Optimization technology for nonlinear microwave circuits integrating electromagnetic simulations

We review relevant concepts, formulations, and algorithms for microwave circuit optimization. Emphasis is given to recent advances in the state of the art: Automated electromagnetic (EM) design, Space Mapping, Huber optimization, an integrated CAD environment, and parallel computation. We address integration of previously disjoint simulation technologies for automated EM optimization of linear and nonlinear microwave circuits. We incorporate EM analyses of passive microstrip structures and SPICE models of active devices into harmonic balance optimization of nonlinear circuits, even for yield-driven design. Designs of a Class B frequency doubler, a broadband small-signal amplifier, and an attenuator illustrate the integrated approach. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 6–28, 1997.     

MEMS based humidity sensor using Si cantilever beam for harsh environmental conditions

The RF applications like voltage controlled oscillators, tunable filters, resonators etc., requires tunable capacitors in their designs. This paper presents the design of wide range MEMS tunable capacitors for RF applications. This design consists of an air suspended bottom plate and a fixed top plate. The top fixed plate and the suspended bottom plate form the tunable capacitor. The capacitance range of this tunable capacitor is from 69.172 to 138.344 nF. This range is wider compared with the conventional MEMS tunable capacitors of tuning ranges in pico Farads. The fabrication process is similar to that of the existing standard integrated circuit fabrication processes, which makes this design suitable for integrated RF applications.     

Design of wide range MEMS tunable capacitor for RF applications

The RF applications like voltage controlled oscillators, tunable filters, resonators etc., requires tunable capacitors in their designs. This paper presents the design of wide range MEMS tunable capacitors for RF applications. This design consists of an air suspended bottom plate and a fixed top plate. The top fixed plate and the suspended bottom plate form the tunable capacitor. The capacitance range of this tunable capacitor is from 69.172 to 138.344?nF. This range is wider compared with the conventional MEMS tunable capacitors of tuning ranges in pico Farads. The fabrication process is similar to that of the existing standard integrated circuit fabrication processes, which makes this design suitable for integrated RF applications.     

On application of the describing function method for optimization of feedback control systems

Two H_∞ optimization problems of a nonlinear tracking control system: the problem of a nonlinear controller and the problem of a nonlinear plant are considered in the paper. The describing function method is used for linearization of a feedback control system. Theorems, which enable one to replace the optimization of a nonlinear system by the optimization of an approximate linear system are proven in the paper. Methods of H_∞ optimization are used to find the structure of an optimal controller of the approximate system. © 1997 by John Wiley & Sons, Ltd.     

Large-scale nonlinear optimization in circuit tuning

Circuit tuning is an important task in the design of custom digital integrated circuits such as high-performance microprocessors. The goal is to improve certain aspects of the circuit, such as speed, area, or power, by optimally choosing the widths of the transistors. This task can be formulated as a large-scale nonlinear, nonconvex optimization problem, where function values and derivatives are obtained by simulation of individual gates. This application offers an excellent example of a nonlinear optimization problem, for which it is very desirable to increase the size of the problems that can be solved in a reasonable amount of time. In this paper we describe the mathematical formulation of this problem and the implementation of a circuit tuning tool. We demonstrate how the integration of a novel state-of-the-art interior point algorithm for nonlinear programming led to considerable improvement in efficiency and robustness. Particularly, as will be demonstrated with numerical results, the new approach has great potential for parallel and distributed computing.     

Piezoelectrically actuated tunable capacitor

This paper describes the design, fabrication, and characterization of the first MEMS piezoelectric tunable capacitors employing zinc oxide (ZnO) actuation. Relatively simple design rules for the device-structure optimization for largest deflection are shown from simulation results based on theoretical equations. The ZnO-actuated tunable capacitors are accordingly designed and fabricated with both surface and bulk micromachining techniques. Through the surface micromachining process, sacrificial silicon is removed with XeF/sub 2/, and parylene is successfully used as a supporting layer for a piezoelectric unimorph cantilever. For comparison, other two different structures using plasma-enhanced chemical-vapor deposition (PECVD) SiN and SU-8 as supporting layers are also fabricated. Deflection analyses are performed for three specific structures, among which the parylene-supported one is demonstrated to have the largest displacement and most suitable for tunable capacitor application. For bulk-micromachined tunable capacitor, we have implemented a novel design of a large structure driven by a ZnO unimorph, and obtained a tuning ratio of more than 21:1 (0.46 pF-10.02 pF). This is the highest tuning ratio reported to date for parallel-plate tunable capacitors while requiring an applied voltage of only 35 V.     

