Perturbation Analysis of Nonlinear Distortion in Analog Integrated Circuits

A method for predicting the distortion in weakly nonlinear analog circuits is presented, which relies on the classical theory of regular perturbation. Accordingly, a nonlinear circuit is described and analyzed as a perturbation of its linearized model, and the response to a periodic signal is analytically calculated through frequency-domain recurrent formulas. The method is simple and quite straightforward to apply, as it involves the calculation of frequency-domain transfer functions and of Fourier coefficients only, making it easily adaptable to any circuit topology. The method can be a valid alternative to the Volterra series method. A relationship between the proposed method and the Volterra series method is established, showing that they lead to very similar approximants to the solution. The method has been numerically tested in practical circuits wherein the devices are modeled by polynomial and exponential nonlinearities.     

Fast periodic steady-state analysis for large-signal electronic circuits

It is shown that current computer-aided circuit analysis programs that are capable of the transient analysis of nonlinear circuits can be modified to include the determination of the periodic steady-state response of large-signal electronic circuits such as class C amplifiers, frequency multipliers, parametric circuits, and oscillators. With this modification only a portion of the transient response is computed, then a Newton iterative technique is used to find the periodic state of the circuit from which the periodic response can be found by a numerical integration over one period. This technique is especially valuable for analyzing high Q circuits and for design purposes where fast analysis is essential.     

Symbolic Steady-State Analysis for Strongly Nonlinear Circuits and Systems

A symbolic method for steady-state analysis of nonlinear circuits and systems is presented. This method is based on the principle of the Equivalent Small Parameter method (the ESP method), which is an improved perturbation technique combined with the harmonic balance method. Using this method, a set of high-order nonlinear differential equations can be solved and the symbolic expressions of the steady-state periodic solutions for the required variables can be obtained. Two examples are given and show that the method is general and can be used for both weakly and strongly nonlinear circuits, and time-variant nonlinear circuits such as switching mode circuits.     

Distributed integrated circuits: an alternative approach tohigh-frequency design

Distributed integrated circuits are presented as a methodology to design high-frequency communication building blocks. Distributed circuits operate based on multiple parallel signal paths working in synchronization that can be used to enhance the frequency of operation, combine power, and enhance the robustness of the design. These multiple signal paths usually result in strong couplings inside the circuit that necessitate a treatment spanning architecture, circuits, devices, and electromagnetic levels of abstraction     

A unified theory for frequency-domain simulation and sensitivityanalysis of linear and nonlinear circuits

The harmonic balance technique from nonlinear simulation is extended to nonlinear adjoint sensitivity analysis. This provides an efficient tool for the otherwise expensive but essential gradient calculations in design optimization. The hierarchical approach widely used for circuit simulation, is generalized to sensitivity analysis and to computing responses in any subnetwork at any level of the hierarchy. Important aspects of frequency-domain circuit computer-aided design (CAD) such as simulation and sensitivity analysis, linear and nonlinear circuits, hierarchical and nonhierarchical approaches, voltage and current excitations, or open- and short-circuit terminations are unified in this general framework. The theory provides a basis for the next generation of microwave CAD software. It takes advantage of mature techniques such as syntax-oriented hierarchical analysis, optimization, and yield-driven design to handle nonlinear as well as linear circuits. The sensitivity analysis approach has been verified by a MESFET mixer example, exhibiting a 90% saving of CPU time over the prevailing perturbation method     

Stability analysis of circuits including BJT differential pairs

In this paper, a necessary and sufficient condition for robust stability of electronic circuits at high frequency, which contain differential pair (emitter–coupled pair), is proposed. In fact, when emitter–coupled pairs are used as one input signal–one output signal, they have uncertainty in their transfer functions at high frequency. Even it is shown that this uncertainty can cause instability in closed loop electronic circuits at high frequency.The uncertainty is modeled as multiplicative perturbation in the transfer function of the differential pair at high frequency. Based on this uncertainty model, a necessary and sufficient condition for robust stability of above electronic circuits at high frequency is presented. This condition guarantees internal stability of the circuit at high frequency with respect to the uncertainty.     

