Вісники та науково-технічні збірники, журнали
Permanent URI for this communityhttps://ena.lpnu.ua/handle/ntb/12
Browse
9 results
Search Results
Item Application of the frequency symbolic method for the analysis of a quadrature demodulator of a telecommunication system(Lviv Politechnic Publishing House, 2017-02-19) Мандзій, Богдан; Чабан, Ксенія; Шаповалов, Юрій; Бачик, Дарія; Mandziy, Bohdan; Chaban, Ksenia; Shapovalov, Yuriy; Bachyk, Dariya; Lviv Polytechnic National UniversityПроаналізовано роботу квадратурного демодулятора сигналів типу QPSK з урахуванням впливу параметрів фільтра нижніх частот. Такий квадратурний демодулятор широко застосовують у сучасних телекомунікаційних системах, тому що на приймальному пункті виникає завдання розділення сигналу QPSK на два сигнали PSK (синфазний і квадратурний) з наступним детектуванням і прийняттям рішення про характер отриманого бінарного сигналу (“одиниця” чи “нуль”). Це завдання виконує двоканальний демодулятор приймача окремо для синфазної та квадратурної складової сигналу QPSK. Помилкове рішення може бути прийняте внаслідок впливу паразитних складових сигналу, які діють на входах вирішувальних пристроїв. У середовищі системи UDF MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits) проаналізовано вплив параметрів вхідних сигналів та параметрів елементів схеми синхронних детекторів на вихідні сигнали синфазного каналу. На прикладі аналізу синхронного детектора показано, що використання частотного символьного методу дає змогу в явному вигляді визначити вплив параметрів вибраних елементів схеми на характеристики функціональних вузлів телекомунікаційної апаратури.Item Розширення можливостей системи програмних функцій MAOPCs-стосовно формування передавальних характеристик лінійних параметричних кіл(Видавництво Львівської політехніки, 2016) Шаповалов, Ю. І.; Мандзій, Б. А.; Бачик, Д. Р.Описано розширення можливостей системи MAOPCs стосовно обчислення передавальних функцій лінійних параметричних кіл, що являють собою відношення довільних напруг та струмів кола. Теоретичною основою обчислень для такого розширення вибрано табличний метод формування математичної моделі кола. The system program function MAOPCs is designed to study multivariate analysis and optimization of state linear periodically-time-variable circuits. The architecture of the system MAOPCs is based on the principles of softwareMatlab environment, which provides the existence of the independent the software functions and creating the user-defined functions, and because it is an open system, it allows you to supplement it with the new functions. These additions extend the functionality of the system MAOPCs, make its application more efficient for analysis, research or design of the electronic devices, that are modeled by the linear periodically-time-variable circuits. The mathematical software of the systemMAOPCs based on the frequency symbolic method, which allows us to calculate the conjugate parametric transfer functions of linear periodically-time-variable circuits. Such transfer functions linking the input signals with the output signals in the form of approximating polynomials of Fourier in trigonometric or complex form. By the same polynomials of Fourier are approximated the normal parametric transfer functions, which are the basis of assessment of the asymptotic stability of the circuit. The systemMAOPCs implements symbolic methods of calculation, because the conjugate and normal transfer functions usually contain a number of parameters of the elements, that are defined by characters. Substitution of the numerical values in place of the following characters is performed, usually, in the last stages of solving the relevant tasks of the device designing. The limitation of the system MAOPCs is that the current system functions can only determine the transfer functions, which are the ratio nodal voltage of the circuit acting on the circuit signals in the form of the current sources. The aim of this work is to expand the functional capabilities of the systemMAOPCs with respect to the computation of the transfer functions, that are representing random variables of the circuit, among which are the arbitrary node voltages of the circuit, and the arbitrary voltages and currents on the elements of this circuit. Theoretical calculations for such an expansion are using the tabular describing method of the mathematical model of the circuit.Item Application of the frequency symbolic method for analysis of linear periodically-time-variable circuits in the time domain(Publishing House of Lviv Polytechnic National University, 2015) Shapovalov, Yuriy; Mandziy, Bohdan; Bachyk, Dariya; Turyk, MarianThis paper focuses on the problem of using the symbolic frequencymethod for the determining the time dependency of output signals of linear periodically-timevariable circuits by applying the inverse Fourier transform (for a steady-state mode) or the Laplace transform (for a transition mode) to the images of these signals obtained using the transfer functions. The frequency symbolic method allows us to calculate the conjugate parametric transfer functions of linear periodically-time-variable circuits. Such transfer functions link the input signals with the output signals in the form of approximating polynomials of Fourier in trigonometric or complex form. By the same polynomials of Fourier are approximated the normal parametric transfer functions which are the