Showing papers on "Volterra series published in 1970"
TL;DR: In this paper, the authors analyzed the intermodulation distortion of a solid-state feedback amplifier and showed that the feedback is fully effective in reducing the open-loop second-order distortion.
Abstract: This paper analyzes the intermodulation distortion of a solid-state feedback amplifier. Each transistor of the amplifier has been represented by a frequency-dependent model incorporating four nonlinearities. The Volterra series is used as the analysis tool. The primary motivation for this study is that intermodulation distortion is a critical problem in high-frequency long-haul solidstate systems. A computer program that calculates the amplifier intermodulation distortion has been developed. This program can be used to select the optimum bias point of each stage, optimum interstage and feedback networks, and optimum load and source impedances. Good correlation between calculated and measured results was obtained. The closed-form expressions derived show that the feedback is fully effective in reducing the open-loop second-order distortion and that the feedback may not significantly reduce the open-loop third-order distortion, if the "second-order interaction" phenomenon is dominant. The second-order interaction is explained in detail in this paper.
134 citations
TL;DR: In this paper, a method for generating a discrete Volterra type series expansion for certain non-linear difference equations describing a class of nonlinear discrete-data systems is presented.
Abstract: This correspondence deals with a method for generating a discrete Volterra type series expansion for certain non-linear difference equations describing a class of nonlinear discrete-data systems. The method permits the formulation of a criterion for the convergence of the series via the contraction mapping principle.
7 citations
TL;DR: In this article, the authors present a method for including non-zero initial conditions in the Volterra series solution of a class of non-linear systems, and show that simultaneously one determines (for an undriven system) a region of asymptotic stability and (for a driven system) bounded-input bounded-output stability.
Abstract: This paper presents a method for including non-zero initial conditions in the Volterra series solution of a class of non-linear systems. Also, it is shown that simultaneously one determines (for an undriven system) a region of asymptotic stability and (for a driven system) a region of bounded-input bounded-output stability.
6 citations
TL;DR: In this paper, the stability of round-rotor synchronous machines is investigated from a mathematical model which includes winding resistance, leakage reactance and iron loss, and the Volterra boundaries do not lie wholly within the exact computed boundaries, but rather they are an approximation to them.
Abstract: The stability of unsaturated, round-rotor synchronous machines is investigated from a mathematical model which includes winding resistance, leakage reactance and iron loss. Under certain conditions an exact boundary can be obtained and very close agreement is obtained between it and experimental results. The effect on stability of varying the machine loading is demonstrated. When stator resistance and iron loss are neglected the differential equation representing the machine is second order with a linear damping term. The stability of this equation is investigated by a Volterra series method and the resulting stability boundaries are compared with analogue computations. The Volterra boundaries do not lie wholly within the exact computed boundaries, as do for instance Lyapunov boundaries, but rather they are an approximation to them. This approximation ia shown to be good over a wide range for the examples considered.
4 citations
TL;DR: In this article, up to the third order frequency response functions (kernel) are developed and a comparison with the Equivalent Linear Method is presented, and a sensitivity analysis is done to show how the series is affected with the quantity of terms in it.
Abstract: For several years the Equivalent Linear Method was the most used method to solve dynamic problems of stratified soil deposits. This is valid for soils showing small or medium nonlinearities. It is an iterative procedure without a mathematical approach associated to it. The proposed mathematical method is based on the use of the First and Higher Order Frequency Response functions as required by the Volterra series. This method is based in the determination of the functions that relates the input motion to the response. In this study, up to the third order frequency response functions (kernel) are developed. The use of these expressions in some numerical examples and a comparison with the Equivalent Linear Method will be presented. Also, a sensitivity analysis is done to show how the series is affected with the quantity of terms in it. It will be demonstrated that at low or medium shear strain, three terms in the series are acceptable to obtain the result produced by the Equivalent Linear Method.