How do you calculate the cutoff frequency of a low-pass filter?

To calculate the cutoff frequency of a low-pass filter, you'll need the filter's transfer function, which is the mathematical representation of how the filter processes the input signal. The most common type of low-pass filter is the first-order (single-pole) RC filter, which consists of a resistor (R) and a capacitor (C).

For a first-order RC low-pass filter, the cutoff frequency (f_c) can be calculated using the following formula:

f_c = 1 / (2 * π * R * C)

Where:

f_c = Cutoff frequency (in Hertz)

π (pi) ≈ 3.14159 (a mathematical constant)

R = Resistance value in Ohms (Ω)

C = Capacitance value in Farads (F)

To use this formula, you'll need to know the values of the resistor (R) and the capacitor (C) used in your specific low-pass filter circuit. Once you have those values, plug them into the formula, and you'll get the cutoff frequency in Hertz.

It's essential to ensure that the units for R and C are compatible. If you're given the values in kilohms (kΩ) or microfarads (μF), you'll need to convert them to ohms and farads, respectively, before performing the calculation.

Keep in mind that more complex low-pass filter designs may have different formulas for calculating the cutoff frequency, but for a first-order RC low-pass filter, the formula above should work.