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A sinusoidal nonlinear oscillator with adjustable frequency
(2009-12-01)
Hanmeng, Nithima
;
Pranayanuntana, Poramate
A sinusoidal nonlinear oscillator with adjustable frequency was studied. The frequency of oscillation was adjusted via the change of the center frequency of the second order band-pass filter, while keeping the quality factor constant. The describing function method was used to predict the limit cycles and to analyze the stability of oscillation. The proposed circuit consisted of two important parts in the feedback connection configuration: an operational transconductance amplifier (OTA) as a nonlinear element in feedback path; and a bandpass filter in the feedforward path. The experimental results were simulated by the ORCAD CAPTURE and MATLAB computer programs.
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An electronically adjustable amplitude of OTA-based sinusoidal nonlinear oscillator
(2009-11-18)
Pranayanuntana, Poramate
;
Khwankaew, Weerawat
A systematic approach to adjust the amplitude of a sinusoidal nonlinear oscillator is discussed in this paper. Operational transconductance amplifier (OTA) and adjustable high-Q, second order bandpass filter are nonlinear element and linear element, respectively. The describing function method is used to find periodic solutions for nonlinear system. Experimental and simulation results are simulated using ORCAD CAPTURE, while, the numerical results are obtained using MAPLE and MATLAB. © 2009 IEEE.
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A proof of Sn-i (a11,..., ann) ≥ Sn-i (λ1,..., λn), 0 ≤ i ≤ n - 1 for an n × n positive definite symmetric matrix A = [aij]nxn, using mixed determinants
(2007-01-01)
Pranayanuntana, Poramate
By using mixed determinant of special form D (A, n - i; I, i) for positive definite symmetric matrix A, in particular the operator concavity property of the map f : A → D<sup>1/(n-i)</sup> (A, n - i; I, i)I together with unital positive linear map Φ : A → A ο I the Hadamard product of A with the identity matrix I, inequalities of the form S<inf>n-i</inf>(a<inf>11</inf>,..., a<inf>nn</inf>) ≥ S<inf>n-i</inf>(λ<inf>1</inf>,..., λ<inf>n</inf>), 0 ≤ i ≤ n - 1 for an n × n positive definite symmetric matrix A = [a<inf>ij</inf>] with S<inf>k</inf> : IR<sup>n</sup> → IR, k = 1, 2,...,n defined by S<inf>k</inf>(χ) := ∑<inf>1</inf>≤i<inf>1</inf><i<inf>2</inf><...< i<inf>k</inf>≤n χ<inf>i1</inf> χ<inf>i2</inf> · χ<inf>ik</inf>, and called the elementary symmetric polynomials and λ<inf>i</inf>, i = 1, 2,...,n the eigenvalues of A, are derived. This result was first proved using Schur-concavity property of the elementary symmetric function S<inf>k</inf> (χ) together with the fact that for any positive definite symmetric matrix A, the vector of its diagonal entries is majorized by the vector of its eigenvalues. Hence, this suggests relationship among mixed determinant, majorization and Schur-concavity.
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New matrix inequalities for Firey's extension of Minkowski and Brunn-Minkowski inequalities
(2006-07-01)
Pranayanuntana, Poramate
;
Gordon, John
The Brunn-Minkowski theory is a central part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Various matrix analogs of these notions and inequalities have been well known for over a century. We present a few new analogs. The major theorems presented here are the matrix analogs of Firey's Extension of Minkowski inequality and Firey's Extension of Brunn-Minkowski inequality.
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The matrix analog of the Kneser-Süss inequality
(2006-07-01)
Pranayanuntana, Poramate
;
Hemchote, Patcharin
;
Pantaragphong, Praiboon
The Brunn-Minkowski theory is a core part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Various matrix analogs of these notions and inequalities have been well known for a century. We present a few new analogs. The major theorem presented here is the matrix analog of the Kneser-Süss inequality.
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The describing function method and the analysis of the magnitude stabilization phenomenon in a nonlinear OSC
(2005-12-01)
Pranayanuntana, Poramate
;
Anuntahirunrat, Kongsak
;
Fongsamut, Chalermpan
;
Kaewsaiha, Pongrapee
We present a nonlinear analysis of a non-linear oscillator which uses an operational transconductance amplifier (OTA), a second generation current conveyor (CCII), or a current feedback operational amplifier (CFOA) as a nonlinear element. Nonlinear oscillators are nonlinear systems that can display oscillations of fixed amplitude and fixed period without external excitation. These oscillations are called limit cycles, or self-excited oscillations. The magnitude stabilization phenomenon in a nonlinear oscillator is one of the characteristics of stable limit cycles. An equivalent feedback configuration of an oscillator circuit with a nonlinear feedback element is used. The essential tool here is the describing function method used for predicting the existence of limit cycles and, more generally, used to analyze the magnitude stabilization phenomena. We motivate this method for the physical insights into the analysis and design of nonlinear oscillator circuits based on nonlinear devices such as OTA, CCII, CFOA, etc. The describing function method offers also a way for finding the magnitude of an oscillation via an integral equation. Simulation results using MATLAB and PSPICE agree well with the theory. © 2005 IEEE.

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