Re: L/R response time

Andy Ingraham 18-Feb-1997 1154 (ingraham@wrksys.ENET.dec.com)
Tue, 18 Feb 97 11:54:17 EST

> I'm looking for an equation that expresses the output rise time of a
> series LR network as a function of input rise time. An explanation of
> the math behind it or a pointer to the derivation would be nice, too.

If the output is across the R, then you have a simple real-axis pole;
identical to an RC circuit with the output across the C. The time-
constant of the LR network is L/R; for the RC network it's R*C.

Given an ideal, zero risetime input pulse, the output risetime (if
you're talking about 10-90% risetimes) is 2.2 times the time-constant;
or 2.2*L/R. You have probably seen this before for RC networks.

Given a finite risetime input signal, and a system with its own
risetime (in response to ideal stimulus), the rule-of-thumb that I've
seen from time to time, is that the observed risetime is approximately
the root-sum-square of the input and system risetimes:

Tr(out) = sqrt( Tr(in)^2 + Tr(sys)^2 )

This is only an approximation, of course, but I think that's what
you're looking for. The actual response in a detailed analysis would
depend on the input waveform shape, not just its risetime.

Regards,
Andy Ingraham