Low phase noise design of microwave oscillators (invited article)

Time domain methods for numerical nonlinear analysis of the steady state solution as well as the spectral behavior of microwave oscillators are discussed. In addition, a method to minimize the phase noise of oscillators by numerical optimization is outlined and applied to the design of a low phase noise oscillator. Computer simulations are compared with measurement results of the fabricated oscillators. © 1996 John Wiley & Sons, Inc.     

Method of passification in adaptive control, estimation, and synchronization

The main results of the method of passification which are based on applying the Yakubovich-Kalman frequency theorem to the design of the feedback systems and examples of its use in the problems of adaptive control, state estimation, and synchronization were presented. Various types of the adaptive control algorithms with implicit reference model such as the algorithms of stabilization and tracking with the prescribed dynamics, algorithms with adaptive tuning of the standard control laws, and combined signal-parametric algorithm of adaptive control were described. Brief information about the shunting method in the adaptive control problem was given. The experimental results with the adaptive control on the “Helicopter” benchmark were described. Consideration was given to the problem of adaptive control of the nonlinear plants. Examples of applying the method of passification and adaptive observers to the problems of synchronization of the nonlinear oscillators and message transmission by chaotic signals were presented.     

The Use of SI-Algebra in the design of sequencer circuits

One approach to the design of VLSI systems involves the use of asynchronous circuits that communicate by handshaking with each other. The control circuitry generated when following this approach often includes large trees of binary sequencer components. This paper demonstrates that there is scope here for optimization (in order to improve size, speed and energy consumption). Indeed, an industrial-strength silicon compiler has now been modified to take advantage of this fact.The problem that is addressed concerns the design of efficient control circuits that sequenceN four-phase handshakes (N > 2). Muller's speed-independent discipline facilitates the design of such circuits. SI-Algebra, a calculus that supports that discipline, is used to specify the problem and to verify (using recursion-induction) various implementations. Simple counting arguments at the gate level establish that optimization using these implementations is worthwhile.     

A High-Q Widely Tunable Gigahertz Electromagnetic Cavity Resonator

This paper describes the design, fabrication and testing of a quasi-static electromagnetic cavity resonator fabricated using potassium-hydroxide (KOH) etching, shallow reactive-ion etching (RIE), metalization and wafer bonding. The resonator is distinguished by its simultaneous high-Q near 200, and wide high-frequency tuning range, 2.5-4.0 GHz for the experimental resonator presented here. When combined with an integrated actuator, it should be suitable for use in electronically tunable radio-frequency (RF) bandpass filters and oscillators. The experimental resonator, however, is tuned with an external piezoelectric actuator for simplicity     

Robust dynamic ship positioning control system design and applications

This paper describes the robust control system design for a ship dynamic positioning system. The control design is based on an approximate linear model derived from the nonlinear hydrodynamic equations governing the horizontal motions of the ship. The nonlinear models of the ship, seawaves, current, wind and thrusters are derived and simulated for control design verification. The H_∞ control design technique is employed to design the controller. The control problem is formulated in state‐space form and the design specifications are translated into requirements on the weighting functions of the error signal and the thrusters input. A tuning procedure is proposed based on the wind and wave disturbances. The controller is initially tested on the nonlinear ship model and simulation results are presented to demonstrate the robustness of the H_∞ controller. Tank tests results are then presented to assess the controller performance. Copyright © 2001 John Wiley & Sons, Ltd.     

Desynchronization of coupled limit-cycle oscillators through nonlinear output regulation

Synchronization is one of the most important phenomena in coupled oscillators. However, sometimes synchronization may be harmful and suppression of collective synchrony or desynchronization is desired. In this paper, we propose a control strategy for the desynchronization of an ensemble of all-to-all coupled Stuart–Landau oscillators. First, the desynchronization problem is redefined in the nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces Stuart–Landau oscillators (as a paradigm for limit-cycle oscillators) to track exogenous sinusoidal references with different phases. Finally, by considering some modifications, the initial version of the controller is improved to be more applicable in neuronal ensembles as an application of the desynchronization problem. The proposed stimulation is robust against variations of oscillators’ frequencies and can adapt itself with variations of the coupling strength. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.     

Robust optimization of multivariable feedback systems with time-varying nonlinear uncertainties

A design criterion is developed to achieve the input-output decoupling of multivariable feedback systems and the robust stabilization of systems with time-varying nonlinear uncertainties. Moreover, an effective design algorithm is derived to achieve the robust optimization of multivariable feedback systems subjected to time-varying nonlnear uncertainties. The theory of minimum H^∞ -norm and the optimal interpolation technique are employed to solve this robust optimization problem. Since the requirements of internal stability are satisfied, this design algorithm performs appropriately, even if the plant is unstable and/or non-minimum phase. From the result of the robust optimization, we can predict the maximum sector bounds of nonlinear uncertainties that can be tolerated in the multivariable feedback system.     

