X International conference�“Information Technology and Implementation” (IT&I-2023)�Kyiv, Ukraine

1

Dedicated to the tenth anniversary of the Faculty of Information Technology

Computer Model of Tuned Oscillator

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Volodymyr Nakonechnyi

Taras Shevchenko National University of Kyiv

volodym.nakonechnyi@knu.ua

​

Oleksandr Pliushch

Taras Shevchenko National University of Kyiv

oleksandr.pliushch@knu.ua

​

Nikita Bondarenko

Kazakh-British Technical University

ni_bondarenko@kbtu.kz

​

Arman Jangeldinov

Kazakh-British Technical University

a_jangeldinov@kbtu.kz

Current State of the Field

• Tuned oscillators play an important role in electronic communications for creating stable sinusoidal waveforms with the required frequency;
• The tuned power oscillators are electronic circuits without a driver, in which oscillations are maintained by the feedback signal coming from the sinusoidal output voltage;
• They can operate in different modes and with different characteristics.
• Despite its seeming simplicity, tuned oscillators are difficult to analyze.

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Subject of the research: tuned oscillators;

Object of the research: processes in tuned oscillators, including emergence of the oscillations and their establishment

Introduction

There are two main types of design and performance analysis methods

time-domain and frequency-domain ones

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Main methods of tuned oscillators’ design and performance analysis

To describe circuit behavior, it is necessary to solve the nonlinear algebraic equation, or system of equations, which do not generally admit a closed form solution (analytical).

​

• One of the most common numerical methods to solve such equations is a method based on the Newton–Raphson algorithm;
• Another method is quasilinear or Barkhausen–Moeller method based on the use of the ratios between the fundamental-frequency components of currents and voltages;
• Also deployed is the Van der Pol method for analyzing behavior of the oscillation systems described by the nonlinear second-order differential equations;
• Method of the Bessel functions is also used, and so on.

At the same time

Rapid development of the computer technologies create unique opportunities for using computer simulation models for tuned oscillators design and performance analysis

Objective of the research: To develop computer simulation model of the tuned oscillator and to demonstrate that it can be effectively used to design and analyze such devices

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Figure 1: Information flow and the controlling inputs in the oscillator

Diagram and Information flow in the tuned oscillator

Tuned Oscillator Computer Model Design

Choice of the collector current – base voltage characteristic for the active element (transistor).

The authors propose to use a sine wave approximation of the following form:

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

(1)

Where

i_col is the transistor collector current;

I_colmax – maximum collector current;

u_B – base voltage;

U_Bmax – maximum base voltage.

Figure 2: Collector current-base voltage characteristic of the transistor

Tuned Oscillator Computer Model Design

1.1 Differential equations describing output element of the oscillator

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

1. Systems of Differential Equations

(2)

(3)

1.2 Differential equation for the input voltage of the active element (transistor)

(4)

2. Transition from the system of Differential Equations to the one of Difference

(5)

Euler equation

Tuned Oscillator Computer Model Design

In their entirety, equations (6), (7), (8) and (9) represent computer simulation model for the oscillator shown in figure 1. In addition, it has many useful parameters that can be varied for different set-ups of some computer experiments. All this makes the computer model especially useful for research in the field.

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

3. The System of Difference Equations

(6)

(8)

(7)

(9)

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Table 1

Parameters of the oscillator computer simulation model and their values

Computer simulation was done for the following values of the computer simulation model

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 3: Collector current, capacitor voltage and inductance current for the feedback factor 0

Figure 4: Collector current and base voltage for the feedback factor 0

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 5: Collector current, capacitor voltage and inductance current for the feedback factor 0.02

Figure 6: Collector current and base voltage for the feedback factor 0.02

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 7: Collector current, capacitor voltage and inductance current for the feedback factor 0.04

Figure 8: Collector current and base voltage for the feedback factor 0.04

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 9: Collector current, capacitor voltage and inductance current for the feedback factor 0.06

Figure 10: Collector current and base voltage for the feedback factor 0.06

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 11: Collector current, capacitor voltage and inductance current for the feedback factor 0.08

Figure 12: Collector current and base voltage for the feedback factor 0.08

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Computer Simulation Results

Figure 13: Collector current, capacitor voltage and inductance current for the feedback factor 0.1

Figure 14: Collector current and base voltage for the feedback factor 0.1

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Discussion of the Computer Simulation Results

1. The designed computer simulation model correctly represents the processes in the tuned oscillator.
2. It does not contradict the theoretical notions concerning operation of the oscillators.
3. It is clear that the oscillation becomes self-sustaining when the feedback factor reaches around 0.07.
4. Overall analysis of the computer experiments with the designed computer simulation model shows that the model correctly represents operation of the oscillator shown in figure 1 and due to its simplicity and clarity can be successfully used to study processes in such oscillators as well as many others with some minor modifications.

Conclusions

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

• In this paper an alternative approach to studying processes in oscillators has been proposed.
• This approach is based on the computer simulation model implemented in the Matlab environment.
• The developed model has been tested for the scenario of changing feedback factor in the oscillator. Simulation results proved that the model correctly represents the processes in the oscillator, and they comply with the general understanding of the processes in such devices.
• Those results also support the conclusions and assumptions made in scientific literature by other authors. This approach is simple, understandable and can be modified to be used for a wide range of tuned oscillators.
• Designed computer model can be used for doing new promising research in the field as well as improving performance of the existing devices.