Perturbation analysis of nonlinear distortion in analog integrated circuits

Buonomo, Antonio Riccardo; Schiavo, Alessandro Lo

doi:10.1109/tcsi.2005.851695

Cited by 31 publications

(25 citation statements)

References 26 publications

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“…However, formulas are not able to predict a constant phase offset 0 = 5 ∘ , that is, due to the reactive behavior of nonlinearities, which were here assumed to be memoryless. Finally, it should be observed that the accuracy of amplitude formula is better for small injection values as it is derived assuming small injection values and neglecting output harmonics [21][22][23][24][25][26]. Thus, we can conclude that, even if small discrepancies are present between experimental and analytical results, formulas are able to capture the main characteristics of the injectionlocking phenomenon, providing a quite good approximation to experimental results.…”

Section: Resultsmentioning

confidence: 84%

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

Buonomo¹,

Schiavo²

2013

Journal of Electrical and Computer Engineering

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An analytical model and a methodology are presented for the analysis of CMOS injection-locked frequency dividers with direct injection, which are used in modern wireless communication systems. The amplitude and phase of the oscillation in the synchronous operation mode, as well as the locking range, are found in explicit form. The width of the locking range is determined by the condition of the existence and stability of synchronous oscillations. The accuracy of the model and of the presented formulas is validated through a comparison with experimental results, which are in good agreement with the analytical ones.

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Section: Resultsmentioning

confidence: 84%

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

Buonomo¹,

Schiavo²

2013

Journal of Electrical and Computer Engineering

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“…Now, for the first-order approximation of state variables, we compare the coefficients of ε 1 from (25), (26) and (27), and get the following three state variable equations for the state variables x (1) , z (1) and v (1) :…”

Section: Application Of System Model To the Common Emitter Amplifier mentioning

confidence: 99%

“…This is not the case if we work completely in the time domain. In [1], the basic model describing the nonlinear circuit has the form x = Su + Yg(x), where S and Y are linear operators. These form a set of algebraic equations.…”

mentioning

confidence: 99%

“…The method developed in our paper is capable of handling such models, as well as situations in which apart from the differential equations there are also algebraic equations, so that the dynamics of the circuit is given by T dx dt = F(x, u), where T could be a singular matrix. In [1], one of the examples considered a bipolar amplifier where there is only one state variable v be that satisfies a first-order differential equation. It is clear that the method developed in our paper can handle more general situations in which the state variables form a vector.…”

mentioning

confidence: 99%

“…It is clear that the method developed in our paper can handle more general situations in which the state variables form a vector. The model dx dt = F(x, u) in the steady-state sinusoidal situations may be reducible to that given in [1], but our method can handle transient situations. In [3], the Volterra series method has been applied to the Ebers-Moll model of a transistor amplifier.…”

mentioning

confidence: 99%

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Perturbation-Based Fourier Series Analysis of Transistor Amplifier

Rathee

Parthasarathy

2011

Circuits Syst Signal Process

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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.

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An analytical gm/ID‐based harmonic distortion prediction method for multistage operational amplifiers

Xie

Shi

2021

Circuit Theory & Apps

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SummaryAn analytical stage‐based harmonic distortion (HD) analysis method for multistage operational amplifiers (Op Amps) is developed in this work. This work contributes two fundamental methods that make the analytical HD prediction possible at the circuit level. Firstly, we propose that the traditionally used first order small‐signal transistor quantities gm (transconductance) and go (output conductance) in the gm/ID design methodology for bulk complementary metal‐oxide‐semiconductor (CMOS) technology can be extended to the higher order quantities gm(k) and go(k) ( ). With proper normalization, these quantities become neutral to the device dimensions and operation currents, hence can be precharacterized by sweeping simulations and used as lookup tables. Secondly, we further develop analytical nonlinearity expressions for a set of commonly used amplifier stages, represented as the functions of the nonlinearity parameters gm(k) and go(k) of the transistors that form a stage circuit. A combination of these two fundamental methods on hierarchical nonlinearity modeling enables us to apply the existing analytical HD estimation methods for the stage‐form macromodels to predict the circuit‐level HD behavior, overcoming the need of running repeated simulations under device resizing and rebiasing. The proposed harmonic distortion analysis method has been validated by application to real multistage amplifiers, achieving HD prediction results in excellent agreement to fully transistor‐level circuit simulation results but with substantial speedup.

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Perturbation analysis of nonlinear distortion in analog integrated circuits

Cited by 31 publications

References 26 publications

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

Perturbation-Based Fourier Series Analysis of Transistor Amplifier

An analytical gm/ID‐based harmonic distortion prediction method for multistage operational amplifiers

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