Kenneth S. Kundert’s research while affiliated with Cadence Design Systems, Inc. and other places

Six papers were chosen to represent twenty years of research in physical simulation and analysis, three papers addressing the problem of extracting and simulating inter- connect eects and three papers describing techniques for simulating steady-state and noise behavior in RF circuits. In this commentary paper we will try to describe the contribution of each paper and place that contribution in some historical context.

Simulation in the frequency-domain avoids many of the severe problems experienced when trying to use traditional time-domain simulators such as Spice [1] to find the steady-state behavior of analog, RF, and microwave circuits. In particular, frequency-domain simulation eliminates problems from distributed components and high-Q circuits by forgoing a nonlinear differential equation representation of the circuit in favor of a complex algebraic representation. This paper describes the spectral Newton technique for performing simulation of nonlinear circuits in the frequency-domain, and its implementation in Harmonica. Also described are the techniques used by Harmonica to exploit both the structure of the spectral Newton formulation and the characteristics of the circuits that would be typically seen by this type of simulator. These techniques allow Harmonica to be used on much larger circuits than were normally attempted by previous nonlinear frequency-domain simulators, making it suitable for use on Monolithic Microwave Integrated Circuits (MMICs).

Because of the periodically time-varying nature of some circuit blocks of a communication system, such as the mixers, the noise which is generated and processed by the system has periodically time-varying statistics. An accurate evaluation of the system output noise is not straightforward as in the case where all the circuit blocks are linear-time-invariant and the noise that they generate is time-independent. We qualitatively examine here, conditions under which we can treat the noise at the output of every circuit block of a practical communication system as if it were time-invariant, in order to simplify the noise analysis without introducing significant inaccuracy in the noise characterization of the overall communication system.

this paper we present a new mixed frequency-time approach for computing both forms of steady-state distortion. The method is computationally efficient and includes both static and dynamic distortion sources. The method has been implemented in a C program, Nitswit, and results from several examples are presented

In this paper we describe an algorithm for efficient circuit-level simulation of transmission lines which can be specified by tables of frequency-dependent scattering parameters. The approach uses a forced stable section-by-section ` 2 minimization approach to construct a high order rational function approximation to the frequency domain data, and then applies guaranteed stable balanced realization techniques to reduce the order of the rational function. The rational function is then incorporated in a circuit simulator using fast recursive convolution. An example of a transmission line with skin-effect is examined to both demonstrate the effectiveness of the approach and to show its generality.

Gaussian-elimination based shooting-Newton methods, a commonly used approach for computing steady-state solutions, grow in computational complexity like N³ where N is the number of circuit equations. Just using iterative methods to solve the shooting-Newton equations results in an algorithm which is still order N because of the cost of calculating the dense sensitivity matrix. Below, a matrix-free Krylov-subspace approach is presented, and the method is shown to reduce shooting-Newton computational complexity to that of ordinary transient analysis. Results from several examples are given to demonstrate that the matrix-free approach is more than ten times faster than using iterative methods alone for circuits with as few as 400 equations.

Radio-frequency (RF) circuits exhibit several distinguishing characteristics that make them difficult to simulate using traditional SPICE transient analysis. The various extensions to the harmonic balance and shooting method simulation algorithms are able to exploit these characteristics to provide rapid and accurate simulation for these circuits. This paper is an introduction to RF simulation methods and how they are applied to make common RF measurements. It describes the unique characteristics of RF circuits, the methods developed to simulate these circuits, and the application of these methods

Design of communications circuits often requires computing steady-state responses to multiple periodic inputs of differing frequencies. Mixed frequency-time (MFT) approaches are orders of magnitude more efficient than transient circuit simulation, and perform better on highly nonlinear problems than traditional algorithms such as harmonic balance. We present algorithms for solving the huge nonlinear equation systems the MFT approach generates from practical circuits

We have simulated the phase noise of a voltage controlled oscillator (VCO) using an RF circuit simulator, SpectreRF^TM. This simulator uses a variation of the periodic noise analysis first proposed by Okumura, et al (1993). It computes the power spectral density of the noise as a function of frequency. By assuming that only white noise sources are present in the oscillator, it is possible to derive a simple relationship between the level of the phase noise and the jitter. This excludes flicker noise from consideration, however, since flicker noise is a low-frequency phenomenon, excluding it only affects the accuracy of the long-term jitter. We compared the jitter with measurement and found the error to be less than 2 dB. An AHDL model for the VCO that efficiently exhibits jitter in the time domain is included. The model was written in Verilog-A. This model can be used to determine the affect of VCO jitter on a larger system, such as a phase-locked loop (PLL)