Chapter 1 Circuit Simulation - Iowa State University

1 Chapter 1 Circuit Historical PerspectiveCircuit simulators, as we know them today, first began to appear inthe late 1960 s and early 70 s. However, it was the explosive growth ofthe integrated Circuit market in the 1970 s that precipitated the riseof importance of Circuit Simulation . With integrated circuits, proto-types were expensive to build and difficult to troubleshoot. Circuitsimulators were necessary to evaluate designs before they were fab-ricated. As designs became larger and more complicated, the needto use Circuit simulators groups contributed significantly to the development of the mod-ern Circuit simulator.

2 TheAstapgroup at IBM developed many ofthe numerical method s used. And theSpicegroup at the Univer-sity of California at Berkeley developed and propagated the de factostandard Simulation effort at Berkeley started as a class project of Rohrer. That modest beginning resulted in a flurry of simulationprograms being developed and culminated in the release ofSpicein1972 and thenSpice2 in written by Larry Nagel,then under the guidance of Prof. Don veryimportant for three reasons. First,Spicewasdesignedtobeusedtosimulate integrated circuits. Unlike the simulators that preceded it,Spicehad all the models one needed to simulate integrated circuitsbuilt into it.

3 As such, it was easier to use than earlier 1. Circuit SimulationSecond, the source code forSpicewas made available to anyonewho wanted it at a nominal cost. And third, Berkeley graduatestookSpicewith them as they went to work at electronics companiesthroughout the the late 70 s and early 80 s, most versions ofSpicewere propri-etary and only used in-house by the integrated Circuit the time, it seemed as if every large electronics company in thecountry had developed their own version ofSpice. This occurredbecause Circuit Simulation was vital to IC manufactures and at leastinitially, there were few commercial simulators available that weresuitable for IC design.

4 Also, the IC manufacturers viewed having agood version ofSpiceas a strategic advantage that allowed them toget designs to market quickly and situation began to change in the late 80 s and early 90 s asthe commercial simulators began to surpass the internally developedsimulators in terms of capabilities and performance. When this hap-pened, the strategic value of an internally developed simulator dis-appeared. Commercial simulators starting replacing internal simu-lators, starting with the smaller companies and working up. Today,only the largest companies are still developing their own the late 80 s, Berkeley upgradedSpiceby releasingSpice3, whichhad a new architecture that made it considerably easier to add newcomponent models and was written in C.

5 WhileSpice3 was architec-turally a big step forward fromSpice2, algorithmically it was largelythe the same time, Berkeley also released a new type of Circuit simu-lator called Spectre. Spectre used harmonic balance to directly com-pute the steady- State solution of nonlinear circuits in the frequencydomain. It was targeted for use on microwave circuits. Spectre waspicked up by Hewlett-Packard, where it became known as their Mi-crowave Nonlinear Simulator, or MNS, and by Cadence, where theharmonic balance algorithms were replaced by transient analysis took a slightly different approach with Spectre than is Algorithmic Perspective3ical.

6 Rather than trying to increase the speed of the simulator byloosening the tolerances or employing faster, but less reliable, timinganalysis algorithms, Cadence instead took a conservative started with the standardSpicealgorithms, discarded those thatreduced reliability, such as bypass, and implemented each one fromscratch with the goal of improving speed, as well as accuracy andreliability. By exploiting the 15 years of evolutionary improvementsin Simulation algorithms that had occurred sinceSpicewas written,Cadence was able to make Spectre 3-5 times faster than traditionalversions ofSpice, while improving its accuracy and was during the process of developing Spectre than many of theissues that are discussed in this book were first encountered andexplored.

7 It is because Spectre was designed to address these issuesthat it plays a central part in this book. However, the book doesnot focus exclusively on Spectre. It discusses issues applicable to allsimulators and so is useful for anyone that uses a Circuit more comprehensive history of Circuit Simulation in general, andSpicein particular, is available from Pederson [pederson84] and inVladimirescu sThe SPICE Book[vladimirescu94]. Algorithmic PerspectiveThe algorithms used inSpicenow define the traditional approach tocircuit Simulation . This approach is referred to as thedirect methodfor simulating a Circuit .

8 With direct methods, the nonlinear ordinarydifferential equations that describe the Circuit are first formulatedand then converted to a system of difference equations by a multi-step integration method such as the trapezoidal rule. The nonlineardifference equations are solved using the Newton-Raphson algorithm,which generates a sequence of linear equations that are solved usingsparse Gaussian elimination. Direct methods have proven to be themost reliable and general methods the late 70 s and early 80 s, attempts were made by several groupsto develop alternate approaches that would provide better perfor-mance on the large digital circuits of the day.

9 Two basic methodswere explored, explicit integration methods and relaxation 1. Circuit SimulationUsing explicit integration methods, such as forward Euler, eliminatesthe need to actually solve the large system of differential equationsthat describe the Circuit . Instead, the solution at a particular timestep is extrapolated from the previous time point. It is assumed thatthere are no floating capacitors and there is at least one capacitorconnecting every node in the Circuit to ground. The extrapolationis performed by evaluating the Circuit equations (not solving them)to determine the current into the grounded capacitors.

10 The slope ofthe voltage waveforms are then computed directly from v(t)=C 1i(t).( )Explicit integration methods are very fast, especially if the groundedcapacitors are linear and so are easily invertible. However, they havenot gained wide acceptance because they are unstable and so generateresults that blow-up if the Circuit contains time constants that areshorter than the time step being used. This is a serious problemthat makes explicit methods unstable on most circuits. Digital MOScircuits tend to have time constants that are all about the same size,so explicit methods can sometimes be used with great methods exploit latency in the Circuit by breaking it intosmaller pieces and solving each piece independently.