Rise Time to Bandwidth

Formula

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.