Low Pass Filter Cutoff Frequency Calculator

Low Pass Filter Cutoff Frequency Formula:

\[ f_c = \frac{1}{2 \pi R C} \]

Cutoff Frequency (f_c):

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1. What is Low Pass Filter Cutoff Frequency?

The cutoff frequency (f_c) of a low-pass filter is the frequency at which the output signal is attenuated to -3dB (about 70.7%) of its maximum value. Frequencies below f_c pass through with minimal attenuation, while higher frequencies are increasingly attenuated.

2. How Does the Calculator Work?

The calculator uses the RC low-pass filter formula:

\[ f_c = \frac{1}{2 \pi R C} \]

Where:

\( f_c \) — Cutoff frequency in Hertz (Hz)
\( R \) — Resistance in Ohms (Ω)
\( C \) — Capacitance in Farads (F)
\( \pi \) — Mathematical constant (~3.14159)

Explanation: The cutoff frequency is inversely proportional to both resistance and capacitance. Increasing either R or C will lower the cutoff frequency.

3. Importance of Cutoff Frequency

Details: The cutoff frequency determines which frequency components of a signal pass through the filter and which are attenuated. It's crucial in audio processing, signal conditioning, noise reduction, and many electronic applications.

4. Using the Calculator

Tips: Enter resistance in Ohms (Ω) and capacitance in Farads (F). For typical capacitor values:

1 μF = 0.000001 F
1 nF = 0.000000001 F
1 pF = 0.000000000001 F

5. Frequently Asked Questions (FAQ)

Q1: What happens at the cutoff frequency?
A: At f_c, the output voltage is 70.7% of the input voltage (-3dB point), and the phase shift is -45°.

Q2: How does this relate to the time constant?
A: The time constant (τ = RC) is the reciprocal of the angular cutoff frequency (ω_c = 1/RC). f_c = 1/(2πτ).

Q3: What's the roll-off rate of a simple RC filter?
A: A first-order RC filter has a roll-off of -20dB per decade (-6dB per octave) above the cutoff frequency.

Q4: Can I use this for active filters?
A: This formula is for passive RC filters. Active filters may have different cutoff frequency formulas depending on their design.

Q5: How accurate is this calculation?
A: The formula is theoretically exact for ideal components. Real-world factors like component tolerances and parasitic effects may cause slight variations.