[SI-LIST] Algorithm for finding derivatives in Hspice
- From: "Dmitriev-Zdorov, Vladimir" <vladimir_dmitriev-zdorov@xxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Wed, 30 Dec 2009 09:48:25 -0700
Ben,
I'm not familiar with HSPICE code in particular, but it should be common
for circuit simulators to internally create a system consisting of
differential and algebraic equations. Very often such systems include
derivatives on capacitor voltage (charge) or inductance current (flux).
After the system is solved at some time point, nothing special is
required to explicitly estimate those derivatives and report them (no
numerical differentiation is needed). Another possibility is to use a
polynomial approximation of the solution vector that is created by the
simulator for predicting LTE error. Once such polynomial is available,
the derivatives of all participating terms could be naturally retrieved,
where the limit on the order of accurately reported derivative is
related to the order of the polynomial that in its turn depends on the
order of numerical integration technique (Gear, trapezoidal, Euler,
etc.)
Elaborating this point further, one could question the situation where
no derivatives present in the circuit equations. Imagine pure resistive
(possibly non-linear) circuit and a source voltage/current given by
sufficient number of sampling points. Are derivatives reported still
accurate?
Vladimir
Date: Tue, 29 Dec 2009 15:43:33 -0500
Subject: [SI-LIST] Algorithm for finding derivatives in Hspice
From: Ben <ben01010@xxxxxxxxx>
Hi you all;
By any chance, does any one of you friends know that, what is the
allegorist
behind the command "deriv" in hspice to calculate the derivatives of
signals.
A very straightforward numerical approach (comes to mind) is working
difference ratio out at subsequent time-points as
(s(t2)-s(t1))/(t2-t1).
This, in spite of being mathematically meaningful, of course does not
bear a
noticeable practical value. (e.g.) for it to be a adequately close
approximation for the derivative waveform of a signal one may need a
very
high sapling rate and then all the practical issues from over-sampling,
understandable.
I managed simple investigations to compare the results from forming the
difference-ration (above) with the ones from deriv command in hspice.
--> It is easily seen that how hspice uses the assumption of causality
in
physical systems to prevent the reduction in the count of
time-points,which
is one per derivative-order.
--> For the first order derivative even one may get a feeling that, the
results from difference-ration (above) is closer to the results from
analytical-form also better understandable in compare with the ones
from
"deriv".
--> Superiority of the hspice "deriv" is revealed when moving to the
second
or higher order derivatives.
--> I got a sense that hspice employs a technique such as (a high order)
interpolation to create inter-samples surrogate data.
I wish a year full of happiness and prosperity for every one of you in
2010.
Regards;
Ben.
------------------------------------------------
ben01010(at)gmail(dot)com
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