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Showing papers on "Electronic circuit simulation published in 1995"


Book
01 Jan 1995
TL;DR: The Designer's Guide to SPICE and Spectrer is an in-depth guide to circuit simulators from a designer's perspective: the pitfalls of circuit simulation, such as convergence and accuracy problems, are explained in terms a circuit designer is comfortable with.
Abstract: From the Publisher: The Designer's Guide to SPICE and Spectrer is an in-depth guide to circuit simulators from a designer's perspective: the pitfalls of circuit simulation, such as convergence and accuracy problems, are explained in terms a circuit designer is comfortable with. The book gives designers insight into why these problems occur and how to avoid them. It also provides practical advice on how to make many difficult measurements with a circuit simulator, such as loop gain of an op-amp or distortion measurements of such clocked circuits as d-to-a converters and sample-and-hold circuits. Finally, suggestions are given about how to handle difficult classes of circuits, such as oscillators, charge-storage or very large circuits. After reading The Designer's Guide to SPICE and Spectrer, you will spend less time fighting your simulator and more time exploring, understanding and designing your circuits.

209 citations


Patent
09 May 1995
TL;DR: In this paper, a C-language module is used to control simulation start, stop, single stepping, polling, interrupting and signal monitoring in an electronic design automation (EDA) system.
Abstract: In an electronic design automation (EDA) system, various models are simulated and interfaced to certain target systems, logic analyzers, modeler, functional testers, emulators, hardware accelerators, hardware modelers, or other simulators. An add-on circuit card connects the simulator to the external systems. A computer program controls simulation start, stop, single-stepping, polling, interrupting and signal monitoring. The software program includes a model input/ouput file, a model input/output parcer, a configuration module, an address generation module, a run-time module, and a C-language module.

124 citations


Journal ArticleDOI
TL;DR: In this article, a unified nonlinear state-space model for arbitrary switching converters is presented, which uses discrete-time modeling of switches and is valid for any electric circuit composed of ideal switches (externally or internally controlled), RLC elements and energy sources.
Abstract: A unified nonlinear state-space model for arbitrary switching converters is presented, which uses discrete-time modeling of switches. Although its compact and powerful notation is valid for all types of switching circuits, perhaps its main application field is power electronics. The proposed model is valid for any electric circuit composed of ideal switches (externally or internally controlled), RLC elements and energy sources. Therefore, the model is general considering semiconductor devices as ideal switches, which are dealt with as discrete-time dynamic systems. Thus the developed model may be either a hybrid continuous-discrete-time one or a full discrete-time one. Moreover, this model is valid as a circuit simulator. >

59 citations


Proceedings ArticleDOI
18 Jun 1995
TL;DR: In this article, the lumped-charge modeling technique is used to build a compact GTO model for power electronic convertor simulation, which consists of simplified fundamental semiconductor equations and provides most of the important characteristics of a GTO device under static and dynamic conditions.
Abstract: A systematic modeling approach, the lumped-charge modeling technique, is used to build a compact GTO model for power electronic convertor simulation. The model consists of simplified fundamental semiconductor equations and provides most of the important characteristics of a GTO device under static and dynamic conditions. >

44 citations


Patent
12 May 1995
TL;DR: In this article, an improved circuit simulator for simulating the response of a circuit to a transient is presented. But the simulator differs from a harmonic balance simulator in that the currents provided by each of the device subroutines include an additional term at each carrier frequency having the time dependency of the modulation envelope at that frequency, which necessitates a time-domain solution of the simulation problem.
Abstract: An improved circuit simulator for simulating the response of a circuit to a transient. The stimulating signal is represented by one or more carriers having time varying modulation envelopes. The simulator differs from a harmonic balance simulator in that the currents provided by each of the device subroutines include an additional term at each carrier frequency having the time dependency of the modulation envelope at that frequency. These additional current terms necessitate a time-domain solution of the simulation problem; however, the time steps are now determined by the time variation of the envelope instead of the time variation of the carrier. As a result, the number of time steps needed in the simulation is greatly reduced. The present invention may be implemented by modifying a conventional harmonic balance simulator. The modifications involve adding code to the various device routines to provide the current term corresponding to the modulation envelope. In the preferred embodiment of the present invention, either a charge term or a current term that depends on present and past values of the modulation envelope is provided by each device routine. The sum of the charge terms at each carrier frequency is then differentiated to provide the sum of the envelope current terms.

40 citations


Patent
Jeh-Fu Tuan, Peiqi He1
17 Apr 1995
TL;DR: In this paper, a method for power net analysis of integrated circuits is provided, where a circuit simulator determines current values for integrated circuit devices at specified supply voltages, and a power net simulator uses the current values to calculate characteristics of the power net.
Abstract: A method for power net analysis of integrated circuits is provided. A circuit simulator determines current values for integrated circuit devices at specified supply voltages. A power net simulator uses the current values to calculate characteristics of the power net. The characteristics include voltage drop, current density and ground bounce. A layout representation of the power net is shown on a computer display along with the user-specified characteristics.

37 citations


Journal ArticleDOI
S.G. Duvall1
TL;DR: This work integrates an efficient statistical circuit simulator with worst case design tools into a hierarchical performance design process, and employs two stages of worst case analysis, calibrated with statistical circuit simulation, serving as filters to screen out circuits that easily meet their performance requirements.
Abstract: Contradictory trends in the industrial design environment have increased uncertainty while decreasing the tolerance to uncertainty. Worst case design techniques, still widely used in industry, do not provide the accuracy required to design under these conditions. On the other hand, statistical design techniques do provide a significant improvement in accuracy, by virtue of their "circuit adaptive" behavior, but at a substantial cost in computational effort. One practical solution to improving the accuracy of worst case design without sacrificing efficiency is considered here. It integrates an efficient statistical circuit simulator with worst case design tools into a hierarchical performance design process. It employs two stages of worst case analysis, calibrated with statistical circuit simulation, serving as filters to screen out circuits that easily meet their performance requirements. This focuses the use of statistical circuit simulation on those circuits for which the improved accuracy provides significant benefit. This methodology has been applied with outstanding results in design and manufacturing. >

34 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of radiated radiofrequency interference (RFI) on the operation of digital systems are studied by simulating the response of simple logic circuits to incident plane waves.
Abstract: The effects of radiated radio-frequency interference (RFI) on the operation of digital systems are studied by simulating the response of simple logic circuits to incident plane waves. The simulation is accomplished by combining a linear electromagnetic moment-method model of the wire structure with a nonlinear circuit model of the solid-state components. The complete model is analyzed in the linear and nonlinear regimes as an example. It is shown how a circuit simulator, such as SPICE, can be used in the analysis of an arbitrary wire network loaded with logic circuits, by the process of representing the linear wire network as a lumped-element N-port /spl pi/ network and interfacing it to the nonlinear circuit simulator. Examples are given that demonstrate the occurrence of both static and dynamic failures under various RFI-field excitations and wire structure geometries. The prediction methods presented in this paper, can be used by EMC engineers to assess the likelihood of failures in RFI-exposed digital systems,.

32 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a simulation program designed for quartz crystal oscillator analysis using the full nonlinear Barkhausen criterion method, which nullifies both real and imaginary parts of a characteristic complex polynomial P(u,j/spl omega/) describing the oscillator behavior.
Abstract: The latest development of a simulation program designed for quartz crystal oscillator analysis is presented in this paper. The simulator being developed uses the full nonlinear Barkhausen criterion method. It consists of finding the frequency /spl omega//sub 0/ and the amplitude u/sub 0/ which nullify both the real and imaginary parts of a characteristic complex polynomial P(u,j/spl omega/) describing the oscillator behavior. Most of the nonlinearities come from the amplifying transistor described by using large signal admittance parameters y(u) obtained by means of an analog circuit simulator (SPICE). This paper presents the method used to derive and code the characteristic polynomial coefficients. This method has been successfully implemented for a Colpitts oscillator and is currently being used to build an oscillator library covering the most widely used structures. The validity and the predictive power of the model have been checked experimentally and the comparison between experimental results and simulation is presented and discussed. >

