RC (Resistor-Capacitor) circuits are fundamental electronic filters used to block or pass specific ranges of frequencies. They are simpler than RLC circuits as they don’t involve inductors.
A **Low-Pass Filter** allows frequencies *below* a certain cutoff frequency to pass through, while attenuating frequencies above it. In a simple RC low-pass filter, the resistor (R) is in series with the input signal, and the capacitor (C) is connected from the junction of R and the output to ground. The output voltage is taken across the capacitor. At low frequencies, the capacitor’s impedance is high, so it acts like an open circuit, allowing the signal to pass to the output. At high frequencies, the capacitor’s impedance becomes low, effectively shorting the high-frequency signals to ground and attenuating them.
A **High-Pass Filter** allows frequencies *above* a certain cutoff frequency to pass through, while attenuating frequencies below it. In a simple RC high-pass filter, the capacitor (C) is in series with the input signal, and the resistor (R) is connected from the junction of C and the output to ground. The output voltage is taken across the resistor. At low frequencies, the capacitor’s impedance is high, blocking the signal. At high frequencies, the capacitor’s impedance becomes low, acting like a short, and allowing the high-frequency signals to pass to the output across the resistor.
The **cutoff frequency ($f_c$)** (also known as the -3dB frequency or half-power frequency) is the point where the output power of the filter is half of the input power, or the output voltage is approximately 70.7% of the input voltage. For a simple RC filter, the cutoff frequency is determined by the values of R and C:
$$f_c = \frac{1}{2\pi RC}$$
Where: