Question

How does a basic RC (resistor-capacitor) circuit filter signals?

Answer 1

Could you specify whether you’re interested in low-pass, high-pass, or another type of RC filter?

Answer 2

A basic RC circuit filters signals by leveraging the properties of resistors and capacitors. The filtering effect depends on how the resistor (R) and capacitor (C) are arranged in the circuit—either in series or parallel—and the frequency of the input signal. Here’s a breakdown of how it works:

### RC Low-Pass Filter

**Configuration:**
- The resistor and capacitor are arranged in series, with the output taken across the capacitor.

**Operation:**
- **Low-Frequency Signals:** At low frequencies, the capacitor's reactance (opposition to AC current) is high, which means it behaves like an open circuit. The majority of the input signal passes through the resistor and appears across the capacitor, allowing low-frequency signals to pass through to the output.
- **High-Frequency Signals:** At high frequencies, the capacitor's reactance decreases, making it behave more like a short circuit. This results in most of the high-frequency signal being shunted to ground rather than appearing across the capacitor. Thus, high-frequency signals are attenuated (reduced).

**Cutoff Frequency:**
- The point at which the output signal is reduced to about 70.7% of the input signal (or -3dB) is called the cutoff frequency. It is determined by the formula:
  
  \[
  f_c = \frac{1}{2 \pi R C}
  \]

  where \( f_c \) is the cutoff frequency, \( R \) is the resistance, and \( C \) is the capacitance.

### RC High-Pass Filter

**Configuration:**
- The resistor and capacitor are arranged in series, with the output taken across the resistor.

**Operation:**
- **Low-Frequency Signals:** At low frequencies, the capacitor's reactance is high, and it blocks the low-frequency signals. Thus, very little of the input signal appears across the resistor, resulting in low output.
- **High-Frequency Signals:** At high frequencies, the capacitor’s reactance is low, and it allows high-frequency signals to pass through to the output across the resistor.

**Cutoff Frequency:**
- The cutoff frequency for a high-pass filter is also given by the same formula:

  \[
  f_c = \frac{1}{2 \pi R C}
  \]

  where \( f_c \) is the cutoff frequency.

### Summary

- **Low-Pass Filter:** Allows low-frequency signals to pass and attenuates high-frequency signals.
- **High-Pass Filter:** Allows high-frequency signals to pass and attenuates low-frequency signals.

In both cases, the RC circuit acts as a frequency-dependent resistor, where the resistance varies with frequency due to the changing reactance of the capacitor.