23 citations


Journal ArticleDOI
TL;DR: In this paper, an electrical macromodel of Mason's equivalent circuit for an interdigital transducer (IDT) is proposed which is compatible to a widely used general purpose circuit simulator SPICE endowed with the capability to handle negative capacitances and inductances.
Abstract: Surface Acoustic Wave (SAW) devices, are not normally amenable to simulation through circuit simulators. In this letter, an electrical macromodel of Mason's Equivalent Circuit for an interdigital transducer (IDT) is proposed which is compatible to a widely used general purpose circuit simulator SPICE endowed with the capability to handle negative capacitances and inductances. Illustrations have been given to demonstrate the simplicity of ascertaining the frequency and time domain characteristics of IDT and amenability to simulate the IDT along with other external circuit elements. >

23 citations


Proceedings ArticleDOI
25 Apr 1995
TL;DR: A parallel iterative method is presented which is embedded in the concept of a hierarchical circuit simulator where the problem inherent parallelism is used for speeding up purposes.
Abstract: The DiPaCS system, a distributed parallel circuit simulator implementable on multicomputer systems is introduced. Since high complexity and increasing problems in simulating integrated circuits imply an enormous computational expenditure we have tried to reduce the amount of simulation time by parallel processing. A parallel iterative method is presented which is embedded in the concept of a hierarchical circuit simulator where the problem inherent parallelism is used for speeding up purposes. >

31 Dec 1995
TL;DR: Analog IC Techniques lor Low-Voltage Low Power Electronics as discussed by the authors addresses many very important, but recent, techniques which enable electronics to operate at a low supply voltage and consume a minimum amount of power.
Abstract: Analog IC Techniques lor Low-Voltage Low Power Electronics addresses many very important, but recent, techniques which enable electronics to operate at a low supply voltage and consume a minimum amount of power. Apart from investigations at the device, circuit and system levels, the book provides a wealth of practical implementations, many worked out in silicon realizations. The book is intended for both the professional designer of low-voltage low-power analog integrated circuits and the graduate student in this specialized branch of electronics.

Proceedings ArticleDOI
28 Apr 1995
TL;DR: A phase-locked loop model including phase noise in the reference oscillator and voltage-controlled oscillator was developed and simulated and results were analyzed in the frequency domain using the discrete Fourier transform and compared to measurements.
Abstract: A phase-locked loop model including phase noise in the reference oscillator and voltage-controlled oscillator was developed and simulated. Simulations were performed using the transient analysis capabilities of the PSpice circuit simulator. Results were analyzed in the frequency domain using the discrete Fourier transform and compared to measurements.

Proceedings ArticleDOI
28 Apr 1995
TL;DR: An electrical component model for a micromechanical accelerometer that has been implemented in the general purpose circuit simulation tool APLAC and shows an excellent match with the measured frequency responses.
Abstract: An electrical component model for a micromechanical accelerometer is presented. In addition to the varying capacitances, the motion of the seismic mass and the damping gas films are described by means of an electrical equivalent circuit. The resulting model can be analyzed together with the interfacing electronics utilizing all analysis modes available in a circuit simulator. The model has been implemented in the general purpose circuit simulation tool APLAC. The model simulations show an excellent match with the measured frequency responses.

Journal ArticleDOI
TL;DR: In this paper, an integrated hydrodynamic device/harmonic-balance circuit simulators for second-harmonic transferred electron oscillators (TEO's) and heterostructure barrier varactor (HBV) frequency triplers are presented.
Abstract: Accurate and efficient simulations of the large-signal time-dependent characteristics of second-harmonic transferred electron oscillators (TEO's) and heterostructure barrier varactor (HBV) frequency triplers have been obtained. This is accomplished by using a novel and efficient harmonic-balance circuit analysis technique which facilitates the integration of physics-based hydrodynamic device simulators. The integrated hydrodynamic device/harmonic-balance circuit simulators allow TEO and HBV circuits to be co-designed from both a device and a circuit point of view. Comparisons have been made with published experimental data for both TEO's and HBV's. For TEO's, excellent correlation has been obtained at 140 GHz and 188 GHz in second-harmonic operation. Excellent correlation has also been obtained for HBV frequency triplers operating near 200 GHz. For HBV's, both a lumped quasi-static equivalent circuit model and the hydrodynamic device simulator have been linked to the harmonic-balance circuit simulator. This comparison illustrates the importance of representing active devices with physics-based numerical device models rather than analytical device models. >

