**From:** Curry, Clifford (*[email protected]*)

**Date:** Tue Apr 10 2001 - 14:34:23 PDT

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Hi: about rise time adding in an rms fashion....

I believe this approximation comes about by expressing the delay and the rise

time of a system functions of the "moments" of the impulse response. When you

do this, the delay and rise time can be found from derivatives of the frequency

response... or the first couple of terms in a series expansion of the frequency

response around w=0.

Then... the *magnitude* of the frequency response is expressible as a series in

w^2, since it is an even function. The expansion looks like

H(w)= A0 ( 1 - (tr)^2*w^2/( 4*pi) + .....) * exp(phase stuff). tr is the

rise time.

When two networks are cascaded, their magnitude functions are multiplied, and

the series expansion of the result is A01*A02 * ( 1 - (tr1^2 +tr2^2)/(4+pi) +

......) .

So, total rise time = sqrt of sum of squares of component rise times.

I believe this approximation works well for linear systems without overshoot. I

don't have a reference for this, although

the relation of rise time and the series expansion of the frequency response is

talked about in "Signal Analysis" by A. Papoulis on page 107.

Regards,

Cliff Curry

-----Original Message-----

From: [email protected] [mailto:[email protected]]

Sent: Tuesday, April 10, 2001 1:44 PM

To: [email protected]

Subject: [SI-LIST] : Rise Time Degradation

Hello All.

I am involved in some discussions (arguments) over an EIA test spec for rise

time degradation (RTD) of connectors/interconnects. The spec in question is

EIA-364-102. It is downloadable from:

http://www.ec-central.org/PDF/Engineering/EIA364/EIA-364-102.pdf.

Basically, this spec uses a "square root of the sum of the squares" type of

calculation, where, first, the RTD of a test fixture is measured. The

connector or whatever DUT is then inserted into the fixture, and the RTD of

this combination is measured. The RTD of the DUT is then calculated from

these two measurements using the sum of squares method.

Does anyone know where this method originated? I have seen a few references

that refer to it as a rule of thumb type calculation for cascading RTD's of

various devices. I have also seen a basic mathematical justification for it

in relation to oscilloscope bandwidths/risetimes. But in that case, it was

assumed that the devices being cascaded where R-C type networks. And even

then, I believe they said it was an approximation.

Not that I want to question the technical reasoning of the EIA or anything,

but does anyone out there have an opinion on how accurate this method might

be when applied to interconnects? Or might someone possibly even have a

mathmatical/physical justification for this method?

Thanks for any help anyone might offer.

Julian Ferry

Samtec, Inc.

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