basis of assessment of the asymptotic stability of the circuit. To determine the conjugate and normal parametric transfer functions, there are the appropriate functions in the system of software functions Multivariate Analysis and Optimization of the Parametric Circuits (MAOPC), The system of software functions MAOPCs based on the frequency symbolic method and is implemented in the environment of MATLAB software. The paper presents the results of computational experiments obtained by the system of software functions MAOPCs which show the adequacy of the definition of steady-state and transient modes of linear periodically-time-variable circuits in the time domain using the transfer functions determined by frequency symbolic method. The coincidence of the results obtained by the system of software functions MAOPCs and the Micro-Cap7.0 program demonstrates the adequacy of applying the inverse Fourier and Laplace transforms for the investigations of linear periodically-time-variable circuits in the steady and transient modes in the MAOPCs environment. З’ясовано проблему застосування частотного символьного методу до визначення часових залежностей вихідних сигналів лінійних параметричних кіл на підставі застосування оберненого перетворення Фур’є (для усталеного режиму) чи Лапласа (для перехідного режиму) до зображення цих сигналів отриманих з використанням передавальних функцій. Частотний символьний метод дає можливість обчислювати спряжені параметричні передавальні функції лінійних параметричних кіл, що зв’язують вхідні сигнали з вихідними у вигляді апроксимуючих поліномів Фур’є у тригонометричній чи комплексній формі. Такими ж поліномами Фур’є апроксимуються нормальні параметричні передавальні функції, які є основою оцінювання асимптотичної стійкості кола. Для визначення спряжених та нормальних передавальних функцій ми використовуємо систему програмних функцій MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits), передбачено відповідні програмні функції. Система програмних функцій MAOPCs основана на частотному символьному методі. У роботі наведено результати обчислювальних експериментів, отриманих за системою програмних функцій MAOPCs, що показують адекватність визначення усталених та перехідних режимів лінійних параметричних кіл у часовій області за допомогою спряжених передавальних функцій, визначених за частотним символьним методом. Збіг результатів, отриманих за допомогою системи програмних функцій MAOPCs та за програмою Micro-Cap7.0, свідчить про адекватність застосування оберненого перетворення Фур’є та Лапласа для дослідження лінійних параметричних кіл в усталеному та перехідному режимах у середовищіMAOPCs.Item Дослідження стійкості параметричних підсилювачів у середовищі MAOPCs(Видавництво Львівської політехніки, 2015) Шаповалов, Ю. І.; Мандзій, Б. А.; Бачик, Д. Р.У пропонованій роботі наведено результати дослідження асимптотичної стійкості одно- та двоконтурного параметричних підсилювачів. Оцінка стійкості у системі функцій MAOPCs основана на визначенні коренів знаменника параметричної нормальної передавальної функції кола, що має вигляд степеневого полінома від комплексної змінної. 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 systemMAOPCs 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.Item Tolerance analysis and optimization of linear periodically time-variable circuits based on the frequency symbolic method(Publishing House of Lviv Polytechnic National University, 2014) Shapovalov, Yuriy; Mandziy, Bohdan; Bachyk, DariyaThe paper presents the procedures of tolerance analysis and optimization of linear periodically time-variable circuits, based on the frequency symbolic method and realized by the system of functions MAOPCs in an environment MATLAB. The peculiarity of tolerance analysis and circuit optimization consists in the fact that previously the assessment of asymptotic stability of the investigated linear periodically time variable circuit within the given limits of changes of circuit parameters is carried out and the permissible areas of their change in which the circuit is stable are determined. Exclusively in these areas tolerance analysis and optimization is realized. Розглянуто процедури аналізу допусків та оптимізації лінійних параметричних кіл, які основані на частотному символьному методі та реалізовані системою функцій MAOPCs у середовищі MATLAB. Особливість аналізу допусків та оптимізації полягає у тому, шо попередньо проводиться оцінка стійкості (асимптотичної) досліджуваного лінійного параметричного кола в заданих межах зміни параметрів та визначення областей допустимої їх зміни, у яких коло є стійким. Виключно у цих областях відбувається аналіз допусків та оптимізація.Item Про зменшення громіздкості математичної моделі лінійного параметричного кола(Видавництво Львівської політехніки, 2014) Шаповалов, Ю. І.; Мандзій, Б. А.; Бачик, Д. Р.Досліджено вплив вибору змінних диференціального рівняння, що описує лінійне параметричне коло у часовій області, на зменшення громіздкості такого рівняння. Запропоновано правила формування системи лінійних диференціальних рівнянь кола, що забезпечують її прийнятну громіздкість. In this paper are investigated the influence of variables the differential equation describing the linear periodically time-variable circuits in the time domain on decrease of bulkiness such equation. Rules of forming a system of linear differential equations of circuit that provide its acceptable bulkiness are proposed. Communication of voltages and currents on elements of an electric circuit looks like algebraic, differential and integral equations. As showed computer experiments, on the bulkiness of system of the equations, that describe in particular LPTV circuit and its further transformation in time domain, essentially influences presence of integrated expressions in this system. Since the input and output variables are usually given you must to choose such method of formation of system of equations, which would provide absence in it integral expressions. The first rule of formation of the system of equations of circuit is as follows: to provide absence the integral expressions in the system of equations describing a circle in the time domain, as variables in it need to choose the voltage on the capacitor and current in the inductor. One of the perspective methods of forming of equations is the tabular method. By the tabular method in system of equations as variables are selected nodal voltages, currents and voltages on the elements of the circuit, and the equations themselves may be formulated so that the integral expressions were absent. It follows the second rule of formation of system of differential equations which is as follows: in the absence of other requirements, mathematical model of circuit in the time domain advisable to form by the tabular method that provides absence the integral expressions in equations without additional action to remove them. In addition, the tabular method does not impose restrictions on the structure and elements of circuit. Under condition of performance of the presented two rules the system of the equations describing a circuit less bulky than without it. Normally in such systems variables which do not interest the researcher further are eliminated, and the equation in which there are only two variables is formed. Bulkiness of the last equation too can be different, and it depends on what variables left in it. The third rule of forming a differential equation that describes a circle in the time domain and that provides acceptable bulkiness is as follows: despite the fact which variables of circuit is an output variables, in a mathematical model of circuit that was formed by a rule 2, we eliminate all variables, except what correspond to an input signal and a parametric element. If sources of input signal or parametric elements in the circuit a few then such equations necessary to form few - one for each pair of “input - parametric element.” The differential equation that formed by the three rules using method L.A. Zadeh is transferred into the frequency domain and is solved by the frequency symbolic method. As a result we receive symbolic parametric transfer functions which are a basis for formation of a frequency symbolic model of each parametric element. Such models in turn are a basis for creation of frequency symbolic model of circuit as a whole. Such frequency symbolic model of circuit contains or determines output signals. Values of output signals of circuit may be are converted to the time domain.Item Cистема MAOPCS для багатоваріантного аналізу та оптимізації лінійних параметричних кіл у середовищі matlab(Видавництво Львівської політехніки, 2013) Шаповалов, Ю. І.; Бачик, Д. Р.; Маньковський, С. В.This paper considers the software realization the system of functions MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits) for multivariate analysis and optimization of linear parametric circuits based on frequency symbolic method. This method is based on the formation of the approximated transfer functions of linear parametric circuits in the form of Fourier trigonometric polynomials. The use of symbolic transfer functions allowed to form functions of sensitivity of linear parametric circuits, which, in turn, allowed to calculate the relative deviations of functions of linear parametric circuits at change of their parameters. The further development of frequency symbolic methods allowed to solve the task of multivariate analysis and optimization. The system of functions MAOPCs realized in the environment of MATLAB. The presence of powerful mathematical symbolic apparatus in MATLAB allowed to realize this system. The system MAOPCs represents a 17 functions, each of which has parameters (input data) and arguments and performs over them defined the conversions. The results obtained during the execution of one function (in some cases of several functions) can be parameters to other functions. Thus, based on of the developed system of functions the user can create algorithms and programs of computer computational experiments for multivariate analysis and optimization of parametric circuit, which we investigate. For research of linear parametric circuits in the environment ofMATLAB, using a system MAOPCs, need perform the system requirements. They are consist in the fact that, necessary to create the file with text of programof research of circuit , where indicate: parameters that carry information about the circuit, accuracy of calculations, location to save the results, the parameters of functions, functions MAOPCs in the sequence that corresponds to the algorithm of carrying out of investigation. After it is necessary execute the file in the environment of MATLAB. Research results are saved in another file. These results together with the intermediate data we can view using MATLAB, which will be displayed