Multisinusoidal Input Research Articles

Wheeled Robot Formation Control under Uncertainty Including Adaptive Rejection of Harmonic Disturbances with Arbitrary Frequencies

This work addresses an adaptive regulation problem for formation control of uncertain unicycle-like dynamical robots. The control goal is to drive a finite number of robots to a prescribed formation despite the presence of multi-sinusoidal input disturbances of unknown frequencies and despite uncertainties in the unicycle model, (mass and inertia’s are unknown). Numerical Simulations were done to illustrate the viability of the suggested strategy. The only measurements available for control are the orientation of the unicycles and the relative positions and velocities according to a given connectivity graph.

Harmonic and intermodulation performance of double-gate CMOS inverting voltage amplifier

This paper presents a simple mathematical model for the transfer characteristic of the double gate (DG) CMOS inverting voltage amplifier. The model yields closed-form expressions for the amplitudes of the fundamental and distortion components of the output voltage resulting from a multisinusoidal input voltage for different scenarios and values of the bottom gates voltages. The special case of a two-tone equal-amplitude input voltage is considered in detail. The results show that the distortion performance of the DG-CMOS inverting voltage amplifier is strongly dependent on the bottom gates voltages and the amplitudes of the input sinusoids with the third-order intermodulation component dominating over the whole range of the input voltage amplitudes and different bottom gates voltages.

New single-parameter models for electronic circuits with even symmetry nonlinearity

In this paper single-parameter models are presented for the instantaneous characteristics of electronic circuits/systems exhibiting even-symmetry nonlinearities. The models can easily provide closed-form expressions, in terms of the ordinary Bessel functions, for the amplitudes of the second-harmonic and second-order intermodulation components at the output of the nonlinear circuit/system excited by a multisinusoidal input signal. Moreover, by combining the proposed models with the previously published models for instantaneous characteristics exhibiting odd-symmetry nonlinearities, a new method and apparatus are proposed for characterizing nonlinear circuits/systems exhibiting both even- and odd-symmetry nonlinearities. The proposed method and apparatus use the amplitudes of the measured output second- and third-order intermodulation components resulting from a two-tone equal-amplitude input signal.

Harmonic and intermodulation performance of MoS2FET- and GFET-based amplifiers

This paper presents a simple mathematical model for the output---input voltage characteristic of the graphene field effect transistor (GFET)- and the molybdenum disulfide field effect transistor (MoS2FET)-based inverting amplifiers. The model, basically a Fourier series, yields closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output voltage resulting from a multisinusoidal input voltage. The special case of a two-tone equal-amplitude input voltage is considered in detail. The results show that the harmonic and intermodulation performance of the complementary GFET- and the MoS2FET-based inverting amplifiers is strongly dependent on the bias voltage and the amplitudes of the input tones with the third-order intermodulation component dominating over a wide range of the input voltage amplitudes.

Harmonic and intermodulation performance of carbon nanotube field-effect transistor-based and single-electron tunnelling transistor-based inverting amplifiers

This article presents a simple mathematical model for the output-voltage/input-voltage characteristics of the carbon nanotube field-effect transistor (CNTFET)-based and the single-electron tunnelling transistor (SET)-based inverting amplifiers. The model, basically a Fourier-series, yields closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output voltage resulting from a multisinusoidal input voltage. The special case of a two-tone equal-amplitude input signal is considered in detail. The results show that the harmonic and intermodulation performance of the CNTFET-based and SET-based inverting amplifiers is strongly dependent on the values of the bias voltage and the amplitudes of the input tones. Moreover, the results show that for the CNTFET-based inverting amplifier, either the relative second-order or the relative third-order intermodulation component is dominant, while for the SET-based inverting amplifier, the relative third-order intermodulation is always dominant. The results also show that all the harmonics and intermodulation products may exhibit minima at different values of the input bias voltages and tone amplitudes.

Theoretical convergence analysis of FxLMS algorithm

In system identification when a secondary path follows the adaptive filter, the FxLMS algorithm is usually applied for updating the adaptive filter. Although several FxLMS convergence analyses have been conducted in detail, only a few have intended to derive a convergence condition. In fact, available FxLMS convergence conditions are only accurate for simplified cases with pure delay secondary paths or multi-sinusoidal input signals. This paper studies the FxLMS convergence behavior for moving average secondary paths and stochastic input signals. A novel model for predicting the FxLMS convergence behavior is developed. Based on this model, a necessary and sufficient condition for the convergence of the FxLMS is derived. Also, the condition leading to the fastest convergence is proposed. Compared to previously derived convergence conditions, the proposed condition applies to more general secondary paths. Results obtained from this study are found to correspond very well to those obtained from simulation experiments.

