A general-purpose computer program for the Volterra-series analysis of nonlinear microwave circuits

Frequency-domain based methods are not valid to analyze a nonlinear microwave circuit with general, arbitrary nonlinearities. Therefore, analysis of nonlinear microwave circuits in time-domain is presented. Subharmonics and instabilities can be predicted. As examples, Josephson junction and the Schottkybarrier mixer diode are discussed.

This paper offers a review of simulation methods currently available for the transient and steady-state analysis of nonlinear RF and microwave circuits. The most general method continues to be the time-marching approach used in Spice, but more recent methods based on multiple time dimensions are particularly effective for RF and microwave circuits. We derive nodal formulations for the most widely used multiple time dimension methods. We put special emphasis on methods for the analysis of oscillators based in the warped multitime partial differential equations (WaMPDE) approach. Case studies of a Colpitts oscillator and a voltage controlled Clapp-Gouriet oscillator are presented and discussed. The accuracy of the amplitude and phase of these methods is investigated. It is shown that the exploitation of frequency-domain latency reduces the computational effort.

Harmonic Balance is nowadays the most efficient method for the periodic steady state analysis of microwave circuits. Unfortunately this method cannot conveniently handle realistic wide band input signals, because its computation time grows rapidly with the number of harmonics. A new method is proposed which resolves the above mentioned limitation of the Harmonic Balance. A substantial computation time saving is obtained with respect to the Harmonic Balance.

The paper proposes an analysis method of nonlinear microwave circuits referred to as the frequency-domain-continuation intermodulation balance method (FDCIBM). This technique introduces a generalised complex matrix to represent (in the frequency domain) the steady-state variables of the nonlinear circuit with multifrequency large-signal excitation. In terms of this generalised complex matrix and a generalised complex-matrix convolution operator defined here, the frequencydomain- balance equation of the nonlinear circuit is a system of complex-variable nonlinear algebraic equations, that is solved using the continuation method. As an example, the intermodulation analysis of a GaAs MESFET amplifier is given.

This paper introduces a new approach to steady-state analysis of nonlinear microwave circuits under periodic excitation. The new method is similar to the well-known technique of harmonic balance, but uses wavelets as basis functions instead of Fourier series. Use of wavelets allows significant increase in sparsity of the equation matrices and, consequently, decrease in CPU cost and storage requirements, while retaining accuracy and convergence of the traditional approach. The new method scales linearly with the size of the problem and is well suited for simulations of highly nonlinear, multitone, and broad-band circuits.

A quasi-2-D physics-based MESFET model has been used in conjunction with a modified harmonic-balance nonlinear algorithm for the large-signal analysis of nonlinear microwave circuits. The feasibility of the procedure has been demonstrated.

The paper presents the theoretical foundations for an approximate form of the piecewise harmonicbalance technique, suitable for the analysis of nonlinear microwave circuits driven by slowly modulated signals. Possible applications include transient RF regimes and analog processing of digitally modulated carners.

This study describes a systematic approach for the stability analysis of RF and microwave non‐linear circuits in the time‐domain and that can be useful also for the verification of other non‐linearities, like intermodulation. The time‐domain analysis is the most reliable approach for the evaluation of complex non‐linear phenomena but, in general, the transient behaviour of non‐linear circuits is difficult to verify at high frequencies, where distributed elements are common. The solution here addressed overcomes this limitation and it may be applied, without restrictions, also to monolithic microwave integrated circuits and EM‐based designs. Examples of application to hybrid prototypes are provided, and the comparison between simulations and measurements illustrates the accuracy and reliability of the proposed approach.

A novel sparse-matrix approach to the simulation of nonlinear microwave circuits by the Newton-iteration-based piecewise harmonic-balance technique is presented. Selected elements of the Jacobian matrix are set to zero according to some physical criterion, which leads to a sparse Jacobian with a preselected pattern of nonzeros. This allows the use of specialized sparse-matrix solvers, with an effective optimization of both memory storage and CPU time. The code has been developed in both a scalar and a vectorized version optimized for the Cray Y-MP supercomputer. >

A review of several techniques related to the combination of geometrical decomposition of mixed geometry problems coupled with the inclusion of single and multiple linear and nonlinear circuit elements is addressed for use with the FDTD method. As a demonstrator of the algorithmic aspects related to this problem, a slot loop antenna will be analysed. Several variants of the antenna are described, the simplest variation consisting of a slot loop antenna fed by a CPW line connected via a slotline transition. More elaborate variations include techniques for the inclusion of lumped linear and/or nonlinear elements into the FDTD code. The inclusion of three terminal lumped active devices is demonstrated in order to describe the algorithmic details of the slot loop operated as an active antenna. Where possible, experimental and theoretical predictions are compared in order to validate the methodologies adopted.

