[SI-LIST] Re: why do I need mixed mode S parameters?
- From: "Loyer, Jeff" <jeff.loyer@xxxxxxxxx>
- To: <vince_cavanna@xxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Thu, 23 Sep 2004 08:14:36 -0700
My take, some of which was articulated in others' responses.
I have been forced to become familiar with mixed-mode S-parameters
because they indicate what I need to know about the behavior of a
differential bus, which is what many high-speed busses are now. The
single-ended S-parameters for a PCI Express Transmission Line (a coupled
differential pair), for instance, won't give you much indication of the
losses vs. frequency for that T-line. In fact, they may give you a very
erroneous representation. You need mixed-mode S-parameters to make
sense of your return and insertion losses for differential busses. =20
For example, for the following circuit:
p1 ------- p2
p3 ------- p4
p1 & p3 represent the 2 input halves of a differential pair (coupled),
routed as microstrip, p2 & p4 the output.
Take single-ended measurements of 1/2 of this coupled, microstrip
differential pair (S11 & S21, with ports 3 & 4 terminated to 50ohms).
If the trace is long enough and your VNA goes to a high enough
frequency, you'll find dramatic resonances (S21 drops significantly at
certain frequencies). Much of your energy appears to be "lost" at key
frequencies. What you've inadvertently created is a "coupled line
coupler", described in detail in Pozar's book. If you're unfamiliar
with mixed-mode parameters, you might conclude that a terrible thing is
happening at those resonant frequencies (and you will be in excellent
company, in my opinion). However, if you then measure S41, and from
that measurement calculate SDD21 (for reciprocal, symmetric systems, mag
SDD21 is mag(S21 - S41)), you'll find that, for the differential case,
there is no resonance. P.S. - nothing too exotic here, this can be
duplicated in Hspice. Single-ended S-parameters gave an erroneous
indication of a resonance that doesn't occur when the system is excited
differentially; mixed-mode S-parameters were needed to judge the actual
quality of the system.
Similar things might occur if you only measure single-ended S-parameters
for a differential pair going over a slot in a reference plane -
single-ended S-paramaters show horrible return loss (reflection), while
mixed-mode S-parameters indicate little reflection.
As another example, take the circuit below:
SE_p1 ------ SE_p2
Diff_p1 Diff_p2
SE_p3 ------ SE_p4
SE_p5 ------ SE_p6
Diff_p3 Diff_p4
SE_p7 ------ SE_p8
Here, SE_p1 and SE_p3 represent the 2 input halves of one differential
pair (Diff_p1), while SE_p5 and SE_p7 represent the inputs of another
differential pair. If these are signals going through a connector,
you're probably most interested in SDD11 (differential return loss),
SDD21 (differential insertion loss), SDD31 (differential NEXT), and
SDD41 (differential FEXT). S21, S63, S33, etc. won't tell you much
about the behavior of the differential signals going through the
connector. Also, you may not be interested in things like SCD31
(near-end crosstalk that ends up as common mode).
Again, mixed mode S-params are necessary to give you info. about what
you care about - single-ended S-params won't.
To my knowledge, no VNA equipment exists to measure mixed-mode S-params
directly (for the GHz frequencies I care about). You must measure the
single-ended S-params, and mathematically derive the mixed mode S-params
from those.
A very good explanation of mixed-mode S-params is the "RF Balanced
Device Characterization" webcast by Greg Amorese and David Ballo of
Agilent.
I think many future models will have to be 12-port representations (2
differential aggressors, 1 differential victim), possibly as 12-port
S-params (single-ended). Results from simulations that use those models
may then be converted to mixed-mode S-params to understand those
results.
Hope this helps without muddying the waters...
Jeff Loyer
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of vince_cavanna@xxxxxxxxxxx
Sent: Wednesday, September 15, 2004 1:59 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] why do I need mixed mode S parameters?
I have some philosophical questions about mixed mode S parameters that I
=3D
have been struggling to understand as I re-enter the field of signal =3D
integrity and attempt to catch-up on some of the new =3D
measurement/analysis techniques. I would appreciate any insight you can
=3D
offer.
I understand mixed mode S parameters and can compute them from standard
=3D
(single-ended) S parameters or from a model - or the other way around.
=3D
I can appreciate their usefulness in understanding how an n-port, that =
=3D
may have been designed to operate mainly under differential stimulus, =
=3D
responds to (reflects and scatters the incident power) differential and
=3D
common-mode stimulus.
What I am trying to understand is why I would ever want to use mixed =3D
mode S parameters in a time-domain or frequency domain simulation, and =
=3D
how to use them. I am also interested to learn what simulators support =
=3D
mixed mode S parameters directly, as using them in a simulator such as =
=3D
Hspice seems cumbersome. My approach today is to simply use standard S =
=3D
parameters directly.
The "why" I really don't understand at all. With regards to the "how", I
=3D
know of one approach but it is cumbersome and does not seem worthwhile.
=3D
I would be interested to know if there are circuit simulators that =3D
handle mixed mode S parameters directly but most important I need to =3D
understand why I need them.
One way to use mixed mode S parameters, that has been suggested on this
=3D
mailing list, is to use the S element in Hspice, but represented with =
=3D
the mixed mode S parameters instead of the standard mode S parameters, =
=3D
and recognizing that the ports are conceptual (differential and common =
=3D
mode) as explained in [ref1]. In order to interface the conceptual =3D
n-port to my circuit (which expects real ports) I then have to wrap the
=3D
device with a circuit that converts the actual port waves of my circuit
=3D
into the differential and common mode waves that need to be applied to =
=3D
the conceptual n-port. This approach should work but seems cumbersome =
=3D
and, more important to me, I don't understand what I gain from it.=3D20
The approach I described seems like a round-about way to attempt to use
=3D
the mixed mode S parameters directly when they can easily be converted,
=3D
with no loss of information, into standard mode S parameters and used =
=3D
directly with the S element of Hspice. Even better I would prefer to get
=3D
standard S parameters for my components so I don't need to do any =3D
conversions at all. In my simulations I prefer to see the physical ports
=3D
rather than the conceptual differential port and common mode port =3D
described in [ref1], and so the most appropriate model for me seems to =
=3D
be the standard s parameters. I can easily compute the various =3D
differential or common quantities from the circuit if that is what =3D
interests me.
I also don't understand why I would need mixed mode S parameters of a =
=3D
device from a vendor when I can compute them from the single-ended S =3D
parameters. I do understand that there may be benefit in mixed mode S =
=3D
parameters that have been extracted using a true mixed-mode (pure mode?)
=3D
VNA, but my understanding is that most VNAs available today actually =3D
apply single-ended stimulus and measure the standard S parameters, and =
=3D
then *compute* the mixed mode S parameters. That means I derive no real
=3D
benefit from the mixed mode s parameters other than the convenience of =
=3D
not having to do any computations. I don't consider this benefit =3D
significant since the calculations are quite straightforward and do not
=3D
suffer from numerical instabilities.
I may be missing some fundamental aspect about the mixed mode S =3D
parameters that would explain their popularity and if so I would love to
=3D
understand that.=3D20
Vince
[ref1]
Combined Differential and Common-Mode Scattering Parameters: Theory and
=3D
Simulation
David Bockelman and William Eisenstadt
IEEE Transactions on Microwave Theory and Techniques, vol 43, no. 7, =3D
july 1995
=3D20
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