Proceedings ArticleDOI
M. Rittweger1, M. Werthen1, J. Kunisch1, Ingo Wolff1, P. Chall2, B. Balm2, P. Lok2 
16 May 1995
TL;DR: In this paper, a 3D electromagnetic simulation of an entire mold injected plastic package including its coplanar environment is presented, where active elements are substituted by inner ports and the resulting network is connected with measured transistor data using a circuit simulator.
Abstract: A 3d electromagnetic simulation of an entire mold injected plastic package including its coplanar environment is presented. The active elements are substituted by inner ports. The resulting network is connected with measured transistor data using a circuit simulator. A comparison of the simulated data with measured results is shown. The influence of the package and therefore the meaning of such a simulation procedure is discussed. >

Journal ArticleDOI
01 Nov 1995
TL;DR: The paper describes a new synchronisation algorithm that avoids backtracking and prevents deadlock in mixed signal simulation, based on the draft standard for a simulation backplane published by the CAD framework initiative.
Abstract: The paper describes how mixed signal simulation has been performed using a simulation backplane. This work is based on the draft standard for a simulation backplane, published by the CAD framework initiative. The simulation backplane allows two or more circuit, logic or behavioural simulators to be coupled. A circuit is partitioned between the simulators, and changes in analogue and digital signals connecting the simulators may be passed through the backplane. Synchronisation of the various simulators is handled by the backplane, and the paper describes a new synchronisation algorithm that avoids backtracking and prevents deadlock. A version of SPICE has been integrated into the backplane, and true mixed signal simulation has been demonstrated. These results show that the simulation backplane is a viable technique for linking multiple simulators, but that the overheads caused by interprocess communications are significant.

Proceedings ArticleDOI
21 May 1995
TL;DR: In this paper, a circuit modeling technique based on time domain measurements for power/ground systems in electronic packages is presented, which is then incorporated with the circuit model of high speed digital drivers for switching noise simulation.
Abstract: In this paper, a circuit modeling technique based on time domain measurements for power/ground systems in electronic packages is presented. Equivalent circuit model of power/ground systems for an MLC package is then incorporated with the circuit model of high speed digital drivers for switching noise simulation.

Proceedings Article
01 Sep 1995
TL;DR: In this paper, a layout-to-circuit extractor, Space Space, is proposed to extract the parasitics of a circuit from the layout of the circuit, including the interconnect resistances, the ground and coupling capacitances and the substrate cross-talk.
Abstract: In modern VLSI design it is of vital importance to know the influence of parasitics on the behaviour of the circuit The most important parasitics are the interconnect resistances, the interconnect (ground and coupling) capacitances and substrate cross-talk In this paper we present new methods to model these parasitics directly from the layout of a circuit All methods are implemented in a layout-to-circuit extractor, Space Space scans the IC layout and during this process a netlist of the circuit is produced This netlist can be simulated with a circuit simulator, after appropriate stimuli have been added Thus it can be decided whether the design specifications are met or not The layout-to-circuit extractor, Space, is suitable for MOS, bipolar and BiCMOS processes It is capable of recognizing all common active and passive devices Furthermore it encorporates several methods to model parasitic effects, including substrate cross-talk, both in a heuristic and a fundamental approach In this paper we only discuss the fundamental, physics-based methods to obtain 3D models of the interconnect parasitics and the substrate cross-talk Basically we use principles from numerical methods and network theory to obtain a reduced, accurate electrical network describing the parasitics After the introduction of the methods, we illustrate the use of the proposed methods on practical examples for device characterization and detailed circuit verification We show that a good agreement with measurements is obtained

Proceedings ArticleDOI
21 May 1995
TL;DR: This article describes how an affordable SPICE-based analog circuit simulator is used to model mechatronic systems and discusses the modelling of electromechanical actuators and planar mechanisms more in detail.
Abstract: Mechatronic systems consist of components from different technologies, like electronics, electro-mechanics and mechanics. Simulation allows to examine the interactions between the various components. This article describes how an affordable SPICE-based analog circuit simulator is used to model mechatronic systems. A schematic editor has been customised to ease model entry. A large multitechnical library, consisting of electrical, electromechanical, mechanical and hydraulic components has been developed, in order to allow rapid prototyping of mechatronic systems. The article discusses the modelling of electromechanical actuators and planar mechanisms more in detail.

