colpitts oscillator by rasikh tariq

COLPITTS OSCILLATOR

by

Rasikh Tariq

ME-113006

&

Mehroze Ali Najmi

ME-113077

A Project Report submitted to the DEPARTMENT OF ELECTRONIC ENGINEERING

in partial fulfillment of the requirements for the degree of BACHELORS OF SCIENCE IN MECHANICAL ENGINEERING

Faculty of Engineering

Mohammad Ali Jinnah University

Islamabad

June, 203

ii

Copyright 2012 by MAJU Student

All rights reserved. Reproduction in whole or in part in any form requires the prior

written permission of Rasikh Tariq & Mehroze Ali Najmi.

iii

Colpitts Oscillator is designed for generation of high frequency waves

ranging from 10 kHz to 1000 MHz. They are widely used in commercial

purposes. They had got a lot of application in “Signals & Systems”.

iv

DECLARATION

It is declared that this is an original piece of my own work, except where

otherwise acknowledged in text and references. This work has not been submitted in

any form for another degree or diploma at any university or other institution for

tertiary education and shall not be submitted by me in future for obtaining any degree

from this or any other University or Institution.

Rasikh Tariq

ME-113006

Mehroze Ali Najmi

ME-113077

June, 2013

1

ABSTRACT

We have formulated a Colpitts Oscillator starting from a crude/reformable

circuit. Then we had formulated a better form of Colpitts Oscillator using computer

softwares like Personal Computer Simulation Program (PSPICE) and Printed Circuit

Board Wizard (PCB). Then we had implemented our project on Printed Circuit Board

by soldering circuit components.

As a result of completing the above procedure, we had got some results from

our circuit. We had achieved 1MHz (approx.) frequency of our circuit. We had

achieved almost the same results both theoretically and experimentally.

After this project we realized that certain engineering things are not so much

complicated then we really assume them. Now, we believe that Colpitts Oscillator

circuit is as simple as like rest of the circuits.

Chapter 1 Project Charter Purpose

The purpose of the Project is:

Disseminate a brief summary about Colpitts Oscillator.

Provide an introduction to some of basic electronic components like Inductors,

Capacitors, Resistors and Transistors.

Provide an introduction about working of Colpitts Oscillator.

Chapter 2 Project Executive Summary

The project is devoted towards “Colpitts Oscillator”. Starting from the circuit

components used in our project then we had moved towards the advanced/complex

working of Colpitts Oscillator. Working of Tank Circuit is also introduced in our

project. The contributions of Personal Computer Simulation Program (PCB) and

Printed Circuit Board Wizard (PCB) in our project have also been introduced.

Chapter 3 Introduction

3.1 Oscillator An oscillator is a mechanical or electronic device that works on the principles

of oscillation: a periodic fluctuation between two things based on changes in energy.

Computers, clocks, watches, radios, and metal detectors are among the many devices

that use oscillators.

3

3.2 Hartley Oscillator

The Hartley oscillator is an electronic oscillator circuit that relies on two

inductors and a capacitor for its operation. The circuit was invented in 1915 by

American engineer Ralph Hartley. The Hartley oscillator is distinguished by its use of

two inductors (or one tapped inductor) and only one capacitor in its resonant tank.

Chapter 4

Colpitts Oscillator Electronic Components

Electronic Circuit Elements used in Colpitts Oscillator were:

4.1 Resistor

A resistor is a passive two-terminal electrical component that implements

electrical resistance as a circuit element.

The current through a resistor is in direct proportion to the voltage across the resistor's

terminals. This relationship is represented by Ohm's law:

� =�

�

Where:

V= Voltage across resistor

I= Current flowing through resistor

R= Resistance of resistor.

We had used 4 different resistors of rating 2k, 22k, 10k and 1k ohm.

4.2 Capacitor

A capacitor is a passive electronic component that stores energy in the form of

an electrostatic field. In its simplest form, a capacitor consists of two conducting

plates separated by an insulating material called the dielectric.

4

In the case of capacitor, current passing through it is equal to time derivative of

voltage across it. Represented as follows:

�(�) = ��(�)

��

Where:

dt= Change in time

C= Capacitance of Capacitor

Generally, Capacitors don’t permit Direct Current (DC) across it but they permit

Alternating Current (AC).

4.2.1 Solving Capacitors Combinations

To find equivalent capacitance Ceq in parallel configuration of capacitors we use:

�� = �� + ��+�� +∙∙∙∙∙∙∙∙∙ +��

To find equivalent capacitors Ceq in series configuration of capacitors we use:

1

��=

1

��+

1

��+

1

��+∙∙∙∙∙∙∙∙∙ +

1

��

We had used 3 different capacitors in our circuit having market codes of: .102, 103,

and 104.

4.3 Inductor

An inductor, also called a coil or reactor, is a passive two-terminal electrical

component which resists changes in electric current passing through it. It consists of a

conductor such as a wire, usually wound into a coil. When a current flows through it,

energy is stored in a magnetic field in the coil. When the current flowing through an

inductor changes, the time-varying magnetic field induces a voltage in the conductor,

according to Faraday’s law of electromagnetic induction, which by Lenz's law

opposes the change in current that created it.

Voltage across inductor is given by the formulae:

� = ��

��

Where:

L=Inductance of inductor.

4.3.1 Solving Inductors Combination

To find equivalent inductance I

To find equivalent inductance I

1

��=

1

��+

1

��+

We had used 1 inductor in our circuit of rating

27uH.

