RLC Circuit Bandwidth
BW = f0 / Q
Quick answer
This calculator solves BW = f0 / Q for Bandwidth. With Resonant Frequency 100 kHz, Quality Factor 0.5, the result is 0.2 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The bandwidth of a resonant RLC circuit is the range of frequencies over which the response is within 3 dB of its peak value. Higher Q means narrower bandwidth and sharper selectivity, while lower Q gives a broader, flatter response. This relationship is fundamental to tuned circuit design in receivers, transmitters, and filters. The -3 dB bandwidth is symmetric on a logarithmic frequency scale around the center frequency. For a series RLC circuit, BW = R/(2πL), showing that lower resistance gives narrower bandwidth.
Variables
- BW — -3 dB bandwidth (Hz)
- f0 — Resonant (center) frequency (Hz)
- Q — Quality factor (dimensionless)
Practical Notes
In filter design, the required Q determines component sensitivity and implementation difficulty. Q values above 10-20 require tight component tolerances. Active filters can synthesize high Q with resistors and capacitors. For very high Q requirements (>1000), crystal or ceramic resonators are used instead of LC circuits.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| BW | Bandwidth | Hz | Hz, kHz, MHz, GHz |
| f0 | Resonant Frequency | kHz | Hz, kHz, MHz, GHz |
| Q | Quality Factor | — | — |
Step by step
- 1. What you know: Resonant Frequency 100 kHz, Quality Factor 0.5
- 2. The relation: BW = f0 / Q
- 3. Substitute: f0 = 100 kHz, Q = 0.5
- 4. Result: Bandwidth = 0.2 MHz
Worked examples
Minimum range
Given: Resonant Frequency 100 Hz, Quality Factor 0.025
Result: Bandwidth = 4 kHz
Low range
Given: Resonant Frequency 1 kHz, Quality Factor 0.25
Result: Bandwidth = 4 kHz
Typical
Given: Resonant Frequency 100 kHz, Quality Factor 0.5
Result: Bandwidth = 0.2 MHz
High range
Given: Resonant Frequency 0.5 MHz, Quality Factor 0.8
Result: Bandwidth = 0.625 MHz
Maximum range
Given: Resonant Frequency 5 MHz, Quality Factor 8
Result: Bandwidth = 0.625 MHz
Solving for each variable
Solve for Bandwidth
Resonant Frequency 100 Hz, Quality Factor 0.025 → 4 kHz
Solve for Resonant Frequency
Bandwidth 5 Hz, Quality Factor 0.025 → 0.125 Hz
Solve for Quality Factor
Bandwidth 5 Hz, Resonant Frequency 100 Hz → 20
How Bandwidth changes with Resonant Frequency
| Resonant Frequency (input) | Bandwidth (result) |
|---|---|
| 10 kHz | 20 kHz |
| 25 kHz | 50 kHz |
| 50 kHz | 100 kHz |
| 75 kHz | 150 kHz |
| 100 kHz | 0.2 MHz |
| 150 kHz | 0.3 MHz |
| 0.2 MHz | 0.4 MHz |
| 0.4 MHz | 0.8 MHz |
| 0.7 MHz | 1.4 MHz |
| 1 MHz | 2 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 200000 |
| kHz | 200 |
| MHz | 0.2 |
| GHz | 0.0002 |
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<p><a href="https://vbatpower.com/formulas/rlc-bandwidth/">RLC Circuit Bandwidth</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate RLC Circuit Bandwidth?
Use BW = f0 / Q. With Resonant Frequency 100 kHz, Quality Factor 0.5, Bandwidth works out to 0.2 MHz.
How do you calculate formula of bandwidth in rlc circuit?
Rearrange for Bandwidth: with Resonant Frequency 1 kHz, Quality Factor 0.25, Bandwidth is 4 kHz.
What is the formula for RLC Circuit Bandwidth?
The formula is BW = f0 / Q. The bandwidth of a resonant RLC circuit is the range of frequencies over which the response is within 3 dB of its peak value.
How do you find Resonant Frequency when you know the other values?
Rearrange for Resonant Frequency: with Bandwidth 5 Hz, Quality Factor 0.025, Resonant Frequency is 0.125 Hz.
How do you find Quality Factor when you know the other values?
Rearrange for Quality Factor: with Bandwidth 5 Hz, Resonant Frequency 100 Hz, Quality Factor is 20.
What units does RLC Circuit Bandwidth use?
Bandwidth is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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