Abstract — RF circuits exhibit several distinguishing characteristics that make them difficult to simulate

In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 2-3 orders of magnitude larger than was previously practical. The results reported here extend our previous work [1] which only considered large circuits operating in a mildly nonlinear regime. The new implementation is based on quadratically convergent Newton methods and is able to simulate general nonlinear circuits. The significant efficiency improvement is achieved by use of Krylov subspace methods and a problem-specific preconditioner for inverting the harmonic balance Jacobian matrix. The analysis of radio-frequency mixers, implemented in integrated circuit technology, is an important application of our new method. We describe the theory behind the method, then report performance results on a complete receiver design using detailed transistor models. I. Introduction The method of Harmonic Balance is well established for fast and accurate steady-state analysi...

Abstract — The principles employed in the development of modern RF simulators are introduced and the various techniques currently in use, or expected to be in use in the next few years, are surveyed. Frequencyand time-domain techniques are presented and contrasted, as are steady-state and envelope techniques and large- and small-signal techniques. I. RF CIRCUITS The increasing demand for low-cost mobile communication systems has greatly expanded the need for simulation algorithms that are both efficient and accurate when applied to RF communication circuits. RF circuits have several unique characteristics that are barriers to the application of traditional circuit simulation techniques. Over the last decade, researchers have developed many special purpose algorithms that overcome these barriers to provide practical simulation for RF circuits, often by exploiting the very characteristic that represented the barrier to traditional methods. Despite dramatic progress, the average design cycle of an RFIC is still twice the length of that for other ICs found in a communication system, such as a cellular phone. This represents a significant practical barrier to integration of the RF and baseband sections of a transceiver onto a single chip. Clearly, more progress is necessary. This paper is a overview of RF simulation methods that seeks to provide an understanding of how the various methods address the RF simulation problem, and how they relate to each other. It begins by describing the unique characteristics of RF circuits. The basic solution methods of transient analysis, harmonic balance, and shooting methods are presented and contrasted. Small-signal analysis versions of both harmonic balance and shooting methods are covered. Composite methods are next. These methods apply the base

Fast and accurate computation of the steadystate response of large nonlinear networks under periodic and quasi-periodic drive is a key simulation problem for integrated RF designs. In this paper we describe recent work which extends the method of Harmonic Balance to networks containing several million unknowns. A new implementation is described, which includes new methods of preconditioning linear solves and an efficient method of storing derivative information. Then we report simulation and bench measurement results for several large designs, including a complete dual-conversion transmitter chip with extracted layout parasitics. I. Introduction The explosive growth in RF silicon ICs, largely for portable wireless communication, has placed new demands on transistor-level simulation tools: (1) The need to find the steady-state response of a nonlinear network driven by one or more periodic stimuli; In the case of more than one periodic stimulus, the driving periods may not always be har...

Data structures such as *BMDs, HDDs, and K*BMDs provide compact representations for functions which map Boolean vectors into integer values, but not floating point values. In this paper, we propose a new data structure, called Multiplicative Power Hybrid Decision Diagrams (*PHDDs), to provide a compact representation for functions that map Boolean vectors into integer or floating point values. The size of the graph to represent the IEEE floating point encoding is linear with the word size. The complexity of floating point multiplication grows linearly with the word size. The complexity of floating point addition grows exponentially with the size of the exponent part, but linearly with the size of the mantissa part. We applied *PHDDs to verify integer multipliers and floating point multipliers before the rounding stage, based on a hierarchical verification approach. For integer multipliers, our results are at least 6 times faster than *BMDs. Previous attempts at verifying floating point multipliers required manual intervention. We verified floating point multipliers before the rounding stage automatically.

The design of the radio frequency (RF) section in a communication integrated circuit (IC) is a challenging problem. Although several computer-aided analysis tools are available for RFIC design, they are not effectively used, because there is a lack of understanding about their features and limitations. These tools provide fast simulation of RFIC's. However, no single tool delivers a complete solution for RFIC design. This paper describes the shortcomings of conventional SPICE-like simulators and the analyses required for RF applications with an emphasis on accurate and efficient simulation of distortion and noise. Various analysis methods, such as harmonic balance, shooting method, mixed frequency-time methods, and envelope methods, that are currently available for RFIC simulation are presented. Commercial simulators are compared in terms of their functionalities and limitations. The key algorithmic features and the simulator-specific terminology are described. Index Terms---Circuit simulation, cyclostationary noise, distortion, envelope method, frequency-domain methods, harmonic distortion, intermodulation, linear time-varying analysis, mixed frequency-time methods, mixer noise, noise, periodic steady-state, phase noise, quasiperiodic steady-state, RFIC simulation, SPICE harmonic balance, shooting method, time-domain methods. I.

Heron, Patrick Lascelles Modeling and Simulation of Coupling Structures for Quasi-Optical Systems. Under the direction of Michael B. Steer and James W. Mink Sponsored research was directed toward developing millimeter wave power sources utilizing quasi-optical techniques. A system consisting of an array of oscillators that radiated into a quasi-optical resonator was analyzed. Each oscillator was comprised of a solid state device and a radiating structure. A dyadic Green's function was developed for a Fabry-Perot resonator which consisted of a metallic planar reflector and a shallow spherical metallic reflector. The Green's function was applied to determine the driving point impedance matrix for an array of electrically small antennas within the resonator. An experimental X-band resonator was designed and fabricated, then one and two-port measurements were used to validate the theoretical calculations. A technique was determined for simulation of antennas that are not electrically ...

In this paper we introduce a new method of performing direct solution of the harmonic balance Jacobian. For examples with moderate number of harmonics and moderate to strong nonlinearities, we demonstrate that the direct solver has far superior performance with a moderate increase in memory compared to the best preconditioned iterative solvers. This solver is especially suited for Fourier envelope analysis where the number of harmonics is small, circuits are nonlinear and Jacobian bypass can be used for additional speed. For examples with large number of harmonics and moderate to strong nonlinearities, the performance advantage is maintained but the memory requirements increase. We propose efficient preconditioners based on direct solution of harmonic balance matrices which provide the user with a memory-speed trade-off.

LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.

The paper provides an overview on the state of the art and future trends in physics-based electron device modelling for the computer-aided design of monolithic microwave IC’s. After a review of the main physics-based approaches to microwave modelling, special emphasis is placed on innovative developments relevant to circuit-oriented device performance assessment, such as efficient physics-based noise and para-metric sensitivity analysis. The use of state-of-the-art physics-based analytical or numerical models for circuit analysis is dis-cussed, with particular attention to the role of intermediate be-havioural models in linking multidimensional device simulators with circuit analysis tools. Finally, the model requirements for yield-driven MMIC design are discussed, with the aim of point-ing out the advantages of physics-based statistical device modelling; the possible use of computationally efficient ap-proaches based on device sensitivity analysis for yield optimi-zation is also considered.