# FW: [SI-LIST] : Differential TDR "Measurements"

From: Teddy Chou ([email protected])
Date: Tue Apr 25 2000 - 00:40:53 PDT

Hi Mike, Pat and all gurus,

For approach 2, it seems not clear to state how to get
differential impedance. In my opinion, the "magical
mathematics" is explained in one book, "C. R. Paul,
Introduction to Electromagnetic Compatibility, chap. 10,
1992". I state simply its results as follows.

For weakly coupled, electrically short lines ( or we can say
it's in the LOW FREQUENCY RANGE ), the coupling is a linear
combination of contributions due to the mutual inductance
Lm between the two circuits (inductive coupling) and the
mutual capacitance Cm between the two circuits (capacitive
coupling).
MEASUREMENT : Network Analyzer
Input end : at the source end ( of the aggressor line ),
so ...... Zsource = 50
Output end : at the far end ( of the victim line ),
so ...... Zfar_end = 50
i) For Zload =0, Znear_end =0,
=> | s21 | = 2 * w * Lm / Zsource
where w = 2 * pi * f.
ii) For Zload = Znear_end = infinite,
=> | s21 | = 2 * w * Zfar_end * Cm

-----------------------------------------------------
Utilizing | s21 |, we can get "Lm" and "Cm". They are
independent of frequency (?). Then

Zodd = ((Lself - Lm) / (Cself + 2 * Cm)) ^ 0.5
todd = ((Lself - Lm) * (Cself + 2 * Cm)) ^ 0.5

So it's equivalent to approach 1 measured in TDR
measurement.

Sincerely,

Teddy Chou
Signal & Timing Integrity Engineer,
VIA Technologies, Inc. Taipei, Taiwan, ROC
TEL : 886-2-22185452 ext : 6046
mailto:[email protected]
http://www.via.com.tw

> -----Original Message-----
> From: Mike Jenkins [mailto:[email protected]]
> Sent: Tuesday, April 25, 2000 11:05 AM
> To: [email protected]
> Subject: Re: [SI-LIST] : Differential TDR "Measurements"
>
>
> Pat,
>
> I've used both approaches. From a mathematical viewpoint,
> they are equivalent (assuming the system is linear and
> time-invariant -- which are pretty good assumptions).
>
> From a practical point of view, Approach 1 is a bit more
> expensive. However, the processing is "canned" inside
> the instrument, so less error prone. Approach 2 gives
> good insight to principles that anyone using dif'l signals
> ought to understand (e.g., coupling between lines lowering
> the impedance). But the chances of screw-ups are higher.
> For instance, if the two waveforms to be subtracted are
> not time-aligned, it's a mess.
>
> Hope that helps.
>
> Mike
>
> ps: You didn't explicitly state it for Approach 2, so
> I will note that TWO signals must be recorded for
> each measurement, the "rho(11)" reflection and the
> "rho(12)" coupling (although recording rho(21) in
> the second measurement is redundant, since it equals
> rho(12) theoretically).
>
> "Zabinski, Patrick J." wrote:
> >
> > We're working more and more with differential signals,
> > and subsequently dealing with more differential printed
> > circuit boards (PCBs). Over the past few years, we've
> > had difficulty with several PCB vendors
> > trying to obtain a controlled impedance 100 ohm
> > differential pair.
> >
> > The problem generally boils down to "who's measurement
> > do we believe"? We measure one impedance, while the
> > PCB vendor measures another.
> >
> > We've done some digging, and there appears to be two
> > approaches to measuring differential impedance, and I'd
> > like to hear what folks have to say about them.
> >
> > Approach 1: inject two signals of opposite polarity,
> > one into the true and one into the complement. The
> > complement signal is substracted from the true, and
> > you read the impedance just like a single-ended
> > measurement.
> >
> > Approach 2: Inject one signal into the true trace and
> > record its signal. Then, inject a signal into the complement
> > trace and record its signal. Then, with the magic of
> > mathematics, compile these two different captured signals
> > into an effective differential measurement.
> >
> > The equipment we have in-house uses Approach 1, while
> > nearly every board vendor we work with uses Approach 2.
> > Can anyone shed some light into the accuracies, sensitivities,
> > etc. of these two approaches? Are there cases where one
> > approach is better/worse than the other?
> >
> > Thanks,
> > Pat
> >
> > -----
> > Pat Zabinski ph: 507-284-5936
> > Mayo Foundation fx: 507-284-9171
> > 200 First Street SW [email protected]
> > Rochester, MN 55905 www.mayo.edu/sppdg/sppdg_home_page.html
> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Mike Jenkins Phone: 408.433.7901 _____
> LSI Logic Corp, ms/G715 Fax: 408.433.7461
> LSI|LOGIC| (R)
> 1525 McCarthy Blvd. mailto:[email protected] | |
> Milpitas, CA 95035 http://www.lsilogic.com |_____|
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
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