The ability of a SPICE simulator to reliably produce correct results depends on how well these methods are implemented.

Newton iteration involves expanding each nonlinear circuit device I-V curve as a Taylor series but keeping only the first two terms and then solving the resultant system of simultaneous linear equations.

Robustness of Newton iteration depends on (1) having all circuit element I-V curves being continuous in value and slope and (2) all nonlinear elements being bypassed with capacitance so that the previous time step solution is a good starting point for the Newton iteration of the current time point.

The Taylor series is multidimensional—one dimension for each unknown voltage node in the circuit. A better approach is to simply to get the processor to do the math at the theoretical FLOP limit of the underlying hardware.

LTspice eliminates the overhead in getting the data to the FPU with self-authoring assembly language source written at run time, after matrix memory has been allocated, and the addresses returned from malloc() are known.

Analog circuit simulation requires numerical integration of differential equations to track the behavior of the capacitances and inductances. Trap ringing has been feared to be so unacceptable to analog circuit designers7 that trap integration has been eliminated from one commercial SPICE implementation, PSpice, leaving the slower and less accurate Gear integration as the only available option. But Gear integration doesn’t just dampen numerical ringing, it dampens all ringing, even physical ringing, making it possible for a circuit that malfunctions in real life, due to an oscillation, to simulate as perfectly stable and functional because the instability was damped out of numerical existence. In principle, Gear integration error could be reduced by having the IC designer stipulate a small maximum time step. PSpice’s documentation states that it uses a modified Gear method and does indeed seem better at picking a small enough time step to reduce the error than the Gear integration implementation in Berkeley SPICE. Figure 3 shows that PSpice’s modified Gear integration artificially dampens the ringing, whereas LTspice immediately yields the correct solution. Figure 3 shows PSpice Gear integration clearly doesn’t correctly integrate the two reactances of a trivial circuit with only one node.

PSpice incorrectly simulates this circuit as stable, whereas LTspice gives the correct result. Figure 5 compares PSpice’s erroneously stable result (left) with the correct, oscillating result from LTspice (right).

What is needed is a method with the speed and accuracy of trap but without the ringing artifact. LTspice uses an integration method, modified trap, that has the speed and accuracy of trap but without the ringing artifact. To demonstrate the ability of LTspice modified trap to eliminate trap ringing, we need a circuit that is prone to trap ringing.

Since LTspice has been the most popular SPICE program for the last ten years,9 it has seen a lot of circuits and there is a lot of knowledge libraried into the solver to avoid trap ringing, so one has to work a little to find a counter example. Note that most SPICE programs won’t run this deck as intended because most SPICE programs use the Meyer capacitance model for this type of MOSFET. Both LTspice and PSpice have replaced the Meyer capacitance model with the Yang-Chatterjee charge model. LTspice was not the first SPICE implementation, nor is it the only free SPICE, but it is the best and most widely used SPICE implementation.

Newton iteration, sparse matrix methods, and implicit integration are the core numerical methods of SPICE. In the end, a SPICE simulator needs to earn designers’ confidence that it can correctly solve for circuit behavior. Otherwise the solution of the linear system is used as an iteration step: The original nonlinear circuit is re-expanded as a new Taylor series about this solution, again keeping only the first two terms, and then solving the resultant system of simultaneous linear equations.

Eliminating the unknowns of a matrix involves mostly addition, subtraction and multiplication. Literature on this points out the numerical solution is not singular if a small enough time step is guaranteed, but in practice, an approach with explicit integration and limited time step size doesn’t work unless you can numerically integrate with infinite precision.

Some users are predisposed to be suspicious of SPICE because of popular literature denigrating the value of SPICE simulation. LTspice is downloaded four times per minute and is the topic of the largest users’ group of any simulator. LTspice® IV is a powerful, fast and free simulation tool, schematic capture and waveform viewer with enhancements and models for improving the simulation of switching regulators.

Three numerical methods used in SPICE account for its success in analog circuit simulation.

