Investigation of Stability of Parametric Amplifiers in an Environment MAOPCs

Received: May 15, 2015
Accepted: September 16, 2015
Authors: 
Yu.I. Shapovalov, B.А. Mandziy, D.R. Bachyk

Lviv Polytechnic National University

The paper considers the question of the research of assessment of the stability of linear periodically time-variable circuits by the frequency symbolic method. The function system MAOPCs, which is based on the frequency symbolic method, is an effective tool of investigation of linear periodically time-variable circuits and in particular parametric amplifiers. The assessment of circuit stability in the system MAOPCs is carried out by the real parts of the denominator roots of a normal parametric transfer function of the inertial part of circuit, which is also defined by the frequency symbolic method in the form of approximation by the Fourier trigonometric polynomials. If the real parts of roots are negative, the circuit is asymptotically stable and is not stable if the real part of at least one of the roots is equal to zero or positive. This criterion of asymptotic stability deservedly gained great importance with the appearance of such an effective method of formation of parametric transfer functions as frequency symbolic method. This paper presents the results of research of asymptotic stability of one- and double-circuit parametric amplifiers. For a single-circuit parametric amplifier with two parametric elements maps of stability for different phase differences of parametric elements were built. When the phase difference is 0 ° zone of stability is the biggest and when the phase difference 180 ° zone of stability is the smallest. These two cases are called in literature a synchronous and asynchronous modes and it is shown that energies brought into the circuit by change of capacitance and inductance in the first case are deducted, and in the second case are attached. This fact has received full confirmation in experiments carried out in the system MAOPCs. In this paper it is shown that the formation of parametric transfer function by the frequency symbolic method and determining the roots of the denominator in which parameters of the circuit set in symbolic form nowadays is the most effective tool of assessment of the asymptotic stability of electronic devices which are represented by linear periodically time-variable circuits. This approach allows you to build the trajectories of roots and maps of stability under multiple change of numerical values of symbolic parameters of circuit. The results of computer experiments presented in this paper made it possible to draw the following conclusions:
˗ complete coincidence of the results between programs MAOPCs and Micro-Cap proves the adequacy of transfer functions formed by frequency symbolic method and high accuracy of assessment of stability through the roots of the polynomial;
˗ the frequency symbolic method allows you to effectively assess stability and to form trajectories of roots or map of stability of circuit by the change of its random parameters that it is sufficiently comfortable at stability control in tasks of statistical character and optimization of parametric devices;
˗ computer experiments have shown that the formation of parametric transfer function by the frequency symbolic method and determining the roots of its denominator nowadays is the most effective tool of assessment of the asymptotic stability of electronic devices which are represented by linear periodically time-variable circuits.