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Rise time, bandwidth and critical length calculator

From the rise time of a signal, get its bandwidth and knee frequency and the trace length above which reflections matter. Longer traces need controlled impedance and termination.

How it is calculated

Bandwidth. For a 10–90 % rise time tr, the 3 dB bandwidth of a single-pole response is BW = 0.35/tr. The knee frequency, above which the spectrum of a digital edge falls off quickly, is fknee = 0.5/tr.

Critical length. A trace behaves as a lumped connection while its delay is short compared with the edge. The calculator uses the common rule that a line longer than one sixth of the edge length needs to be treated as a transmission line: Lcrit = tr·v/6, with v = c/√εeff. Some guides use a quarter or a half instead of a sixth, which gives longer limits.

References

  1. H. Johnson, M. Graham, High-Speed Digital Design: A Handbook of Black Magic, Prentice Hall, 1993, chapters 1 and 4.
  2. E. Bogatin, Signal and Power Integrity – Simplified, 3rd ed., Prentice Hall, 2018.

Questions

Why does rise time matter more than clock frequency?

Reflections and crosstalk depend on how fast the edge changes. A slow clock with fast edges needs the same care as a fast clock.

Which effective dielectric constant should I enter?

For a stripline use the dielectric constant of the material. For a microstrip it is lower, about 3.0 to 3.4 on FR-4. The microstrip calculator gives the exact value for your trace.

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