Book ChapterDOI
01 Jan 1995
TL;DR: This chapter presents the fundamental aspects of circuit-level electrothermal simulation and their implementation in the newly developed circuit simulator IETSIM and discusses a generalization of Miller's formula to account for temperature-dependent avalanche breakdown phenomena.
Abstract: The scope of previous work on electrothermal simulation using network analysis techniques has been limited due to the lack of avalanche breakdown models which can efficiently describe the temperature dynamics [59, 58, 89]. For EOS/ESD, an accurate description of temperature-dependent device electrical behaviour including breakdown phenomena is of central importance. This chapter presents the fundamental aspects of circuit-level electrothermal simulation and their implementation in the newly developed circuit simulator IETSIM. In Section 7.1, the temperature-dependent device parameters of the device models used in SPICE [6] are reviewed. This section also discusses a generalization of Miller’s formula [72] to account for temperature-dependent avalanche breakdown phenomena. Section 7.2 presents an algorithm that enables circuit simulators to safely handle avalanche breakdown characteristics. Section 7.3 introduces a thermal model that enables efficient coupling of the thermal and electrical device phenomena for circuit simulation. With all of these elements in place, Section 7.4 introduces the electrothermal circuit simulator iETSIM.

Proceedings ArticleDOI
TL;DR: The work described in this paper presents a method to simulate a complete comb-drive rate microgyroscope using the SPICE electronic simulation tool, and a set of important new findings are revealed from the analysis using this new tool.
Abstract: Microgyroscope applications are increasing in many fields, creating a need to develop low cost, compact gyroscopes. A full understanding of the operation principles and limitations of a rate gyroscope are essential in creating a small and low-cost device. Currently, there is no simulation tool available that can simulate both the electronic and nonelectronic components of a complete device. The work described in this paper presents a method to simulate a complete comb-drive rate microgyroscope using the SPICE electronic simulation tool. The simulation method given here can be generalized to a wide range of MEMS devices. An equivalent circuit was developed and simulated using SPICE. Results of the frequency response, and transient analysis are given. The results obtained reproduce the reported device operation. A set of important new findings are revealed from the analysis using this new tool. Using the transient analysis, for example, we can see that the requirement of a large quality factor of the sensor causes a very slow (open-loop) response and that a closed-loop operation is essential in this device. In addition, the nonideal factors are described and are analyzed using SPICE.

Proceedings ArticleDOI
28 Apr 1995
TL;DR: A multitechnical library has been developed for PSpice, a well-known, relatively inexpensive circuit simulator, which consists of electrical, electro-mechanical, mechanical and hydraulic components and contains models at different abstraction and accuracy levels.
Abstract: By applying the energy conservation principle, mechatronic systems can be converted to electric circuits, and be modeled in an analog circuit simulator. For rapid prototyping of mechatronic systems, an extensive component model library is required. At VTT Automation, a multitechnical library has been developed for PSpice, a well-known, relatively inexpensive circuit simulator. The library consists of electrical, electro-mechanical, mechanical and hydraulic components and contains models at different abstraction and accuracy levels. A schematic editor has been customized to allow user-friendly input of multitechnical systems.

Journal ArticleDOI
01 Feb 1995
TL;DR: In this article, a physical but compact Si/sub 1-x/Ge/sub x/Si heterojunction bipolar transistor (HBT) model is presented, which is based on the de Graaf-Kloosterman formalism for the modelling of the bipolar transistors, but adds important heterostructure device physics as well as physical properties of SiGe material.
Abstract: A physical but compact Si/sub 1-x/Ge/sub x//Si heterojunction bipolar transistor (HBT) model suited for device design and circuit simulation is presented. The model is based on the de Graaf-Kloosterman formalism for the modelling of the bipolar transistors, but adds important heterostructure device physics as well as physical properties of SiGe material. The model, implemented in the APLAC circuit simulator, shows how currents and charges depend on minority carrier concentrations, which in turn are functions of the heterojunction voltages. In this way, the influence of the built-in electric fields due to Ge concentration and doping density gradients, the bias-dependent transit times and the Early effect can be incorporated naturally. Comparisons between the model prediction and the experimental data for the DC current/voltage characteristics and cutoff frequencies in Si/sub 1-x/Ge/sub x//Si HBTs are included to demonstrate the model utility and accuracy.

