Bessel Filter Group Delay
τ = R × C
Quick answer
This calculator solves τ = R × C for Group Delay. With Resistance 10 kΩ, Capacitance 100 nF, the result is 1 ms. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Bessel (Thomson) filters are designed for maximally flat group delay, meaning all frequency components within the passband experience the same time delay. This preserves the waveshape of transient signals and prevents pulse distortion. For a first-order section, the group delay equals the RC time constant. Bessel filters have the gentlest rolloff of all classical filter types but excel in applications where signal fidelity matters more than frequency selectivity, such as pulse measurement, medical instrumentation, and audio crossovers.
Variables
- τ — Group delay of the filter section (s)
- R — Resistance (Ω)
- C — Capacitance (F)
Practical Notes
Bessel filter rolloff is only 20 dB/decade per order initially but steepens at frequencies well above cutoff. The step response has no overshoot for orders up to about 6. Bessel filters are harder to design than Butterworth because the pole locations are not evenly distributed. Pre-computed Bessel polynomial coefficients are used for practical designs.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| tau | Group Delay | µs | ps, ns, µs, ms, s, min, h |
| R | Resistance | kΩ | mΩ, Ω, kΩ, MΩ |
| C | Capacitance | nF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Resistance 10 kΩ, Capacitance 100 nF
- 2. The relation: τ = R × C
- 3. Substitute: R = 10 kΩ, C = 100 nF
- 4. Result: Group Delay = 1 ms
Worked examples
Minimum range
Given: Resistance 100 Ω, Capacitance 100 pF
Result: Group Delay = 10 ns
Low range
Given: Resistance 1 kΩ, Capacitance 1 nF
Result: Group Delay = 1 µs
Typical
Given: Resistance 10 kΩ, Capacitance 100 nF
Result: Group Delay = 1 ms
High range
Given: Resistance 100 kΩ, Capacitance 1 µF
Result: Group Delay = 100 ms
Maximum range
Given: Resistance 1 MΩ, Capacitance 10 µF
Result: Group Delay = 10 s
Solving for each variable
Solve for Group Delay
Resistance 100 Ω, Capacitance 100 pF → 10 ns
Solve for Resistance
Group Delay 100 ns, Capacitance 100 pF → 1 kΩ
Solve for Capacitance
Group Delay 100 ns, Resistance 100 Ω → 1 nF
How Group Delay changes with Resistance
| Resistance (input) | Group Delay (result) |
|---|---|
| 1 kΩ | 100 µs |
| 2.5 kΩ | 0.25 ms |
| 5 kΩ | 0.5 ms |
| 7.5 kΩ | 0.75 ms |
| 10 kΩ | 1 ms |
| 15 kΩ | 1.5 ms |
| 20 kΩ | 2 ms |
| 40 kΩ | 4 ms |
| 70 kΩ | 7 ms |
| 100 kΩ | 10 ms |
The same result in other units
| Unit | Value |
|---|---|
| ns | 1000000 |
| µs | 1000 |
| ms | 1 |
| s | 0.001 |
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<p><a href="https://vbatpower.com/formulas/bessel-delay/">Bessel Filter Group Delay</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Bessel Filter Group Delay?
Use τ = R × C. With Resistance 10 kΩ, Capacitance 100 nF, Group Delay works out to 1 ms.
What is the formula for Bessel Filter Group Delay?
The formula is τ = R × C. Bessel (Thomson) filters are designed for maximally flat group delay, meaning all frequency components within the passband experience the same time delay.
How do you find Resistance when you know the other values?
Rearrange for Resistance: with Group Delay 100 ns, Capacitance 100 pF, Resistance is 1 kΩ.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Group Delay 100 ns, Resistance 100 Ω, Capacitance is 1 nF.
What units does Bessel Filter Group Delay use?
Group Delay is shown in ns, µs, ms, s. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Filters formulas →Need more features?
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