This article outlines why LTspiceIV® is better at yielding correct results than other SPICE implementations. If the solution of the linear system is indeed the very point about which the Taylor series was expanded, then, because the Taylor approximation is exact at that point and accurate near it, the solution of this linear system is in fact the correct solution to the original nonlinear circuit.1 Success of convergence of Newton iteration results in finding a numerical proof that the correct solution of your circuit was found. Conditions (1) and (2) are met by any physical circuit, but SPICE programs usually don’t get this right because the semiconductive devices in Berkeley SPICE have discontinuities and these implementation errors have spilled over to pay-for SPICE implementations. Such discontinuities exist in most of the semiconductive devices in PSpice but none of the semiconductive devices in LTspice. For an analog IC, this can be 100,000 distinct voltage nodes, leading to a conductivity matrix of 100,000 by 100,000, or eighty billion bytes for double precision matrix coefficients.

The issue is that it takes longer to get the numerical data to the FPU than it does to actually perform the FLOP.

Ultimately, this is a consequence of the fact that all operating systems use dynamic memory allocation.

This late-authored code can resolve concrete matrix element addresses in line with the code so the data can be efficiently loaded, allowing the FPU to operate with the pipeline full once the code is assembled and linked with LTspice’s built-in assembler and linker.

This is where one sees some of the largest differences between one SPICE implementation and another: the method(s) available for integrating the differential equations. But this is not a viable solution because (1) small time steps slow simulation speed to a crawl and (2) there’s no way to ensure that the time step is small enough anyway. It is easy to compose a trivial circuit and see the PSpice numerically integrated result deviate dramatically from the true solution than can be found by inspection.

The error in PSpice can be reduced by stipulating a smaller maximum time step (fourth number in the .tran statement). The nature of the error of Gear integration is to make circuits look more stable in simulation than they actually are in real life. PSpice Incorrectly Indicates the Circuit as Stable in the Face of a Large Signal Transient. To this quest, whereas PSpice eliminated trap ringing by using Gear integration but tries to pick a good time step, another approach is to use a de-tuned version of trap integration so that it will damp trap ringing but only introduce a hopefully acceptably small error in the true circuit behavior. You might be able to find a value of trapdamp that duplicates the integration behavior of HSPICE8. Modified trap is a method I invented some years ago and was widely available first in LTspice. Note that there is no change in ringing amplitude even after it rings for thousands of cycles. Trap ringing is initiated when discrete time step second order integration has trouble representing the exact continuous-time circuit behavior. Figure 6 shows a circuit that causes trap ringing due to the highly nonlinear capacitance of the gates of an unusually dimensioned MOSFET inverter. Because the Meyer capacitance model doesn’t conserve charge and is inaccurate for short channels, it fell into obsolescence in the 1990s. Since both simulators use the same updated charge storage equations, they should give the same results. The simulator’s robustness, speed and integrity hinge on how well these methods are implemented. This is impossible if the solver doesn’t perform the core numerical methods correctly. The process repeats until the proof that the correct solution has been found is successful.

The error doesn’t add up to infinity because of round off error but because of approximating the derivative with sampled finite differences. Using distribution and use figures of other SPICE implementations based on private communication with representatives from the respective companies that sell those other SPICE programs, LTspice is distributed and used three orders of magnitude more than any other SPICE program. The value of a simulator hangs on how well it can predict physical reality, and how quickly it can produce results. For example, even if you write out the conductively matrix of a circuit that looks like a fishnet grid of resistors, the matrix is almost diagonal because each node is resistively connected only to adjacent nodes. At the time the simulator is written and compiled, the memory location storing the matrix data isn’t known. LTspice is unique in implementing a self-authoring, self-assembling and self-linking sparse matrix solver. But trap integration can give rise to a numerical artifact where the integrated discrete time step solution oscillates time step to time step about the true continuous-time behavior. Consider Figure 2, which shows a parallel tank circuit with a parallel piecewise linear current source. To put the consequences of this error in the perspective of a practical example, Figure 4 shows an audio power amplifier that isn’t stable because compensation capacitor C2 is too small. If a small enough time step is stipulated in the PSpice simulation, you can force it to approach the correct solution, suggesting that PSpice is interpreting the device equations of the transistors correctly, PSpice just isn’t accurately integrating the differential equations. Nevertheless, I do not recommend using this option because it dampens real circuit behavior and it isn’t necessary in LTspice, which uses a better method of eliminating trap ringing. To the best of my knowledge, it is the best means to integrate the differential equations of an analog circuit and is not duplicated in any other SPICE program. This demonstrates that LTspice modified trap does not introduce artificial numerical damping. It can be reduced or eliminated with judicious use of time step and integration order control. If you would like to reproduce this result in LTspice, go to the SPICE pane of the Control Panel and select trapezoidal integration instead of the default, modified trap. But when we compare the PSpice simulation to LTspice, as shown in Figure 8, PSpice shows remarkably erroneous results. Since analog circuit matrices are so sparse, improving LU factorization with SuperLU does not give as much speed advantage as one might hope.

