RC Filter Frequency Response

Lesson notes

Overview

A simple RC low-pass filter attenuates frequencies above its cutoff by 20 dB per decade. This topic is rated intermediate and is number 35 of 93 in Engineering. Builds on the basics with relationships, methods and trade-offs.

What you are seeing

The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

The gain of a first-order RC low-pass filter is |H| = 1/√(1 + (f/f_c)²). It is flat in the passband, falls to −3 dB at the cutoff, and then drops by 20 dB for every tenfold increase in frequency, a decade. On a Bode plot, with log frequency, the roll-off is a straight line of slope −20 dB/decade. Steeper filters use more stages, with a slope of −40 dB/decade for each additional pole pair.

Reading the relationship

The expression "|H| = 1/√(1 + (f/f_c)²)" is a compact summary of the idea. It uses the symbols H, f, f_c; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, and a square root, so the result grows more slowly than the quantity inside it. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.

Try this

Predict the outcome first, then test extreme slider values to find where the pattern changes or breaks.

Common pitfalls

Always ask what the safety margin is and which assumption would break the design first. Idealised models hide losses, noise and limits.

How it connects

It builds on “Amplitude Modulation”, the topic before it in Engineering. Once you are comfortable, continue with “Pulse-Width Modulation”.

Why it matters

Engineers use this idea to design structures, machines and systems that are safe, efficient and reliable.