies leak away to ground, leaving only the slow signals → low-pass. Swap the positions of R and C and you get the exact opposite → high-pass.

The filter’s "boundary line" is the cutoff frequency fc = 1/(2πRC): there the output drops to 70.7% (−3 dB) and the phase shifts by −45°. Beyond that boundary, every 10× increase in frequency weakens the signal by another 10× (−20 dB). The Bode plot alongside is the map of this behavior.

Formulas

Zc = 1 / (2πfC)

fc = 1 / (2πRC)

|H(fc)| = −3 dB, ∠H(fc) = −45°

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Test Yourself

For R = 10 kΩ and C = 100 nF, what is the approximate cutoff frequency?

Answer: 159 Hz — fc = 1/(2π·10k·100n) ≈ 159 Hz.

In a low-pass RC filter, roughly how much attenuation occurs at 100× fc?

Answer: −40 dB — A single-pole filter falls −20 dB per decade; 2 decades → −40 dB.

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