Filters and Frequency Response

Why it matters: filters determine what frequencies pass through a circuit — essential for audio, sensors, and signal conditioning.

What you’ll learn: build RC and RL filters, calculate cutoff frequencies, and interpret Bode magnitude and phase plots.

Prerequisites

• Comfortable with Ohm's law and basic circuit concepts from the beginner series
• Familiarity with complex numbers (phasors) is helpful but not mandatory

Learning objectives

• Compute cutoff frequency for simple RC and RL networks
• Sketch and interpret magnitude and phase responses (Bode plots)
• Measure frequency response and compare to theory

Parts list

• Resistors (various values)
• Capacitors (10 nF — 10 µF)
• Inductors (small values for RL examples)
• Function generator or audio source (optional)
• Oscilloscope or sound card + software for measurements

Hands-On Mini Task: assemble a simple RC low-pass, measure the amplitude vs frequency, and sketch the Bode plot.

Diagram:

Step-by-step

1. Build an RC low-pass: input -> R -> C -> ground, output taken across the capacitor.
2. Calculate the theoretical cutoff: f_c = 1 / (2πRC).
3. Drive the circuit with a sine source and sweep frequency (audio generator or function generator).
4. Measure amplitude at each frequency (scope or sound-card + software) and plot magnitude (dB) vs frequency.
5. Compare measured cutoff and slope to the theoretical -20 dB/decade low-pass behaviour.

Worked example

Calculate f_c for R = 1 kΩ and C = 100 nF.

f_c = 1 / (2πRC) = 1 / (2π × 1e3 × 100e-9) ≈ 1.59 kHz.

Expected result

• The measured corner frequency should be within component tolerance of the calculated f_c.
• Magnitude plot should show ~0 dB at low frequencies for a unity-input case, and roll off at ~-20 dB/dec.

Navigation

• Previous: Introduction
• Next: Capacitors and Inductors