Effects of UHF stimulus and negative feedback on nonlinear circuits

We investigate the combined effect of rectification and nonlinear dynamics on the behavior of several simple nonlinear circuits. We consider the classic resistor-inductor-diode (RLD) circuit driven by a low-frequency (LF) source when an operational amplifier with negative feedback is added to the circuit. Ultra-high-frequency (UHF) signals are applied to the circuit, causing significant changes in the onset of LF period doubling and chaos. Measurements indicate that this effect is associated with a dc voltage induced by rectification of the UHF signal in the circuit. The combination of rectification and nonlinear circuit dynamics produce qualitatively new behavior, which opens up a new channel of radio frequency interference in circuits.     

Perturbation-Based Fourier Series Analysis of Transistor Amplifier

A perturbation-based Fourier series model is proposed to approximate the nonlinear distortion in weakly nonlinear circuits. This general model is applicable to any set of multi-variable state equations that completely describe a nonlinear circuit. This model is applied to a common emitter amplifier circuit wherein the transistor is represented by Ebers–Moll nonlinear current equations. Appropriate state variables are defined, then the linear and nonlinear parts of the Ebers–Moll current equations are separated, and a small perturbation parameter is incorporated into the nonlinear part. Now these current equations are incorporated into the set of KCL, KVL equations defined for the circuit and the state variables are perturbatively expanded. Hence, multi-variable state equations are obtained from these equations. The state variables are approximated up to first order through Fourier series expansion, as described in the proposed model. The main advantage of the proposed model is that it is simple and straightforward approach to analyze weakly nonlinear circuits, as it involves matrix computations and the calculations of exponential Fourier coefficients.     

Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second- and higher-order responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits—a low-noise amplifier and a switching mixer—are obtained and compared with SPICE3 to validate the effectiveness of this method.     

A 60-GHz HEMT-MMIC analog frequency divider by two

This paper describes an analog frequency divider by two working in the millimeter wave frequency range around 60 GHz. This circuit is analyzed with a new method that allows one to determine the steady-state regime of any synchronized circuits with standard CAD commercial software. The method proposed relies upon the concept of open loop systems and is applicable to any feedback transistor circuits. The designed circuit was processed using a standard 0.25-μm HEMT technology. Four transistors were used for realizing the frequency division function as well as the input and output amplification. More than 10% frequency lock-in bandwidth was achieved, and conversion gain was obtained using input and output buffers. Measured results were found to be in good agreement with simulated ones     

PIN管控制电路功率容量的确定

PIN管控制电路的功率容量是一个重要的电路参数，必须全面考虑PIN管本身的功率容量和电路结构形式、施加的反向偏置电压、射频信号的频率和形式以及电路在系统中的匹配状况、工作环境和可靠性要求等各项因素综合确定。分析了对影响电路功率容量确定的各种因素，介绍了在射频系统中PIN管控制电路功率容量确定的综合方法。     

Steady-state analysis of nonlinear circuits with periodic inputs

In the computer-aided analysis of nonlinear circuits with periodic inputs and a stable periodic response the steady-state periodic response is found for a given initial state by simply integrating the system equations until the response becomes periodic. In lightly damped systems this integration could extend over many periods making the computation costly. In this paper a Newton algorithm is defined which converges to the steady-state response rapidly. The algorithm is applied to several nonlinear circuits. The results show a considerable reduction in the amount of time necessary to compute the steady-state response. In addition, the initial iterates give information on the transient response of the system.     

