3 dB Bandwidth Explained (RC Low-Pass Filter) | Cutoff Frequency Made Simple
n this video, we explain the 3 dB bandwidth of an RC low-pass filter in a clear, step-by-step way—no skipped logic.
We start from the filter response and show how to find the cutoff frequency, where the signal begins to significantly attenuate.
🔍 What you’ll learn
How to compute the magnitude of the filter response
Why the 3 dB point corresponds to half power
Why this leads to a magnitude of 1 divided by square root of 2 (~0.707)
Step-by-step derivation of the cutoff frequency
Why the result is:
👉 cutoff frequency = 1 / (R × C)
🎥 Visual Approach
Built with Manim Community Edition, this video includes:
Why is the cutoff point always 0.707?
This video shows the math AND the intuition behind the 3 dB rule.
Clean step-by-step animated equations
A memory-trail system so you never lose track of the logic
2D graph showing the magnitude response
Visual highlight of the cutoff point (3 dB)
3D visualization of the complex frequency response (real + imaginary parts)
🧠 Key Insight
The “3 dB” point is not arbitrary:
It represents half the power of the signal
Since power depends on the square of the magnitude:
→ magnitude becomes about 0.707 of its maximum value
👉 This is why the cutoff frequency naturally emerges from the math.
📌 Why this matters
Understanding 3 dB bandwidth is essential for:
Filter design
Signal processing
Electronics and communication systems
Interpreting frequency response and Bode plots
🏷️ Tags
3dB Bandwidth, RC Filter, Cutoff Frequency, Low Pass Filter, Signal Processing, Electronics, Bode Plot, Engineering Math, Manim Animation