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

From: Mike Jenkins ([email protected])
Date: Tue Apr 25 2000 - 19:03:35 PDT

Teddy,

* 'Zodd' is half of what people think of as differential
impedance.
* Your implicit assumption seems to be that the dif'l
pair is symmetrical.
* Cself and Cm aren't explicitly defined. I assume they
represent the Spice, "node-to-node" style capacitances,
not elements from a short circuit capacitance matrix.
* The measurement and formulas for Lm and Cm seem to assume
the electrical length is short compared to the wavelength
of 'w'. These formulas are only approximations.
(Watch out for those assumptions!)
* Measurements to isolate Lself and Cself might not be
all that easy. I guess you'd use the s11 in your two
measurements, but separating these values from fixture
parasitics could be tricky. I prefer time-domain,
TDR-based measurements myself to see better what's going on.

Regards,
Mike

Teddy Chou wrote:
>
> 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
> > --

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