This paper presents a compact Nonlinear model Order Reduction Method (NORM) that is applicable for time-invariant and time-varying weakly nonlinear systems. NORM is suitable for reducing a class of weakly nonlinear systems that can be well characterized by low order Volterra functional series. Unlike existing projection based reduction methods [6]-[8], NORM begins with the general matrixform Volterra nonlinear transfer functions to derive a set of minimum Krylov subspaces for order reduction. Direct moment matching of the nonlinear transfer functions by projection of the original system onto this set of minimum Krylov subspaces leads to a significant reduction of model size. As we will demonstrate as part of our comparison with existing methods, the efficacy of model order for weakly nonlinear systems is determined by the extend to which models can be reduced. Our results further indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction. We demonstrate the practical utility of NORM for macromodeling weakly nonlinear RF circuits with time-varying behavior.

Abstract-Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudo-noise testing of a linear device. To illustrate the discussion we present an experimental example, an electro-acoustic transducer. Throughout the paper we emphasize the practical aspects of kernel measurement. V I. INTRODUCTION:PURPOSEAND POINTOFVIEW OLTERRA SERIES have appeared in the engineering literature for 40 years now. There have been many articles devoted to theoretical issues such as existence of Volterra series (e.g., [ l]-[3]) computation of Volterra kernels

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.

In this paper a new behavioral modeling approach for RF systems based is presented, based on a Volterra series input-output map representation. The modeling is done purely in the frequency domain, capturing the typical system level specifications for RF building blocks, independent of the implementation details. A harmonic balance simulation tool has been developed based on those models. The implementation focuses on deterministic effects such as distortion and frequency conversion. The behavioral simulator has been tested for various systems and results are presented.

Abstract—An overview of monolithic radio-frequency (RF) active mixer design is presented. The paper is divided into two parts. The first part discusses the performance parameters that are relevant to the design of downconversion mixers, and how they affect the system performance. The second part presents three common kinds of mixer topologies, namely, unbalanced, singlebalanced, and double-balanced designs. This paper concentrates on active mixers only. The advantages and disadvantages, as well as the design and optimization techniques for the three kinds of mixers, are discussed. Index Terms—Analog integrated circuits, circuit optimization, MIMIC’s, MMIC circuits, mixers, nonlinear circuits. I.

Modeling frequency-dependent nonlinear characteristics of complex analog blocks and subsystems is critical for enabling efficient verification of mixed-signal system designs. Recent progress has been made for constructing such macromodels, however, their accuracy and/or efficiency can break down for certain problems, particularly those with high-Q filtering. In this paper we explore a novel hybrid approach for generating accurate analog macromodels for time-varying weakly nonlinear circuits. The combined benefits of nonlinear Padé approximations and pruning by exploitation of the system’s internal structure allows us to construct nonlinear circuit models that are accurate for wide input frequency ranges, and thereby capable of modeling systems with sharp frequency selectivity. Such components are widely encountered in analog signal processing and RF applications. The efficacy of the proposed approach is demonstrated by the modeling of large time-varying nonlinear circuits that are commonly found in these application areas. 1.

This paper presents a technique for modeling nonlinear distortion of multirate time-varying communication circuits. To properly consider the weakly nonlinear distortion effects in circuits with multiple large-signal excitations, we capture the quasiperiodic boundary condition of the system Volterra kernels using a multivariate formulation. We then extend the model order reduction work of [8][9] to reduce this large multivariate representation for compact modeling. The proposed approach is demonstrated on a heterodyne front-end receiver. 1.

Abstract- In this paper we propose a frequency-separation methodology to generate system-level macromodels for analog and RF circuits. The proposed macromodels are similar in form to those based on Volterra kernel calculations, but are much simpler in terms of characterization and overall model complexity, and can be derived from existing device models. This simplicity is realized by applying some basic assumptions on the form of the input excitations, and via separation of the nonlinearities from the dynamic behavior. In addition, by further separating the ideal model functionality, this macromodel is applicable to strongly nonlinear components such as mixers. While time-varying Volterra series models have been proposed for mixers with a fixed local oscillation (LO) signal, the proposed frequency separation model is completely general and can capture the variations of the LO input during a system-level simulation. The proposed macromodels are demonstrated in a system-level simulation tool based on Simulink for efficient evaluation of the entire RF system and associated components. A GSM receiver system in 0.25pm CMOS process is used to demonstrate the efficacy of these macromodels in our system-level simulation environment. I.

INTRODUCTION The Volterra series technique has been used extensively in various applications in the area of nonlinear circuit analysis and optimization (see e.g. references [1]--[28]). Examples are in the (i) analysis of intermodulation in small signal amplifiers [6]--[12], (ii) determination of oscillation frequency and amplitude in near sinusoidal oscillators [3]--[5], (iii) analysis of mixers with moderate local oscillator levels [13, 14], analysis of communication systems [14]--[18], and (v) analysis of noise in nonlinear networks [24]--[28]. The use of the Volterra series technique basically involves two steps: (i) first, from specified input signal frequencies to determine all relevant Volterra transfer functions of the network, and (ii) next, to determine the output response from the non-linear network based on specified amplitudes of the input signals. One limitation in the use of Volterra series is that the determination of Volterra transfer functions is usually limi

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.