Robust H∞ nonlinear control via measurement feedback

This paper deals with the problem of finite-time-horizon robust H_∞ control via measurement feedback, for affine nonlinear systems with nonlinear time-varying parameter uncertainty. The problem addressed is the design of a control law, which processes the measured output and guarantees a prescribed level of closed-loop disturbance attenuation. Conditions for the existence of such a controller are obtained by solving an auxiliary control problem for a related system which is obtained from the original one by converting the parameter uncertainty into exogenous bounded energy signals. This approach allows us to apply the recently developed H_∞ nonlinear control techniques to solve the robust control problem. The problem is investigated in both the continuous- and discrete-time cases. The results are demonstrated by a simple example. © 1997 by John Wiley & Sons, Ltd.     

NONLINEAR NETWORK STRUCTURES FOR FEEDBACK CONTROL

A framework is given for controller design using Nonlinear Network Structures, which include both neural networks and fuzzy logic systems. These structures possess a universal approximation property that allows them to be used in feedback control of unknown systems without requirements for linearity in the system parameters or finding a regression matrix. Nonlinear nets can be linear or nonlinear in the tunable weight parameters. In the latter case weight tuning algorithms are not straightforward to obtain. Feedback control topologies and weight tuning algorithms are given here that guarantee closed-loop stability and bounded weights. Extensions are discussed to force control, backstepping control, and output feedback control, where dynamic nonlinear nets are required.     

Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs

This paper proposes a dynamic compensation scheme for input-constrained feedback linearizable nonlinear systems to cope with the windup phenomenon. Given a dynamic feedback linearizing controller designed without considering its input constraint, an additional dynamic compensator is proposed to account for the constraint. This dynamic anti-windup is based on the minimization of a reasonable performance index. The proposed strategy is a nonlinear extended version of [Park, J.-K., & Choi, C.-H. (1995). Dynamic compensation method for multivariable control systems with saturating actuators. IEEE Transactions on Automatic Control, 40(9), 1635–1640] with simplified derivation of an optimization solution under relaxed assumptions. The parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes. During input saturation, the role of the anti-windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation. The local asymptotic stability and the total stability of the resulting systems are proved. The usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system.     

Fundamentals of optimization

The structural design problem is formulated as a general nonlinear optimization problem with constraints. Characteristics of such problems and the solutions are discussed. Methods of solution for constrained as well as unconstrained problems are reviewed, with special emphasis on penalty function methods for constrained problems. A simple example on the solution of a design problem with discrete variables is shown, and a realistic example on the application of optimization methods in midship section design of OBO-carriers is presented.     

Scalar control of a group of free-running oscillators

For a system consisting of an arbitrary number of free-running oscillators, consideration was given to the problem of speed. The system is governed by a bounded scalar control, the terminal point being defined by the desired configuration of oscillations. Solution of the problem was illustrated by examples.     

Optimal Orthogonal Tiling of 2-D Iterations

Iteration space tiling is a common strategy used by parallelizing compilers and in performance tuning of parallel codes. We address the problem of determining the tile size that minimizes the total execution time. We restrict our attention to uniform dependency computations with two-dimensional, parallelogram-shaped iteration domain which can be tiled with lines parallel to the domain boundaries. The target architecture is a linear array (or a ring). Our model is developed in two steps. We first abstract each tile by two simple parameters, namely tile periodP_tand intertile latencyL_t. We formulate and partially resolve the corresponding optimization problem independent of the machine and program. Next, we refine the model with realistic machine and program parameters, yielding a discrete nonlinear optimization problem. We solve this analytically, yielding a closed form solution, which can be used by a compiler before code generation.     

Variable bandwidth,wide tunable frequency,voltage tuned filter

This article discusses the development of an electronically tuned filter capable of a wide tunable frequency range and simultaneous 3-dB bandwidth variations at any frequency within its tuning range. Varactor-tunable filters are designed using high-dielectric, soft-substrate material for printed resonators as well as also high-Q ceramic resonators, and their test data are compared. Greater than 50% tuning range with low insertion loss at a center frequency in the L and S frequency bands is demonstrated with a 4:1 change in 3-dB bandwidth—30 to 120 MHz for printed resonators and 14 to 46 MHz for ceramic resonators. The concept of tuning a filter's 3-dB bandwidth with voltage is demonstrated and the effect of the bandwidth tuning elements on the tunable filter performance is discussed. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 64–72, 2004.