I must be about my Father's business and some ME time tooooo.A I won't be online, nor will I have a computer. Discrepancy between simulated and real performance can send a product into costly iterative debugging cycles. To illustrate an example, Figure 1 shows the I-V curve of a diode in PSpice2 versus LTspice. At run time the simulator requests memory with function call malloc(), which returns an address at which the simulator is allowed to safely store matrix data.

This can cause the user to be suspicious of the correctness of the simulator even though each trapezoid contains the correct integrated area. Modified trap is also used by LTspice to produce Figure 5, where LTspice correctly exposes the amplifier’s instablity. Since it isn’t humanly possible to give each matrix element its own name, arrays are used.

The solution should be that the tank circuit resonance is excited by the spike of current and thereafter ring at constant amplitude.

LTspice does also support the use of the other known methods, trap and Gear, but simply so that a user can duplicate the erroneous results from other SPICE simulators to verify that the models are interpreted the same and only the integration method is different. This artifact is almost certainly due to an error in differentiating the Yang-Chatterjee charge equations to capacitances in the PSpice Yang-Chatterjee charge model implementation. In fact, the Greek tense used in that verse tells us that God actually commandsA us to come to Him when we need wisdom. This means the simulator asks for fewer, but larger, pieces of memory, and the individual coefficients are indexed off the base address returned by malloc().

All that is known at simulator compile time is the address of the address of the base address off which one indexes to reach the matrix element. The word para means alongside of, and it depicts a very close, side-by-side, intimate position next to someone else.

If we want wisdom,we must come right up alongside of God in order to obtain it.A You see, God wants a relationship with us. But for us to get what we request, we must ask a€?of God.a€? In other words,we must come right up alongside of God, getting as close to Him as possible, and then make our request. If we will fulfill this requirement of coming close to God and opening our hearts to Him and to His touch, He will then gladly open His hand and show us every answer we need.A But be prepared for God to show you additional things you werena€™t expecting to see! When you come into His glorious light, that light penetrates you and reveals defects and dark places in your soul and behavior patterns that need to be changed. That is why James says that God a€?a€¦giveth to all men liberally, and upbraideth nota€¦.a€? The word a€?givetha€? is the Greek worddidontos, which comes from the word didomi. The wordA didomi means to give, but the form used here is didontos, which describesA one who is in the habit of constantly giving. This assuredly tells us that God is not one who holds out on His people or who refrains from giving them wisdom when they need it. Instead, James tells us that God isA in the habit of giving wisdom to His people when they need it.

It depicts something that is given generously, abundantly, plentifully, bountifully, and open-handedly. You see, if wea€™ll meet Goda€™s requirement to come close to Him, He will profusely answer the questions we have and impart the wisdom we need.A The words a€?upbraideth nota€? are from the Greek wordA oneididzo, which means to rebuke or to reprove.

Youa€™ll find God to be open-heartedA and ready to answer any question you ever put to Him. Ita€™s time for you to learn how to spend time in the Presence of theA Lord so He can shine His glorious light upon your life!

Let HisA glory shine on you and reveal the dark areas in your life that need to be changed. Stay in His PresenceA long enough to let the wisdom you are seeking sink into your spirit and soul.A Never forget that God is a€?the giving Goda€? who wants to meet your need. I am so sorry for the times Ia€™ve been in such a hurry that I neglectedA spending time with You. He wants to give me all the wisdom and answers I need, but firstA I must meet His requirement to come close to Him. When I get right next to God, He isA obliged to open His hand and show me everything I need to see.

What results have you experienced in your life because of the dailyA quiet time you spend with the Lord?A 3.

Youa€™ll find God to be open-hearted and ready to answer anyA question you ever put to Him.

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