Theoretical Analysis of Carbon-Nanotube-Based Mixers and Frequency Multipliers

In this paper closed-form expressions are presented for the current components in a CNT-based p-n junction diode resulting from a multisinusoidal input voltage. The expressions obtained, in terms of the modified Bessel functions, are simple and can be used for calculating the amplitudes of the fundamental, harmonics and intermodulation (mixing) current components in the CNT-based p-n junction diode. Using these expressions the performance of the CNT-based p-n junction diode excited by an equal-amplitude two-tone was studied in detail. The results obtained show that the amplitudes of the harmonic and mixing components are strongly dependent on the DC bias voltage, the series resistance and the ideality factor of the p-n junction diode.

Harmonic and Intermodulation Performance of Metallic Carbon Nanotube (MCNT) and Complementary Carbon Nantube Field Effect Transistor (CNTFET) Amplifier

This paper presents a simple mathematical model for the output-voltage (current)/ input-voltage characteristic of the carbon nanotube field effect transistor (CNTFET) complementary inverting amplifier and the metallic carbon nanotube (MCNT) interconnect. The model, basically a Fourier series, yields closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output voltage (current) resulting from a multisinusoidal input voltage. The special case of a two-tone equal-amplitude input voltage is considered in detail. The results show that the harmonic and intermodulation performance of the complementary CNTFET-based inverting amplifier and the MCNT interconnect is strongly dependent on the values of the amplitudes of the input tones with the third-order intermodulation component dominating over a wide range of the input voltage amplitudes. The results also show that while the harmonics may exhibit minima, the intermodulation products are almost monotonically increasing with the increase in the input voltage amplitude and exhibit no minima.

Harmonic and Intermodulation Performance of Quantum-Well Mach-Zehnder Electro-Optic Modulators with Electrical Biasing

A mathematical model for the transfer function of the Mach-Zehnder interferometers based on the quantum-confined Stark effect (QCSE) is presented. The model, basically a cosine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of any scenario of large-amplitude multisinusoidal voltages. The special case of three-tone equal-amplitude input voltage is considered in detail. The results show the strong dependence of the harmonic and intermodulation performance on the electrical biasing. The results also show that for a proper selection of the electrical biasing the third-order intermodulation or the second-order intermodulation can be minimized. While the results obtained are in excellent agreement with previously published results, the present analysis is applicable to multisinusoidal input voltages with different scenarios and is not restricted to small-amplitude two-tone inputs only.

Prediction of Gain Expansion and Intermodulation Performance of Nonlinear Amplifiers

A mathematical model for the input-output characteristic of an amplifier exhibiting gain expansion and weak and strong nonlinearities is presented. The model, basically a Fourier-series function, can yield closed-form series expressions for the amplitudes of the output components resulting from multisinusoidal input signals to the amplifier. The special case of an equal-amplitude two-tone input signal is considered in detail. The results show that unless the input signal can drive the amplifier into its nonlinear region, no gain expansion or minimum intermodulation performance can be achieved. For sufficiently large input amplitudes that can drive the amplifier into its nonlinear region, gain expansion and minimum intermodulation performance can be achieved. The input amplitudes at which these phenomena are observed are strongly dependent on the amplifier characteristics.

Large signal performance of micromachined silicon inductive microphones

A mathematical model for the open-circuit output voltage of a micromachined silicon inductive microphone is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the output components resulting from a multisinusoidal input acoustic pressure. The special case of an equal-amplitude two-tone acoustic pressure input is considered in detail. The results show that, the microphone generates both even and odd-order harmonic and intermodulation products.

Large signal performance of micromachined silicon condenser microphones

A mathematical model for the open-circuit output voltage of a micromachined silicon condenser microphone with a single deeply corrugated diaphragm as a function of the applied acoustic pressure is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the output components resulting from a multisinusoidal input acoustic pressure. The special case of an equal-amplitude two-tone acoustic pressure input is considered in detail. The results show that the microphone generates only odd-order harmonic and intermodulation products. The results also show that the amplitudes of these components are strongly dependent on the microphone parameters, the corrugation depth and the ratio between the half-length of the diaphragm and its thickness. Moreover, the results show that the acoustic pressure required to produce a pre-specified output open-circuit voltage is strongly dependent on these parameters.

