[SI-LIST] Re: (no subject) - full summary
- From: Matthew Herndon <mherndon@xxxxxxxxx>
- To: "'si-list@xxxxxxxxxxxxx'" <si-list@xxxxxxxxxxxxx>
- Date: Tue, 21 Jan 2003 16:21:33 -0800
There were over 25 requests for my longer summary of the "(no subject)"
thread about s-parameter simulation in SPICE and about dispersion, so
here it is!
Happy reading!
-matt
Matt Herndon, PhD
ECAD Group
Apple Computer
Using s-parameters in SPICE, and comparison of dispersion and loss.
====================================================================
Summary of SI-list thread from December 2002, with subject "(no
subject)".
by Matthew K. Herndon, PhD
ECAD Group
Apple Computer, Inc., Cupertino, CA
The original question was submitted by Mick Zhou of Agere on Dec 6,2002
[1]:
Has "anybody successfully generate broadband (DC-20GHz) SPICE model
from S matrix for complex structures using the SPICE generator in
ADS?"
Responses indicated that the following additional simulators have this
capability; there was various discussion of accuracy, speed, ease of
use, bugs, etc.
PLEASE NOTE THAT THIS LIST IS NOT INTENDED TO BE COMPLETE --- IT
CONTAINS
ONLY THOSE SIMULATORS WHICH WRERE DISCUSSED IN THE THREAD OR WERE MADE
KNOWN TO ME; I DID NOT DO A PRO-ACTIVE SEARCH.
Appologies for anything missing:
Fullwave SPICE (Ansoft)
IConnect (TDA Systems)
Nspice (Apache)
Broadband Spice (Sigrity)
Apsim (Applied Simulation Technology)
Spectre (Cadence)
ELDO/ADMS (Mentor, formerly Anacad)
Micro-Cap (Spectrum Software, requires easy conversion to Y parameters)
Some circuit simulators do not support frequency-dependent sources. ADS
does not, HSPICE and PSPICE do.
[R6] gives a nice example of the process for simulating with s-parmeters
in PSPICE.
Aside: "Touchstone compatible" is an ASCII format for S-parameter data,
based on Agilent EEsof. For more information, type "Touchstone
s-parameter format" in Google; or see, for example, [R1].
At this point, we split into two sub-threads: generating SPICE models
without frequency-dependent lookup tables, and the relationship between
dispersion and loss.
Spice models without frequency-dependent sources:
=================================================
In theory, one can create accurate lumped-element (RLC) models of
measured s-parameters. In practice, one needs to overcome a few
difficulties, especially for broadband simulation and for long lines. In
particular, it is hard to accurately model complicated frequency
dependencies and dispersion [6]. But this approach does work
well in some situations; and converges for the same reason that the
Fourier transform converges [8] (Note: I would like to know more about
this analogy).
There are two approaches to simulating s-parameters in SPICE-like
simulators (items (1) and (2) here quote and summarize [26]):
(1) Convert S-parameters to certain forms, either equivalent circuit
representations or certain table lookup format, from which SPICE engines
can read and run.
(2) Enable a SPICE solver to read S parameters directly. The SPICE
solver will then internally do the things in (1), or do convolution
directly which can be quite demanding for computer resources for large
number of such circuit components. Often the original S-parameters or
the circuit model representing them may not be stable, causal, and
passive. Also, extrapolation of the S-parameter data to DC is often a
problem and separate DC values may be needed.
Lumped-element models do have some advantages [17]: frequency-dependent
capacitance and inductance are not needed, and we don't have to know
anything about the dielectric properties other than what is implicitly
contained in the measurements. No assumptions are made about TEM or
quasi-TEM propagation. The only assumption is a linear, time-invariant
system. In principle, a linear, time-invariant system can certainly be
accurately represented by lumped elements to within the accuracy of the
measurements themselves, and up to the highest frequency at which the
measurements were taken.
It takes a lot of lumped elements to (perfectly) match the measured
s-parameters. One calculation for a connector came up with 400K
elements. So "curve fitting" approximations are used, analogous to (but
different from) lossy data compression algorithms like JPEG. For
example, a tenth order rational function would require only 40 (?)
elements (10 for the numerator, 10 for the denominator, not sure where
the other factor of 2 comes from).
Questions then arise about how good the approximations are. How high an
order of rational function do you need? Clearly it depends on the
complexity of the shape of the s-parameters curve. And if you happen to
drive the circuit at frequencies where the curve-fit is poor, you can
get erroneous results (imagine a single sinusoid at a point where the
curves are far apart).
One can check the accuracy of the reduced lumped model by running a
time-domain simulation, taking the Fourier transform, and comparing to
the s-parameters. Of course, you can only do this for the linear parts
of the circuit. As [53] says, this "check is only the first step towards
a more complex simulation with on-chip and off-chip elements. If we fail
the simple check, we cannot trust the results of the more complex
simulation."
Dispersion and loss
===================
These terms are sometimes used interchangeably, which is confusing and
should not be done; they are two different concepts.
Dispersion means that the velocity of spectral components of a signal
depend on frequency. This effect is not the same as loss, either skin
effect or dielectric loss. Dispersion means different frequencies travel
at different velocities, effectively scattering or "dispersing" the
arrival times of the signal wavefront [14]. Dispersion happens when Er
varies with frequency (so therefore velocity varies with frequency), as
in a prism.
