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# 2 - Choice of algorithms for the preferred trade-off between
speed and accuracy to increase designer’s productivity |
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Several ways of accelerating mixed signal
simulation:
- change of integrator: accuracy goes down while speed increases. The designer’s expertise serves to determine which algorithm would optimize his need for stability and accuracy of results versus speed of simulation.
- accelerating the model or partitioning the circuit: for any integrator, such a method accelerates simulation with neither loss of stability nor of accuracy
- using linear approximations or table-based simulation: for any integrator, simulation speed then is increased with same stability, but at a loss of accuracy
- using relaxation: whatever the previous choices, this algorithm accelerates simulations for CMOS transistors in switching mode, with a hardly lesser accuracy
Stability is a first order issue: accuracy comes next…
So that a simulator is truthful only if it provides:
stable results,
close to silicon measurements,
with accuracy within 10 % at least…
Speed versus Accuracy and Stability Trade-offs
See how gullibility with respect to Golden
simulators may hurt your design!
Here is a simple examples with
differences of stability and accuracy between basic integrators:
Trapeze (green curve), Gear 2 (blue curve) and Backward Euler
(red curve).
Such a circuit is a simple LC filter structure:
the physically correct result is provided by the Trapeze method
for this kind of circuit.
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Analysis of the stability of
integrators and algorithms for simulating electronic circuits
equations is a considerably more difficult task than finding the
accuracy. To begin with, there are different ways of defining
stability, but it is essentially the capability to provide a truthful
simulation result.
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Stability regions are important because
they reflect the rate at which errors are propagated in approximate
solutions. Just as there are absolute and relative errors in numerical
analysis, there are also absolute and relative measures of stability.
A given numerical method for a problem can be recast into the framework
of approximation theory. The goal is then to study how well this approximant
behaves when compared with the solution. There is a kind of paradox
here, for if the solution were known then you would have no need to
resort to a numerical approximation. Since generically analytic solutions
to problems cannot be found, it is essential to calibrate all simulation
techniques by comparison to silicon measurements for ensuring realism!
This issue illustrates why mixed signal
Systems-on-Chip needing multi-level modeling impose upon the simulator
to put at designers’ disposal simple guidelines and tutorials.
SWIFT for time-domain electrical simulations
Circuit simulators provide accurate time domain current and voltage waveforms from a device level description of an integrated circuit. However, as the size of the circuits increases, the cost of such analyses becomes prohibitive. An important part of the simulation time is dominated by the time required to evaluate model device equations, such as the Berkeley transistor model BSIM3v3 or the even more complex BSIM4v2.
Our patented SWIFT algorithm accelerates time-domain electrical simulations of transistor-based circuits.
Key features
- simplified setup with a single threshold value
- no counter indication concerning the applicable class of circuits
- continuous and dynamical tuning for speed-accuracy trade-off
- acceleration 2 to 3 times for all transistor based circuits in transient analysis
- reduced loss of accuracy (< 1%)
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SWIFT algorithm |
Description of the Innovation
The SWIFT algorithm is a device model approximation by combination of the modes of a simplified device model and of the full device model. While the full mode requires full transient behavior evaluation of transistor model equations, the simplified mode uses a linear approximation based on the small-signal behavior evaluation of the transistor model equations.
SWIFT is more and more efficient at accelerating simulation compared to the conventional mode as:
- the approximation area (threshold value) is larger,
- the percentage of quiet transistors is bigger,
- the maximum time step of simulation is smaller.
Last but not least, thanks to the SWIFT algorithm, SMASH can deliver the results from Monte Carlo and “Imbalance Locate” analyses two to three times faster than simulators using a conventional SPICE algorithm.
Combine simplified and full device model modes
Problem position
With the ever increasing size of circuits, complexity of device model equations and diminishing size of fabricated devices, the need for simulation is twofold: of increased speed and of increased accuracy, both to match the increased performances of actual devices.
However, for true productivity gains, the speed vs. accuracy compromise must be aimed at improving designers’ productivity.
Difficulty of solution
Generally speaking, there are several ways of accelerating time-domain electrical or mixed signal simulations:
- Changing the integration solver method: accuracy goes down while speed increases. The designer’s expertise serves to determine which algorithm would optimize his need for stability and accuracy of results versus speed of simulation,
- Accelerating the model or partitioning the circuit: for any integrator, such a method accelerates simulation with neither loss of stability nor loss of accuracy,
- Using linear approximations or table-based simulation: for any integrator, simulation speed then is increased with same stability, but at a loss of accuracy,
- Using relaxation: whatever the previous choices, this algorithm accelerates simulations for CMOS transistors in switching mode, with a hardly lesser accuracy.
The SWIFT algorithm can be combined with any of the solutions above to produce even faster time-domain electrical simulations!
The Dolphin innovation
Thanks to a patented solution based on the implementation of the SWIFT algorithm, SMASH enables accelerating time-domain electrical simulations:
- the user only needs to specify the value that defines the threshold between the approximation and non-approximation modes. If the threshold value is set to zero, the accurate model is always used.
- the SWIFT algorithm continuously and dynamically tunes the compromise between speed and accuracy.
- unlike other methods, there is no counter indication concerning the applicable class of circuits since the algorithm makes no simplifying hypothesis on weak couplings between nodes.
- the SWIFT algorithm has the advantage of having a reduced loss of accuracy (usually less than 1%) providing fast simulation. The resulting simulation is 2 to 3 times faster according to tested circuits.
An application note is available
And the winner is...
of course the mixed-signal Virtual Components of the FLIP catalog: JAZZ for PLL's, Converters and CODEC as well as RagTime for Embedded Memories!
< SMASH Differentiators
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