Rise Time to Bandwidth

BW = 0.35 / tr

Quick answer

This calculator solves BW = 0.35 / tr for Bandwidth. With Rise Time 10 ns, the result is 35 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Bandwidth (MHz)
—

Formula

BW = 0.35 / tr

Description

This empirical relationship connects the 10-90% rise time of a digital signal to the approximate bandwidth of its frequency content. A signal with a 1 ns rise time contains significant spectral energy up to 350 MHz. This is critical for PCB design because trace lengths that approach a fraction of the wavelength at this bandwidth require controlled impedance and proper termination. The 0.35 constant assumes a single-pole (Gaussian) response; for multi-pole systems the constant may be closer to 0.45.

Variables

  • BW — Approximate bandwidth containing significant spectral content (Hz)
  • tr — Signal rise time, 10% to 90% (s)

Practical Notes

For EMI compliance, the third or fifth harmonic of the knee frequency is often the limiting factor. Faster rise times than necessary create EMI problems without improving digital functionality. Many modern logic families allow slew rate control to optimize the tradeoff between signal integrity and EMI.

Symbols and units

Symbol Meaning Default unit Accepted units
BW Bandwidth MHz Hz, kHz, MHz, GHz
tr Rise Time ns ps, ns, µs, ms, s, min, h

Step by step

  1. 1. What you know: Rise Time 10 ns
  2. 2. The relation: BW = 0.35 / tr
  3. 3. Substitute: tr = 10 ns
  4. 4. Result: Bandwidth = 35 MHz

Worked examples

Minimum range

Given: Rise Time 100 ps

Result: Bandwidth = 3.5 GHz

Low range

Given: Rise Time 1 ns

Result: Bandwidth = 0.35 GHz

Typical

Given: Rise Time 10 ns

Result: Bandwidth = 35 MHz

High range

Given: Rise Time 100 ns

Result: Bandwidth = 3.5 MHz

Maximum range

Given: Rise Time 1 µs

Result: Bandwidth = 0.35 MHz

Solving for each variable

Solve for Bandwidth

Rise Time 100 ps → 3.5 GHz

Solve for Rise Time

Bandwidth 100 kHz → 3.5 µs

How Bandwidth changes with Rise Time

Rise Time (input) Bandwidth (result)
1 ns 0.35 GHz
2.5 ns 140 MHz
5 ns 70 MHz
7.5 ns 46.67 MHz
10 ns 35 MHz
15 ns 23.33 MHz
20 ns 17.5 MHz
40 ns 8.75 MHz
70 ns 5 MHz
100 ns 3.5 MHz

The same result in other units

Unit Value
kHz 35000
MHz 35
GHz 0.035

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Frequently asked questions

How do you calculate Rise Time to Bandwidth?

Use BW = 0.35 / tr. With Rise Time 10 ns, Bandwidth works out to 35 MHz.

How do you calculate bw time rise?

Rearrange for Bandwidth: with Rise Time 1 ns, Bandwidth is 0.35 GHz.

What is the formula for Rise Time to Bandwidth?

The formula is BW = 0.35 / tr. This empirical relationship connects the 10-90% rise time of a digital signal to the approximate bandwidth of its frequency content.

How do you find Rise Time when you know the other values?

Rearrange for Rise Time: with Bandwidth 100 kHz, Rise Time is 3.5 µs.

What units does Rise Time to Bandwidth use?

Bandwidth is shown in kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Digital Logic formulas →
CMOS Dynamic Power Rise Time to Bandwidth Setup Time Margin Static Power Dissipation Clock Skew Timing Margin Logic Noise Margin Digital Fanout Pull-Up Resistor for Logic

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