Harmonic and Intermodulation Performance of Mach-Zehnder Quadratic Electro-Optic

This paper discusses the large signal performance of Mach-Zehnder quadratic electro-optic intensity modulator. Simple, easy-to-evaluate algebraic expressions are obtained for the amplitudes of the fundamental, harmonic, and intermodulation components at the output of the modulator when excited by a multisinusoidal input signal. Special cases are considered and the feasibility of minimizing the amplitudes of the output harmonics and intermodulation products is explored.

Harmonic and intermodulation performance of the Darlington composite bipolar junction transistor

New expressions, in terms of the ordinary and modified Bessel functions, are presented for the amplitudes of the output harmonic and intermodulation products of the Darlington composite bipolar junction transistor excited by a multisinusoidal input voltage. SPICE simulation results confirming the presented theory are included.

Large signal analysis of low-voltage MOS analogue functional elements using Fourier-series approximations

This paper discusses the large signal performance of low-voltage analogue functional elements built around MOS field-effect transistors (MOSFETs). Fourier-series approximations are obtained for the transfer characteristics of the basic building blocks; such as the balanced source-coupled pair, the unbalanced source-coupled pair with different transistor sizes, the source-coupled pair with bias offset and the squaring circuits. Using the Fourier-series approximations of these basic building blocks, closed-form expressions are obtained for the amplitudes of the harmonics and intermodulation products at the output of analogue functional elements; such as the basic differential pairs, half-wave rectifiers, full-wave rectifiers and multipliers excited by a multisinusoidal input signals. Using these expressions comparison between the large signal performance of analogue functional elements can be performed and the parameters required for a predetermined performance can be determined.

Large Signal Analysis of Low-Voltage Bipolar Analog Functional Elements using Fourier-Series Approximations

This paper discusses the large signal performance of low-voltage analog functional elements built around bipolar-junction transistors. Fourier-series approximations are obtained for the transfer characteristics of the basic building blocks; such as the balanced emitter-coupled pair, the unbalanced emitter-coupled pair with different transistor sizes, the emitter-coupled pair with bias offset and the triple-tail cell. Using the Fourier-series approximations of these basic building blocks, closed form expressions are obtained for the amplitudes of the harmonics and intermodulation products at the output of analog functional elements; such as the basic differential pairs, squaring circuits, operational transconductance amplifiers, multipliers, mixers and triplers, excited by a multisinusoidal input signal. Using these expressions comparison between the large signal performance of analog functional elements can be performed and the parameters required for a predetermined performance can be determined.

Nonlinear performance of the CMOS buffer stages

The nonlinear behaviour of the CMOS buffer stages, the single-stage complementary source follower and the complementary source follower cascade are analysed. Closed-form expressions are obtained for the harmonic and intermodulation components resulting from a multisinusoidal input signal. These expressions can be used to predict the limiting values of the input current for a prespecified tolerable distortion percentage.

Harmonnic and Intermodulation Performance of Op-Amp Power-Supply Current and the Dual Translinear Loop

The nonlinear behavior of the op-amp power supply current and the dual translinear loop are analyzed. Closed-form expressions are obtained for the harmonic and intermodulation components resulting from a multisinusoidal input signal. These expressions can be used to predict the limiting values of the input current for a prespecified tolerable distortion percentage.

Large Signal Analysis of Optical Intensity Modulator with Dual-Modulation Compensation

Large signal analysis of an optical intensity modulator with dual-modulation compensation and driven by a multisinusoidal input signal is presented. The special case of a small amplitude single-sinusoid driving signal is considered in details and the results are compared with previously published results.

Harmonic and Intermodulation Performance of Nonlinear Electronic Circuits

A unified technique for mathematical modelling of the input output characteristics of nonlinear electronic circuits is presented. This technique can be easily implemented using simple hand computations without recourse to standard curve-fitting techniques, which invariably requires extensive computing facilities and well-developed software. The mathematical model, basically a sine-series function, can easily yield closed-form series expressions for the amplitudes of the output components resulting from a multisinusoidal input signal to nonlinear electronic circuits. The technique is very helpful in analysing nonlinear electronic circuits under different scenarios of input signals.