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DESIGN OF VARIABLE FREQUENCY

OSCILLATOR

Abstract -This project explores robust design of colpitts oscillator. Considering the difficulties faced by designer to select the values of components like resistors, capacitors, inductors etc., this project shows the development of a program that shall remove this problem. The circuit upon which program has been developed is basic colpitts oscillator circuit. The program will calculate the appropriate values of all the required parameters needed for the circuit as per an algorithm explained later and the oscillator will produce the desired frequency response . Although we have set maximum and minimum values of frequency of operation but the program can be used even for higher and lower frequency ranges.

I. INTRODUCTION

Colpitts and Hartley oscillators are widely used in the communication and computer systems. The Colpitts circuit, like other LC oscillators, consists of a gain device (such as a bipolar junction transistor, field-effect transistor, operational amplifier, or vacuum tube) with its output connected to its input in a feedback loop containing a parallel LC circuit (tuned circuit), which functions as a band pass filter to set the frequency of oscillation.

Usually while designing the oscillator we need to first choose an input frequency. After setting the frequency we need to choose proper values of inductances and capacitances for the tank circuit. The calculations required for designing the amplifier part has also to be done beforehand. After that to produce the sinusoidal curve of the desired frequency is also a tedious task. The program developed here eliminates the need to calculate all such values. The program itself shall calculate the values of all required parameters and produce the desired frequency response. Hence user has to input only the required frequency. Simulation and experimental results will verify the above mentioned results.

II. COLPITTS OSCILLATOR

Oscillators are circuits that generate a continuous voltage output waveform at a required frequency with the values of the inductors, capacitors or resistors forming a frequency selective LC resonant tank circuit and feedback network. The frequency of the oscillatory voltage depends upon the value of the inductance and capacitance in the LC tank circuit.

A.Basic Colpitts Oscillator Circuit

It consists of a tank circuit which is an LC resonance sub circuit made of two series capacitors connected in parallel to an inductor and frequency of oscillations can be determined by using the values of these capacitors and inductor of the tank circuit. This oscillator is almost similar to Hartley oscillator in all aspects; hence, it is termed as electrical dual of Hartley oscillator and is designed for the generation of high frequency sinusoidal oscillations with the radio frequencies typically ranging from 10 KHz to 300MHz. The major difference between these two oscillators is that it uses tapped capacitance,

whereas the Hartley oscillator uses tapped inductance.

III. DEVELOPMENT OF NGSPICE CODE

Ngspice is a general-purpose circuit simulation program for nonlinear and linear analyses. Circuits may contain resistors, capacitors, inductors, mutual inductors,

independent or dependent voltage and current sources, loss-less and lossy

 transmission lines, switches, uniform distributed RC lines, and the five most common semiconductor devices: diodes, BJTs, JFETs, MESFETs,

and MOSFETs.

A. Tank Circuit

The frequency is determined by the tank circuit and is varied by varying the values of the variable inductor L and keeping the values of capacitor C1 and C2 constant or vice versa. Here we have assumed C1=C2=C. The formula for calculating the frequency is given as follows:

Æ’r=1/(2ÐŸâˆš(L1*C T ))

fr=frequency of oscillation

L=Value of inductance

CT=Value of effective capacitance

CT= C1C2/(C1+C2)

Ngspice Code

*PARAM: Parametric netlists

Ngspice allows for the definition of parametric attributes in the netlists. This is an enhancement

of the ngspice front-end that adds arithmetic functionality to the circuit description language.

Syntax:

.param <ident> =<expr>â€¦..

First of all appropriate capacitance is selected for the desired frequency response as calculated

from relevant design equation. The calculations were done on project and final values of each component is given in the following table

TABLE I

Values of Various components involved in oscillator design

 Symbols Components Calculated values Vcc Power supply 6V Vb Bias voltage 1.2V Ib Base current 12uA Ie Collector current 1.2mA R1 Pot. Divider 40k ohm Resistance 1 R2 Pot. Divider 10k ohm Resistance 1 Re Emitter resistance 1k ohm Cb Coupling Capacitor 0.02nF Cc Coupling Capacitor 3.2nF Ce Bypass capacitor 1.6nF

After that as per the formula frequency is calculated. Intermediate constant has been defined to ease the view

B.Amplifier Design

It is a class A amplifier as the output current flow for full cycle of the input signal. It also allows the linear operation of the a.c signal and distortion reduced to

minimum with correct biasing. For this particular oscillator, by taking

Ib = 12ÂµA, the Q - point was located at the intersection and the value of IC at Q - point was obtained from the curve to be 1.2mA. From the values obtained for IC, VCC, VCE, and I B, the numerical values of the biasing resistors and capacitors were These values were calculated by the program using the formulae

IV.SIMULATION

A. AC analysis

The ac analysis of the program is also under the control of input frequency. Starting and stopping frequency is taken approximately ten times lower and higher to that of input frequency so as to produce response perfectly. In this design input frequency of 100GHz is given and sharp peak is produced in magnitude vs frequency response.

3 B.Transient analysis

Transient simulation is also set so that we get oscillator

generated sinusoidal signal. The period of display is twice

of input frequency and step size is one thousand times less

than input frequency. .

.

V. DISCUSSIONS

This project here explores the development of program which is self-sufficient in itself to calculate the required values of all circuit components. This program if taken further can be used as user interface software where user can get to know about the values of circuit component needed for designing oscillator. Hence its time saving and efficient.