Group Delay (Approximation)

τg ≈ 1 / (2π × BW)

Quick answer

This calculator solves τg ≈ 1 / (2π × BW) for Group Delay. With Bandwidth 10 MHz, the result is 15.92 ns. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Group Delay (ns)
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Formula

τg ≈ 1 / (2π × BW)

Description

Group delay represents the time delay experienced by the envelope of a modulated signal passing through a filter or transmission system. For a first-order system with bandwidth BW, the group delay is approximately 1/(2π×BW). Constant group delay across the passband means all frequency components arrive at the same time, preserving signal shape. Variation in group delay (group delay distortion) causes pulse spreading and intersymbol interference in digital communications. Bessel filters are designed specifically for flat group delay.

Variables

  • τg — Group delay (s)
  • BW — 3 dB bandwidth of the system (Hz)

Practical Notes

This approximation applies to simple single-pole systems. Higher-order filters have more complex group delay profiles. Butterworth filters have moderate group delay variation, Chebyshev filters have significant variation near the passband edge, and Bessel filters have maximally flat group delay. In high-speed serial links (PCIe, USB3), group delay variation must be minimized to maintain eye diagram quality.

Symbols and units

Symbol Meaning Default unit Accepted units
tg Group Delay ns ps, ns, µs, ms, s, min, h
BW Bandwidth MHz Hz, kHz, MHz, GHz

Step by step

  1. 1. What you know: Bandwidth 10 MHz
  2. 2. The relation: τg ≈ 1 / (2π × BW)
  3. 3. Substitute: BW = 10 MHz
  4. 4. Result: Group Delay = 15.92 ns

Worked examples

Minimum range

Given: Bandwidth 100 kHz

Result: Group Delay = 1.592 µs

Low range

Given: Bandwidth 1 MHz

Result: Group Delay = 0.1592 µs

Typical

Given: Bandwidth 10 MHz

Result: Group Delay = 15.92 ns

High range

Given: Bandwidth 100 MHz

Result: Group Delay = 1.592 ns

Maximum range

Given: Bandwidth 1 GHz

Result: Group Delay = 0.1592 ns

Solving for each variable

Solve for Group Delay

Bandwidth 100 kHz → 1.592 µs

Solve for Bandwidth

Group Delay 100 ps → 1.592 GHz

How Group Delay changes with Bandwidth

Bandwidth (input) Group Delay (result)
1 MHz 0.1592 µs
2.5 MHz 63.66 ns
5 MHz 31.83 ns
7.5 MHz 21.22 ns
10 MHz 15.92 ns
15 MHz 10.61 ns
20 MHz 7.958 ns
40 MHz 3.979 ns
70 MHz 2.274 ns
100 MHz 1.592 ns

The same result in other units

Unit Value
ps 15920
ns 15.92
µs 0.01592

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Frequently asked questions

How do you calculate Group Delay (Approximation)?

Use τg ≈ 1 / (2π × BW). With Bandwidth 10 MHz, Group Delay works out to 15.92 ns.

How do you calculate group delay?

Rearrange for Group Delay: with Bandwidth 1 MHz, Group Delay is 0.1592 µs.

What is the formula for Group Delay (Approximation)?

The formula is τg ≈ 1 / (2π × BW). Group delay represents the time delay experienced by the envelope of a modulated signal passing through a filter or transmission system.

How do you find Bandwidth when you know the other values?

Rearrange for Bandwidth: with Group Delay 100 ps, Bandwidth is 1.592 GHz.

What units does Group Delay (Approximation) use?

Group Delay is shown in ps, ns, µs. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

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