Physics Insights

Published on July 19, 2025 by Gaurav Pachauri

🔍 What is a Low Pass Filter?

A Low Pass Filter (LPF) is a basic electronic circuit that allows signals with a frequency lower than a certain cutoff frequency to pass through, and attenuates frequencies higher than the cutoff.

Understanding the Low Pass Filter

The low pass filter allows low-frequency signals to pass while attenuating high-frequency signals. Here's an embedded diagram:

Low Pass Filter by Gaurav

As you can see in the diagram above, ...

It is commonly used in audio systems, signal processing, and many areas of physics and engineering where it is necessary to remove high-frequency noise or smoothen a signal.

⚙️ RC Circuit as a Low Pass Filter

A typical LPF is made using a resistor (R) and a capacitor (C) in series, with the output voltage measured across the capacitor. When an alternating signal is passed through, the capacitor’s impedance varies with frequency.

The cutoff frequency $f_c$ is given by:

$$f_c=\frac{1}{2\pi RC}$$

For frequencies much lower than $f_c$, the output is nearly equal to the input. For higher frequencies, the capacitor acts like a short, and the output voltage drops.

📉 Frequency Response

The gain of the filter as a function of frequency is: $$|H(f)|=\frac{1}{\sqrt{1+(2\pi fRC{)}^2}}$$

This equation shows that as $f\to 0$, the gain approaches 1, and as $f\to \mathrm{\infty }$, the gain approaches 0.

🎮 Interactive Simulation

You can experiment with the Low Pass Filter using the interactive simulation below: for eg.

V(input) = 10

R(ohm) = 1000

Z(impedence) = 0.000001

frequency = 1000

🔗 Applications of LPF

• Removing high-frequency noise in analog circuits
• Audio signal processing to smooth output
• Anti-aliasing filter before analog-to-digital conversion
• Extracting low-frequency trends from data (e.g., EEG, ECG)