A linear inverse space-mapping (LISM) optimization algorithm for designing linear and nonlinear RF and microwave circuits is described in this paper. LISM is directly applicable to microwave circuits in the frequency- or time-domain transient state. The inverse space mapping (SM) used follows a piecewise linear formulation, avoiding the use of neural networks. A rigorous comparison between Broyden-based "direct" SM, neural inverse space mapping (NISM) and LISM is realized. LISM optimization outperforms the other two methods, and represents a significant simplification over NISM optimization. LISM is applied to several linear frequency-domain classical microstrip problems. The physical design of a set of CMOS inverters driving an electrically long microstrip line on FR4 illustrates LISM for nonlinear design.

In the past decades, harmonic balance (HB) has been widely used for computing steady-state solutions of nonlinear radio-frequency (RF) and microwave circuits. However, using HB for simulating strongly nonlinear post-layout RF circuits still remains a very challenging task. Although direct solution methods can be adopted to handle moderate to strong nonlinearities in HB analysis, such methods do not scale efficiently with large-scale problems due to excessively long simulation time and prohibitively large memory consumption. In this paper, we present a novel graph sparsification approach for automatically generating preconditioners that can be efficiently applied for simulating strongly nonlinear post-layout RF circuits. Our approach allows to sparsify time-domain circuit modified nodal analysis matrices that can be subsequently leveraged for sparsifying the entire HB Jacobian matrix. We show that the resultant sparsified Jacobian matrix can be used as a robust yet efficient preconditioner in HB analysis. Our experimental results show that when compared with the prior state-of-the-art direct solution method, the proposed solver can more efficiently handle moderate to strong nonlinearities during the HB analysis of RF circuits, achieving up to $20{\boldsymbol \times }$ speedups and $6{\boldsymbol \times }$ memory reductions.

A unified frequency-domain formulation and algorithm has been presented for computing noise in the nonlinear microwave circuits. The method uses stationary components and harmonic power spectral density in its formulation to capture time-varying noise statistics. A description of noise spectrum for the interesting ports in the nonlinear microwave circuits is the central results enabling fast and accurate computation. The method is efficient for large circuits with CAD and can generate information useful for noise macromodels. Finally, the experimental results verify its practicability in the application.

In this article, a recurrent neural network (RNN) method is employed for dynamic time-domain modeling of both linear and nonlinear microwave circuits. An automated RNN modeling technique is proposed to efficiently determine the training waveform distribution and internal RNN structure during the offline training process. This technique extends a recent automatic model generation (AMG) algorithm from frequency-domain model generation to dynamic time-domain model generation. Two types of applications of the algorithm are presented, transient electromagnetic (EM) behavior modeling of microwave structures, and time-domain envelope modeling of power amplifiers (PA). For transient EM modeling, we consider EM structures with varying material and geometrical parameters. AMG automatically varies the EM structural parameters during training and drives time-domain EM simulators to generate necessary amount of data for RNN to learn. AMG aims to model the transient behavior with minimum RNN order while satisfying accuracy requirements. In modeling PA behavior, an envelope formulation is used to specifically learn the AM/AM and AM/PM distortions due to third-generation (3G) digital modulation input. The RNN PA model is able to model these time domain distortions after training and can accurately model the amplifier behavior in both time (AM/AM, AM/PM) and frequency (spectral re-growth). © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.

The authors introduce a rigorous approach to large-signal noise in nonlinear microwave circuits. The analysis is based on the well-known representation of white noise as a set of uniformly spaced pseudosinusoidal signals with random phases. The spectral resolution required for a reliable noise simulation is evaluated by Monte Carlo analysis and is found to he quite high, so that the resulting nonlinear analysis involves spectra of many tens of thousands of lines. This kind of problem may be efficiently solved by the inexact-Newton harmonic-balance technique. With this method, the amplitude of the noise waveforms is arbitrary, so that large-signal noise effects may he directly evaluated.