[SI-LIST] Re: Time domain AMS-SI tools

  • From: Ihsan Erdin <erdinih@xxxxxxxxx>
  • To: Mark_Burford@xxxxxxxxxxx
  • Date: Wed, 30 Nov 2005 12:32:27 -0500

Mark,
Things with frequency dependent parameters are a bit more complicated than
the solution of Laplace's equations for static field distribution in the
cross-section of the lines. The parameters, particularly the resistance and
inductance are first calculated as a function of frequency up to a cutoff
frequency value which is determined by the signal edge rate. Rigorous EM
tools do that by solving the diffusion equation in the cross-section of the
conductor usually using FEM but any other domain discretizing method like
finite difference could be used, as well. Although 2D EM simulators are fast
when computation as a function of frequency is involved the overhead may be
too high for circuit simulators like hspice. They alternatively resort to
less rigorous but fast approaches which take the advantage of the predicted
behavior of the skin effect loss. Take the resistance, for example. It can
be approximated as the square root of the frequency.
The next phase involves the frequency domain data being included in the time
domain computations. For a linear system, we could simply solve the whole
problem in the frequency domain first and get the time domain response by
Fourier transform. But since the driver and receiver circuitry is nonlinear
this is not possible. The spice-like time domain circuit simulators first
convert the frequency dependent lossy parameters into the time domain
and convolve it with circuit equations. The convolution however, requires
the whole time domain data to be processed at every time step, which is
impractical. A technique called recursive convolution is used to speed up
the process. To apply recursive convolution, the frequency dependent
parameter data has to be put in a pole-residue form using a curve-fitting
technique. This mathematically simple technique has big physical
implications. Any noise (measurement, numerical round-off error, etc.) in
the data may easily result in a non-causal system which messes up the time
domain simulation. This issue has been one of the greatest challenges of all
high speed circuit simulators since the last two decades and continues to
be. Currently, the most common technique that simulators use in order to
obtain a causal system is to constrain the data in curve fitting.That,
however results in convergence problems in some cases.
To sum up, there is not a perfect solution to the simulation of frequency
dependent parameters in the time domain simulation engines. However, all the
major tools in the market (that I know) are way better than what they were
five years ago when it comes to the modeling of the transmission medium.
With proper selection of the simulation parameters, one can get results that
match the lab measurements in multi-gigabit range very well. Provided
that the device models have the same level of accuracy...

Regards.

Ihsan


On 11/30/05, Mark Burford <Mark_Burford@xxxxxxxxxxx > wrote:
>
> OK so the tools for the most part I assume now to use FEM and a
> frequency is perhaps used to allocate mesh spacings, higher =
> freq=3Dsmaller
> mesh=3Dmore accurate simulation.  So can anybody tell me exactly how the
> tool would deal with and allocate say resistances / losses as a random
> (and when I say random I mean the tool doesn't know what is coming)
> signal passes through the model with varying edge rates.=20
>
> The interconnect for example would cause a slower rise time of the
> signal if the signal had a faster edge rate as the faster edge rates
> would be attenuated more due to skin effect as one of the hindrances to
> the signal. How would the tool deal with a fast edge and a slow edge in
> the same simulation and hence be able to show ISI for example. I know
> most time domain tools allow ISI to be explored but how can varying edge
> rates be accommodated in a simulation that is only aware of a single
> given frequency?
>
> Surely more (higher) parasitics need to be modelled and simulated for
> faster edge rates and less (lower) parasitics need to be modelled and
> simulated for slower edge rates.
>
> How do tools cope with this?
>
> Mark
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto: si-list-bounce@xxxxxxxxxxxxx]
> On Behalf Of Andrew Burnside
> Sent: 30 November 2005 12:53
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Time domain AMS-SI tools=20
>
> Mark.
> :As is initial stab at understanding to include such effects one must
> :tell the tool at which frequency we would like the simulation run and
> an
> :internal 2D field solver will allocate appropriate parameters for skin
> :effect etc at that frequency and then run waveforms through the model.
>
> The frequency is often used to set the mesh spacing of the 2D field
> solver, as this is a finite element process.
> Obviously, smaller mesh sizes take longer to calculate. Also, knowing
> the frequency will allow enable the use of low frequency approximations
> where appropriate e.g. remove small parasitics.
>
> Regards
>
> Andrew
>
>
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