You can have dispersion without loss e.g., a rectangular wave guide
(RWG). So conceptually the two are not related: dispersion is related to
phase velocity, loss is related to energy [16]. However, you cannot have
frequency-dependent loss without dispersion. So, for example, the skin
effect will cause dispersion. Further, if the dispersion is caused by
the dielectric material (the most common situation in SI), there must
also be loss; this property follows from the Kramers-Kronig relationship
[R7] (aka causality). Kramers-Kronig states that the real and imaginary
parts of the dielectric constant are related to each other [15]. The
real part determines velocity, the imaginary part the loss (due to
dampening of the vibrating dipole moments). So in this sense, you can
say that if a MEDIUM is "dispersive" it must also be "lossy".
Microwave engineering uses a number of models that satisfy the
Kramers-Kronig relation. One example is the Debye model, which was
originally developed in the area of studies of the relaxation of crystal
lattices. It turns out that the physical mechanism of loss is quite
similar to the mechanics and physics of these lattice structures. There
are also other models of dielectric permitivity and loss that are also
physically consistent. All of them require what we call loss tangent
and permitivity (which gives rise to Er) to vary somewhat across
frequency. [49]
[40] FR4 is non-isotropic and has significant changes in Er across
frequency ([R3] says 4.2 to 4.0 over the range 0.5 to 5 GHz). The
dependence of Er on frequency is not a simple, intuitive function. Real
air exhibits some change in Er with frequency due to humidity; pure
(dry?) air does have a flat response and extremely low losses. Likewise
some other materials, e.g., Rogers and some PTFE (teflon) and ceramic
materials (see [R4] and [R5]).
The telegraphers equations (quasi-TEM mode) assume a single,
homogeneous, isotropic material. Dispersion will (always?) occur if the
medium non-homogeneous, e.g., microstrip. If you neglect the losses
(i.e., assume ideal materials), stripline and coax will be
non-dispersive.
There was some discussion of whether dispersive media could actually
SHARPEN an edge. Possible in theory, but wouldn't happen in practice
(would it violate Kramers-Kronig?). There are devices which sharpen
rising edges (at the expense of lengthening falling edges) by varying
propagation velocity with amplitude. These devices construct
lumped-approximations to non-linear transmission lines. See, for
example, [R2].
In reality, manufacturing tolerances and non-uniformity of materials
causes much larger variations in actual transmission line performance
than the change in Er across frequency. However, that does not mean
that such an effect does not exist or does not provide interesting
insights into the workings of E&M phenomena.
References
===========
[R1] http://www.sigrity.com/download/pub/Touchstone.pdf
Touchstone format.
[R2] http://www.picosecond.com/objects/AN-13.pdf (edge compressors)
[R3] Dielectric and Magnetic Properties of Printed Wiring Boards and
Other Substrate Material Baker-Jarvis J., Riddle B, and Janezic M.
NIST Technical Note 1512. 1999
[R4] http://www.rogers-corp.com/mwu/techtip9.htm
Er vs. frequency.
[R5] http://www.dupont.com/kapton/general/spfreq.html
Er vs. frequency.
[R6] http://wwwinfo.cern.ch/ce/ae/Maxwell/apps/2stripem/2stripem.html
Discussion of obtaining s-parameters, using s2spice to create
an equivalent circuit, and simulating in PSPICE.
[R7] http://www.math.utah.edu/~eyre/research/kk/node1.html
Short discussion of Kramers-Kronig.
Following are postings to the SI list for this thread. Please note that
I tried to provide a citation anytime I quoted more than a sentence
from a
posting. Appologies if I missed someone.
[1] From: "Zhou, Xingling (Mick)" <xlzhou@xxxxxxxxx>
Date: Fri Dec 6, 2002 11:42:41 AM US/Pacific
[5] From: "Zhou, Xingling (Mick)" <xlzhou@xxxxxxxxx>
Date: Fri Dec 6, 2002 6:19:42 PM US/Pacific
[6] From: Yu Liu <yu_liu@xxxxxxxxxxxxx>
Date: Fri Dec 6, 2002 9:31:32 PM US/Pacific
[8] From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
Date: Mon Dec 9, 2002 11:05:10 AM US/Pacific
[9] From: "Loyer, Jeff" <jeff.loyer@xxxxxxxxx>
Date: Mon Dec 9, 2002 11:30:45 AM US/Pacific
[15] From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
Date: Mon Dec 9, 2002 4:44:28 PM US/Pacific
[16] From: Xin Wu <lifehappiest@xxxxxxxxxxx>
Date: Tue Dec 10, 2002 6:54:00 AM US/Pacific
[26] From: Raj Raghuram <raghu@xxxxxxxxxxx>
Date: Tue Dec 10, 2002 3:20:06 PM US/Pacific
[40] From: Scott McMorrow <scott@xxxxxxxxxxxxx>
Date: Wed Dec 11, 2002 10:45:28 AM US/Pacific
[49] From: Scott McMorrow <scott@xxxxxxxxxxxxx>
Date: Wed Dec 11, 2002 2:43:33 PM US/Pacific
Other interesting refences:
"Fields and Waves in Communications Electronics" by
Ramo, Whinnery, and Van Duzer?
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