Re: [SI-LIST] : Question about Gear vs Trapezoidal methods for simulations within HSPICe

Dmitri Kuznetsov ([email protected])
Thu, 05 Mar 1998 17:24:29 -0800

Hi Elias,

Higher-order Gear's numerical integration formulas are more accurate
than the trapezoidal rule. However, Hspice uses the second-order
Gear's, which has the same order of accuracy as the trapezoidal. The
difference is that the trapezoidal rule has ideal stability properties,
and Gear's does not.

If the circuit is stable (the response settles down with time),
asymptotically stable (the response keeps oscillating indefinitely), or
unstable (the response grows indefinitely), so will be the trapezoidal
simulation. The second-order Gear's can produce stable results for
unstable and asymptotically stable circuits.

For instance, if you simulate an ideal LC tank circuit using
trapezoidal, it will keep oscillating indefinitely, as it should. With
the Gear's, the oscillations will be damped as if the circuit had loss.
Higher-order Gear's can also produce unstable results for stable
circuits, but you do not have to worry about that in Hspice.

The dampening effect of the Gear's method makes the waveforms look
smooth even if they are not accurate. For the trapezoidal rule, the
error shows up as ripple in the waveforms, so you can see right away
that your timestep is to big.

The "smoothness" of Gear's simulation results is often misinterpreted as
higher accuracy, and even U-element chapter of Hspice manual recommends
using Gear's for this reason. The W element (Hspice's new lossy
multiconductor frequency-dependent transmission-line model) performs the
integration analytically, and is not affected by Gear's or trapezoidal

I would recommend using trapezoidal (which is the default) for all
Hspice simulations, and reduce the timestep if you see the ripple.


Dmitri Kuznetsov, Ph.D.
The W-element Engineer, Hspice Group

Avant! Corporation e-mail: [email protected]
46871 Bayside Pkwy. Tel: (510)413-8631
Fremont, CA 94538 Fax: (510)413-7706

Elias Lozano wrote:
> Hi Everyone:
> I have a question for all of you spice users of tranmission analysis and
> PCB/signal integrity.
> What method have you guys used for simulations? Do you prefer the Gear
> Method or do you prefer the Trapezoidal method? There are some charge
> conservation issues within the process spice model that can affect what
> method is best used.
> Can anyone comment on this for me and explain your reasons for using
> either of the methods?
> Thanks
> Elias