Inducing Chaos in Electronic Circuits by Resonant Perturbations

We propose a scheme to induce chaotic attractors in electronic circuits. The applications that we are interested in stipulate the following three constraints: 1) the circuit operates in a stable periodic regime far away from chaotic behavior; 2) no parameters or state variables of the circuit are directly accessible to adjustment and 3) the circuit equations are unknown and the only available information is a time series (or a signal) measured from the circuit. Under these conditions, a viable approach to chaos induction is to use external excitations such as a microwave signal, assuming that a proper coupling mechanism exists which allows the circuit to be perturbed by the excitation. The question we address in this paper is how to choose the waveform of the excitation to ensure that sustained chaos (chaotic attractor) can be generated in the circuit. We show that weak resonant perturbations with time-varying frequency and phase are generally able to drive the circuit into a hierarchy of nonlinear resonant states and eventually into chaos. We develop a theory to explain this phenomenon, provide numerical support, and demonstrate the feasibility of the method by laboratory experiments. In particular, our experimental system consists of a Duffing-type of nonlinear electronic oscillator driven by a phase-locked loop (PLL) circuit. The PLL can track the frequency and phase evolution of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors     

Automatic Digital Method for Measuring the Permittivity of Thin Dielectric Films

One of the most promising techniques for measuring the electric permittivity at microwave frequencies of thin dielectric materials of the order of 0.1 to 10 /spl mu/m, is the cavity perturbation method. For thin films of this type, it is necessary to determine accurately and display small changes in the resonant frequency and Q factor of the cavity in the presence of the material sample. A circuit for the simultaneous measurement and digital readout of the resonant frequency and Q factor of microwave cavity is described. For the resonant frequency measurement, a very efficient automatic frequency circuit, with a homodyne modulation-detection bridge and frequency stabilization loop, is applied. Theoretical analysis and experiments results with this circuit show that an accuracy of 5x10/sup -7/can be achieved in the resonant frequency measurement. For measuring the Q factor, two similar circuits are described. The technique is based on measuring the phase shift of the envelope of an amplitude modulated microwave signal when this signal is transmitted through a resonant cavity at resonance. Although an accuracy of 0.5 percent in the Q factor can be achieved, it is shown that the main limiting factor in both circuits is the accuracy of phase shift determination at RF frequencies.     

Nonlinear Frequency-Modulation Distortion Analysis for VCO Based on Harmonic Balance Method

The analysis methods for the steady-state responses of the voltage tuning negative resistance oscillator (voltage-controlling oscillator, VCO) by the microwave nonlinear autonomous circuit harmonic balance method in millimeter-wave bands are studied in the paper. Firstly, the quasi-periodic characteristic of the steady-state response of the VCO modulated by a periodic signal is proved. Then, on the bases of the harmonic balance analysis and the inter-modulation balance analysis, a novel method for obtaining the steady-state tuning performance and the nonlinear frequency-modulation distortion characteristic of the VCO is presented. The total analysis process is aimed to a kind of NRD-guide Gunn diode VCO. The large-signal lumped equivalent circuit model of the millimeter-wave P⁺N-junction varactor is also given for explaining the algorithm and the principle of the NRD-guide VCO.     

Frequency-domain bivariate generalized power series analysis ofnonlinear analog circuits

Bivariate generalized power series analysis is introduced for the analysis and behavioral modeling of nonlinear analog circuits and systems. It can be used to model analog subsystems and is compatible with circuit simulation, thereby allowing full circuits and behaviorally modeled analog subcircuits to be simulated together in an analog circuit/system simulator. The entire analysis is performed in the frequency domain, and arbitrary nonlinear circuits and any number of noncommensurable input frequencies can be accommodated. A diode ring demodulator is analyzed as an example     

A circuit reduction technique for finding the steady-state solutionof nonlinear circuits

Computing the steady-state response of large nonlinear circuits is becoming a key simulation requirement due to the rapid market growth of RF silicon integrated circuits. In this paper, we describe a nonlinear circuit reduction algorithm for finding the steady-state response. The proposed algorithm uses a congruent transformation-based technique to reduce the harmonic-balance equations into a much smaller set of equations. The main feature of the reduced circuit is that it shares with the original one a certain number of the derivatives with respect to the RF input power, steady-state analysis is then carried out on the reduced circuit instead of the original circuit