Wavelet harmonic balance

This letter 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 large scale simulations.     

Jacobian calculation using the multidimensional fast Fouriertransform in the harmonic balance analysis of nonlinear circuits

A technique which allows the gradient of frequency-domain simulation variables to be analytically determined using time-domain derivative information and the multidimensional fast Fourier transform is discussed. It is shown that this technique can be efficiently implemented when a circuit is driven by any number of incommensurate input frequencies. A harmonic balance simulator that uses this technique to determine the entries of the Jacobian matrix needed in a quasi-Newton iteration scheme is constructed. A significant reduction of simulation time is observed when compared with a harmonic balance simulator that uses transforms based on matrix multiplication     

Accurate Fourier transform method for almost-periodic response simulation of microwave nonlinear circuits

A generalised Fourier transform, in which an orthogonal sample selection algorithm is used, is presented for accurate simulation of the almost-periodic responses of microwave nonlinear circuits. The measured and simulated results of a MESFET amplifier show the significant improvement in accuracy.<>     

Multitone signal harmonic balance method

A novel approach for generating the frequency/time conversion matrices of multitone signals is presented. Conversion matrices are normally used in the harmonic balance method to evaluate currents/voltages of nonlinear devices. The conditioning number of these matrices is a fundamental aspect and the proposed approach always generated matrices with the best conditioning number     

Matrix synthesis of harmonic oscillator circuits †

A synthesis method is given for oscillators of the type that may be represented as a single two-port network with a transmission matrix [T]=[A, B;C, D] having its output fed directly back to its input, thereby imposing the condition:

A+D?Δ?1=0,

where ΔΞAD? BC. To obtain sustained oscillation at a single real frequency ω₀ this condition is interpolated at ω₀ by a polynomial equation in s. By identifying the two equations a set of functional values may be obtained for the [T] matrix elements. Four sots of basic circuit are developed in detail from the quadratic or cubic polynomial equation, with Δ = 0 or Δ≠0. Those having Δ = 0 arc well-known forms, but those with Δ =0 are novel.     

Cumulative balance testing of logic circuits

We present a new test response compression method called cumulative balance testing (CBT) that extends both balance testing and accumulator compression testing. CBT uses an accumulated balance signature, and it guarantees very high error coverage (over 99%) for various error models. We demonstrate that the single stuck-line (SSL) fault coverage of CBT for many of the ISCAS 85 combinational benchmark circuits is 100%, and for all but one circuit, the fault coverage is over 99.5%. To make processor circuits self-testing, any existing accumulators and counters can be exploited to implement CBT. Its ease of implementation, provably high error coverage, and exceptionally high SSL fault coverage, even with reduced (nonexhaustive) test sets, make CBT suitable for the built-in self testing of processor circuits that require a guaranteed level of test confidence     

Application of genetic algorithm to sample balance analysis ofnonlinear circuits

A genetic algorithm has been applied for the first time to the sample balance method for nonlinear circuit analysis. Results for a circuit containing an ideal diode show this to be a viable approach which does not suffer from the limitations of other techniques for solving sample balance and harmonic balance equations. The algorithm does not require a good initial estimate nor does it need a Jacobian formulation of the circuit equations     

A method to predict harmonic distortion in small-geometry MOS analog integrated circuits

A method to predict the small-signal linear gain and level of harmonic distortion in analog MOS circuits is presented. This method, based on a generalized nonlinear transfer function approach, lends itself to implementation in the AC small-signal analysis routine of the circuit simulation program SPICE. A low-frequency nonlinear distortion model based on the CSIM simulator MOSFET model is applied to three simple MOSFET circuits. Results presented emphasize the need to consider small-signal quantities in the development of MOSFET models and in the determination of device parameters. The method can be easily extended to include capacitive effects and a prediction of intermodulation distortion.     

Analysis of harmonic generator circuits for step recovery diodes

This paper gives formulas for the transients in a simple lossless harmonic generator circuit consisting of a step recovery diode, two inductors, and two capacitors. By means of graphic plots of the instantaneous values of currents and voltages, it is concluded that high efficiency requires approximately equal values of the two inductors.     

Analysis of harmonic distortion in single-channel MOS integrated circuits

Presents a general analysis for the calculation of harmonic distortion in single-channel monolithic analog MOS integrated circuits. Power series expressions are obtained for basic stages often used in an analog MOS technology. These include the depletion load inverter, enhancement load inverter, depletion load source follower, enhancement load source follower, and the differential pair. From the power series expressions, the second-order harmonic distortion is calculated. These results are compared with data obtained from a test chip.     

Computation of the average and harmonic noise power-spectral density in switched-capacitor circuits

Switched-capacitor (SC) circuits are periodically time-varying circuits and the noise at the output of these circuits is cyclostationary. This noise is therefore characterized by the average and harmonic spectral densities. We extend the method proposed in a previous paper to compute the average and harmonic noise-spectral densities in periodically varying circuits. We derive expressions for the average and harmonic spectral densities and use the mixed-frequency-time technique for the computation. The results for the average spectral density are compared with published results. The contribution of the harmonic spectral densities to the average noise-spectral density at the output of a cascaded block is estimated.     

