Question 1

How do I calculate the cutoff frequency of an RC filter?

Accepted Answer

The -3 dB cutoff of a first-order RC filter is fc = 1 / (2 x pi x R x C), where R is in ohms and C is in farads. For example, 10 kohm with 100 nF gives 1 / (2 x pi x 10000 x 1e-7) = 159.2 Hz. The same formula applies to both low-pass and high-pass RC filters.

Question 2

What is the resonant frequency of an LC circuit?

Accepted Answer

The resonant frequency of an ideal LC circuit is f0 = 1 / (2 x pi x sqrt(L x C)), with L in henries and C in farads. At resonance the inductive and capacitive reactances are equal and opposite, so they cancel. For example, 100 uH with 100 nF resonates near 50.3 kHz.

Question 3

Is the cutoff frequency the same for RC low-pass and high-pass filters?

Accepted Answer

Yes. A single resistor and capacitor form a first-order filter whose -3 dB corner is fc = 1 / (2 x pi x R x C) regardless of topology. Swapping which element the output is taken across turns a low-pass into a high-pass, but the corner frequency itself is unchanged.

Question 4

What is the time constant of an RC or RL circuit?

Accepted Answer

For an RC circuit the time constant is tau = R x C; for an RL circuit it is tau = L / R, both in seconds. One time constant is the time to charge or decay to about 63 percent of the final value, and the circuit is considered settled after roughly five time constants.

Question 5

Are these formulas exact for real filters?

Accepted Answer

They are ideal first-order (single-pole) and lossless-resonator equations. They ignore source and load impedance, capacitor ESR, inductor series resistance and parasitic capacitance, and component tolerance. Use the result as a starting point and verify on the bench, especially at high frequency where parasitics dominate.

RC / LC Filter& Resonant Frequency

RC / LC Filter
& Resonant Frequency