in working window. The example of research of single-circuit parametric amplifier using the system of functions MAOPCs is presented. In the task on research are described an algorithm of carrying out of experiment. The fragments (screenshots) of file, where describes the parameters and algorithm research are presented and fragment (screenshot) with reflection of results in working window ofMATLAB also is presented. Conclusions are drawn about what system functions MAOPCs allows you to: – compose an algorithm and a program of carrying out of computational experiments of research of linear parametric circuits without delving into the depths of mathematical apparatus of the realized methods and using the powerful symbolic apparatus and other internal functions in MATLAB in full; – locate functions in any order and replenish her new functions. Розглянуто програмну реалізацію системи функцій MAOPCs для багатоваріантного аналізу та оптимізації лінійних параметричних кіл на основі частотного символьного методу.Item Особливості визначення чутливості лінійних параметричних кіл у частотній області(Видавництво Львівської політехніки, 2013) Шаповалов, Ю. І.In software which are dedicated for the design of electronic circuits with constant parameters is widely used function of sensitivity, which allows you to focused solve the tasks of multivariate analysis and optimization of such circuits. The function of sensitivity of linear parametric circuits not used widely because there was no reliable methods of symbolic computation of parametric transfer functions. We proposed such method (frequency symbol method [3]), so, filling the existing gap in article discusses the possibility of forming functions of sensitivity of linear parametric circuits and is given account the peculiarities of their determination. For a basis of definition the concept of sensitivity of linear parametric circuit was taken definition of the concept of sensitivity of linear circuits with constant parameters. This feature of sensitivity of linear parametric circuit which consists in the fact that this sensitivity: a) is a function of two variables – complex variable and time; b) by the frequency symbolic method is determined based on approximated parametric transfer functions. It is shown that, typically, the sensitivity of parametric linear circuit varies periodically in time with period T, which is chosen in presentation the transfer function by trigonometric polynomial of Fourier. It was emphasized that the sensitivity of some parameters of parametric circuit in time can grow infinitely. This applies to the parameters that define the period T. We considered the example of elementary parametric linear circle, consisting of a single parametric capacity. The example illustrates the change the different functions of sensitivity of such circuit in time. It is shown that at sufficient accuracy of approximation of parametric transfer function by trigonometric polynomial of Fourier, derivatives on parameters of elements of circuit obtained from approximated parametric transfer functions enough to accurately reproduce derivatives on parameters of elements of circuit the original parametric transfer functions and, therefore, can be used to form the functions of sensitivity, as well as in solution of tasks multivariate analysis and optimization of linear parametric circuits. This conclusion shows a perspective application of frequency symbolic method to the mentioned problems. For illustration of material relating to the correctness of the definition of derivatives of parametric transfer functions on parameters of elements of parametric circuit is selected single-circuit parametric amplifier, in oscillatory contour, which the capacity varies with a period T. It is shown when the number of harmonic components in the approximated parametric transfer function k³ 4 then results in the calculation of the derivative of this function on the parameter does not change. Therefore, the value of derivatives that were obtained when k=4 were taken as a basis in these calculations. Obviously, the calculation for the selected k<4 will be inaccurate, and if k>4 it takes unjustified big time. It is shown the dependence the sensitivity of module of transfer coefficient of the input current to the output voltage from the depth of modulation of parametric capacity and time. Розглянуто особливості визначення чутливості лінійних параметричних кіл за апроксимації передавальних функцій тригонометричними поліномами Фур’є.Item Optimization of parametric balanced modulator based on frequency symbolic method(Publishing House of Lviv Polytechnic National University, 2012) Shapovalov, Yuriy; Mandziy, Bohdan; Bachyk, DariyaApplication of the frequency symbolic method for analysis of established modes of linear periodically time-variable (LPTV) circuits to solving an optimization task conditioned by the control of their asymptotic stability is considered. The results of optimization of a parametric balanced modulator with respect to the criterion which is based on calculation of the parametric transfer functions approximated by Fourier trigonometric polynomials are presented. Розглянуто застосування частотного символьного методу аналізу усталених режимів лінійних параметричних кіл до розв’язування оптимізаційної задачі за умови контролю їх асимптотичної стійкості. Наведено результати оптимізації параметричного балансного модулятора.