Journal ArticleDOI
TL;DR: A method which enables dynamical electro-mechanical simulations within an electronical circuit simulator and extends this work to system descriptions including partial differential equations by applying the method of finite differences.
Abstract: The simulation of microsystems requires to handle the close coupling between electronical and mechanical components. This interaction between electronics and mechanics often is an inherent and essential property of such systems. Therefore, dynamical electro-mechanical simulations are indispensable for the examination of the system behavior. For this purpose, we developed a method which enables dynamical electro-mechanical simulations within an electronical circuit simulator. To accomplish this, the mechanical behavior of the system is modeled through electronical devices. This modeling process is automated by the CAD-tool MEXEL which translates systems of (partial) differential and algebraical equations to SPICE-3 netlists. In this way, electro-mechanical systems can be handled with one simulator and one simulation approach. Problems caused by coupling different simulators do not occur any more. All reported approaches, e.g. Herbert (1992) or Paap et al. (1993), are restricted to the simulation of ordinary differential equations within a circuit simulator. We extend this work to system descriptions including partial differential equations by applying the method of finite differences. The suitability of our method is shown by dynamical simulation of a capacitive pressure sensor system including its readout circuitry.

01 Jan 1995
TL;DR: A simulation technique for a fast and accurate transient analysis of lossy coupled transmission lines is presented and it can be shown that Eldo provides a high degree or accuracy and requires little computation time.
Abstract: A simulation technique for a fast and accurate transient analysis of lossy coupled transmission lines is presented. The kernel of this technique is an algorithm that works entirely in the time domain. Together with formulae for AC analysis this algorithm has been implemented in the circuit simulator Eldo 1 as a macromodel called LOSSYWIRE. Using LOSSYWIRE, Eldo is capable of simulating large lossy line systems in a nonlinear circuit environment. Simulation results for three different transmission line structures are given. They are compared with appropriate measurement data and simulation results from SPICE. It can be shown that Eldo provides a high degree or accuracy and requires little computation time

Proceedings ArticleDOI
21 Feb 1995
TL;DR: Performance of practical implementations of a proposed model in widely-used versions of SPICE by hard-coding and by using user-defined controlled sources are presented with experimental data.
Abstract: Accurate simulation of power electronic circuits involving power diodes requires mathematically-based power diode models to describe the forward recovery and reverse recovery characteristics realistically. Performance of practical implementations of a proposed model in widely-used versions of SPICE by hard-coding and by using user-defined controlled sources are presented with experimental data. The discussion also includes an implementation in Saber using the analog hardware description language MAST. >

Journal ArticleDOI
01 Apr 1995
TL;DR: In this article, a method for reducing the number of frequency points needed to estimate circuit response is presented, based on a parametric statistical model from an initial base simulation of the circuit, which is used in conjunction with results from future simulations made at the reduced frequency set omega /sub 1/, to estimate g( omega ) when the circuit is run under different input conditions, providing an efficient method of circuit optimisation.
Abstract: In electronic circuit simulation in the frequency domain the response is a function of frequency, g( omega ). Typically, to estimate g( omega ) the circuit is simulated at a large number of frequency points omega /sub 0/, and to optimise the circuit a large number of simulations are made. A method for reducing the number of frequency points needed to estimate circuit response is presented in this paper. From an initial base simulation of the circuit an estimate of g( omega ) is developed using a parametric statistical model from a fixed subset of omega /sub 0/, namely omega /sub 1/, carefully selected using the proven statistical method of cross-validation combined with simple thinning out of omega ,. The estimated model is used in conjunction with results from future simulations made at the reduced frequency set omega /sub 1/, to estimate g( omega ) when the circuit is run under different input conditions, providing an efficient method of circuit optimisation. The method is illustrated with an example which explores the effect of reducing frequency points for simulation on model accuracy. This shows the number of frequency points can be significantly reduced while still estimating the response curves accurately.

Proceedings ArticleDOI
28 Apr 1995
TL;DR: A comparison of symbolic analysis, approximation and macromodeling techniques for statistical circuit design is presented and the applicability of these methods for statistical design of analog integrated circuits is stressed through practical examples.
Abstract: A comparison of symbolic analysis, approximation and macromodeling techniques for statistical circuit design is presented in this paper. The applicability of these techniques for statistical design of analog integrated circuits is stressed through practical examples. Difficulties and open problems are also discussed with emphasis on statistical circuit design.