New high-compliance CMOS current mirror with low harmonic distortion for high-frequency circuits

A new low-distortion high-compliance CMOS current mirror is presented. The large-signal nonlinear characteristic of MOS transistors in saturation, combined with capacitances present in current mirror circuits, causes harmonic distortion. This effect is explained for a well-known current mirror circuit, and the new circuit is described which substantially reduces harmonic distortion while using only one extra standard process component.<>     

General-purpose harmonic balance analysis of nonlinear microwavecircuits under multitone excitation

A powerful software tools for the simulation of nonlinear microwave circuits under single- or multiple-frequency excitation is described. The program operates in a truly general-purpose fashion, both circuit topology and active-device equivalent circuits being arbitrarily established by the user at the data entry level. Built-in facilities based on the multidimensional Fourier transform allow a straightforward and unrestricted treatment of mixer and intermodulation problems. The capabilities of the program are illustrated by a number of practical examples     

Low-power circuits for the wireless ligament balance measurement system in TKA

A low power system for the ligament balance measuring in Total Knee Arthroplasty is presented in this paper. The system consists two parts: a front-end Ligament Balance Measuring System (LBMS) which is inserted into the knee joint during the operation, and the display part. LBMS is comprised of a sensors array including eight precise force sensors, signal conditioning circuits that support up to 15 force sensors, a sub-threshold microprocessor, power circuits and a 433?MHz RF transceiver for data transmission. The force corresponding to its distribution is transmitted wirelessly and displayed in 3-D in real time with an accuracy of 0.049?N. The signal conditioning circuits, the sub-threshold 8?bit microprocessor and the application specific integrated circuits chip have been designed and fabricated in 0.18???m CMOS process. The tested resolution is 60.1???V_pp (1.35?g) with ±100?mV_pp input. The chip can operate under 1.2 to 3.6?V voltage supply for single battery application with 116?C160???A power consumption. The testing results of the microprocessor show that the leakage power is 46?nW and the dynamic power is 385?nW @ 165?kHz with operating voltage of 350?mV. The simulation results show that the power circuits can provide the supply voltage ranging from 0.3?V to 0.6?V for the sub-threshold microprocessor. Experimental results verified the system. Some clinical experiments will be carried out in the future.     

Physical modeling of the step recovery diode for pulse and harmonic generation circuits

A simple charge-controlled switching model describes most fundamental aspects of the step recovery diode. However, it is shown that switching speed and the associated loss are related to the width of the i layer and to the doping level. A switching model appropriate for general computer use is given, and examples of its application are shown in pulse and harmonic generator circuits.     

Analysis and CAD implementation techniques of total harmonic distortion in analog VLSI circuits

This paper presents a new methodlogy to accurately evaluate the total harmonic distortion (THD) behavior of modern integrated circuits. The methodology is general, technology independent and is used to determine large-signal or reactive THD of signal processing circuits operating in the voltage or the current domain. It is based on Fourier series analysis and Parseval's theorem, where numerical integration may be needed to accurately compute THD. For low-frequency THD, the numerical integration can be simplified to a small number of summation without degrading the accuracy. The new methodology is incorporated in a computer-aided environment which accurately estimates THD, and the speed of calculation for many circuit is several orders of magnitude faster than SPICE or other commercial CAD tools. In addition, optimization of transistor sizes to reduce THD can be achieved by incorporating the methodology in an object-oriented CAD tool such as APLAC.Currently on leave as a Fulbright-Hays professor at the Helsinki University of Technology, Finland.     

Nonlinear processing of digitally modulated carriers by theinexact-Newton harmonic balance technique

The Newton-iteration based harmonic-balance (HB) technique is generally acknowledged as the principal method for the simulation of nonlinear circuits driven by multitone excitations. The authors propose a new implementation of the HB principle. Named the inexact-Newton harmonic balance (INHB). This method provides a well-behaved and efficient solution to the problem of HB simulation with very large numbers of closely spaced spectral lines     

Improved harmonic balance implementation of Floquet analysis for nonlinear circuit simulation

We present a novel algorithm for the efficient numerical computation of the Floquet quantities (eigenvalues, direct and adjoint eigenvectors) relevant to the assessment of the stability and noise properties of nonlinear forced and autonomous circuits. The approach is entirely developed in the frequency domain by means of the application of the Harmonic Balance technique, thus avoiding lengthy time–frequency transformations which might also impair the accuracy of the calculated quantities. An improvement in the computation time around one order of magnitude is observed.     

用“不变本征算符法 ”求解均匀外电场中带电谐振子的量子化能谱

采用不变本征算符法求出均匀外场中带电谐振子的能级间隔,利用“积分变换法”求出均匀外场中带电谐振子的基态能量和相应波函数,通过分析推求出均匀外场中带电谐振子的量子化能谱。     

Harmonic balance and frequency-domain simulation of nonlinearmicrowave circuits using the block Newton method

An efficient algorithm using block Newton and chord methods for the iterative minimization of the spectral balance error in the analysis of nonlinear microwave circuits is presented. The algorithm is then used in the harmonic balance and frequency-domain spectral balance simulation of a MESFET amplifier with single-tone and two-tone excitation