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An RC filter’s cutoff is called the −3 dB point because, at that frequency, its output power is half the passband power. With the same impedance, that corresponds to an output voltage about 70.7% of the passband voltage—not 50%. The label marks a point on a gradual response curve, not a frequency where the filter suddenly stops working.
How the −3 dB value comes from half power
Decibels express ratios on a logarithmic scale. For power, the level change is 10 log10(Pout/Pin). At half power, this is 10 log10(1/2) = −3.0103 dB, conventionally rounded to −3 dB.
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For voltage, the decibel formula is 20 log10(Vout/Vref). When the compared voltages are across equal impedances, power varies with voltage squared. Half power therefore means a voltage ratio of 1/√2, or about 0.707. The IEEE Technology Navigator describes the half-power point as an approximately 0.707 voltage ratio and a 3.01 dB drop: IEEE Technology Navigator.
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Where the corner occurs in a first-order RC low-pass
For an ideal, unloaded first-order low-pass with output taken across the capacitor, the transfer-function magnitude is |H(jω)| = 1/√(1 + (ωRC)2). At the corner, ωRC = 1, so the magnitude is 1/√2 of its passband value.
Since angular frequency ω = 2πf, the cutoff is fc = 1/(2πRC), or equivalently ωc = 1/RC. Microchip’s Bode Plot technical reference identifies this first-order RC relationship as the −3 dB point.
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What happens at and beyond cutoff
- At cutoff: The ideal first-order low-pass output is about 70.7% of its passband voltage; under equal-impedance comparison, its power is half. Its phase shift is −45°.
- Above cutoff: The low-pass continues to attenuate rather than switching off. Its ideal first-order magnitude response approaches a slope of −20 dB per decade.
- For a high-pass RC filter: The same half-power criterion is measured relative to the high-frequency passband, with the passband direction reversed.
Why a built circuit can differ from the simple formula
The expression fc = 1/(2πRC) assumes a simple first-order section that is not significantly loaded. Source resistance and the load connected to the output can change the effective circuit values and shift the observed corner. If a measured cutoff does not match the calculation, check the source and load impedances as well as the nominal resistor and capacitor values.
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The −3 dB convention gives a useful reference point, but a cutoff number alone does not describe an entire filter. When comparing designs, consider the required corner frequency, attenuation farther into the stopband (which depends on response and order), passband behavior, phase response, and the source and load impedances. Higher-order filter families may use other cutoff conventions or design definitions, so the −3 dB meaning should not be assumed without checking the specific response.
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