4.4 Tank or LC Circuit

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit,

consists of an inductor, represented by the letter L, and a capacitor, represented by the

letter C. When connected together, they can act as an

analogue of a tuning fork, storing energy oscillating at the circuit's resonant

frequency.

LC circuits are used either for generating signals at a particular frequency, or

picking out a signal at a particular frequency f

key components in many electronic devices, particularly radio equipment, used in

circuits such as oscillators, filters, tuners and frequency mixers.

The frequency “f”

4.5 Transistor

A transistor is a semiconductor device used to amplify and switch electronic

signals and electrical power. It is composed of semiconductor material with at least

three terminals for connection to an external circuit.

Basically a transis

transistor has 3 legs:

Emitter

Base

Collector

We had used an npn (C945)

Solving Inductors Combinations

To find equivalent inductance Ieq in series configuration of inductors we use:

�� = �� + ��+�� +∙∙∙∙∙∙∙∙∙ +��

To find equivalent inductance Ieq in parallel configuration of inductors we use:

+1

��+∙∙∙∙∙∙∙∙∙ +

1

��

We had used 1 inductor in our circuit of rating

Circuit

n LC circuit, also called a resonant circuit, tank circuit, or tuned circuit,


letter C. When connected together, they can act as an electrical resonator, an electrical



picking out a signal at a particular frequency from a more complex signal. They are


circuits such as oscillators, filters, tuners and frequency mixers.

“f” of LC circuit can find by using relation:

� =1

2�√��



three terminals for connection to an external circuit.

Basically a transistor has 2 types, npn transistor and pnp transistor. One

(C945) transistor in our circuit.

in series configuration of inductors we use:

configuration of inductors we use:

n LC circuit, also called a resonant circuit, tank circuit, or tuned circuit,


electrical resonator, an electrical



rom a more complex signal. They are




tor has 2 types, npn transistor and pnp transistor. One

Chapter 5

Colpitts Oscillator

A Colpitts oscillator, invented in 1918 and patented 1927 by American

engineer Edwin H. Colpitts, is one of a number of designs for LC oscillators,

electronic oscillators that use a combination of inductors (L) and capacitors (C) to

determine the frequency

oscillator is that the feedback for the active device is taken from a voltage divider

made of two capacitors in series across the inductor.

The Colpitts oscillator is very similar to the

except that two capacitors are used in the tank circuit instead of a tapped coil (the

figure below). The Hartley oscillator has a tap between two coils, while the Colpitts

has a tap between two capacitors. You can change the f

by varying the inductance of the coil or by varying the capacitance of the two

capacitors in the tank circuit.

Basically, a Colpitts Oscillator can produce waves of frequency ranging from

10 kHz to 100 MHz.

Chapter 5

Formulating

Figure

Colpitts Oscillator: An Overview




determine the frequency of oscillation. The distinguishing feature of the Colpitts


made of two capacitors in series across the inductor.

The Colpitts oscillator is very similar to the shunt-fed Hartley oscillator,



has a tap between two capacitors. You can change the frequency of the Colpitts either


capacitors in the tank circuit.

, a Colpitts Oscillator can produce waves of frequency ranging from

Formulating Colpitts Oscillator using PSPICE

Figure 1: Schematic Diagram (Collpits Oscillator)




of oscillation. The distinguishing feature of the Colpitts


fed Hartley oscillator,



requency of the Colpitts either


, a Colpitts Oscillator can produce waves of frequency ranging from

using PSPICE

5.1 Cicuit Diagram of Colpitts Oscillator

Figure 1 shows the circuit diagram that we had formulated using PSPICE for our

Colpitts Oscillator Project.

After adding all the components in the

PSPICE workspace we had switched on “Transient

Analysis” option from PSPICE. Figure 2 shows the

values that we had set for our analysis.

Then we had observed voltage-time and voltage-

frequency graphs of our circuit. By these two graphs

we had calculated frequency of our Oscillator. Figure

3. and figure 4. shows voltage-time and voltage-

frequency graphs respectively.

Now, at this stage we had calculated the

frequency from our Voltage-Time Graph i.e. Figure

3. At 1.0ns our one wave is completed so frequency

can be calculated using:

� =�

�=

�

��= 1��

Figure 2

Figure 3: Voltage – Time Graph

Thus, we had got a frequency of 1MHz from our circuit made by using PSPICE. The

same thing can also be verified using Fourier Transform of voltage-time graph i.e.

Figure 4.

Chapter 6

Working of Colpitts Oscillator

The transistor amplifiers emitter is connected to the junction of capacitors, C3

and C4 which are connected in series and act as a simple voltage divider. When the

power supply is firstly applied, capacitors C3 and C4 charge up and then discharge

through the coil L1. The oscillations across the capacitors are applied to the base-

emitter junction and appear in the amplified at the collector output.

The amount of feedback depends on the values of C3 and C4 with the smaller

the values of C the greater will be the feedback.

The amount of feedback is determined by the ratio of C3 and C4 which are

generally "ganged" together to provide a constant amount of feedback so as one is

adjusted the other automatically follows. The frequency of oscillations for a Colpitts

Figure 4: Voltage - Frequency Graph (Fourier Transform)

9

oscillator is determined by the resonant frequency of the LC tank circuit and is given

as:

Colpitts Oscillation Frequency Equation

� =1

2��

�� + ��

The configuration of the transistor amplifier is of a Common Emitter

Amplifier with the output signal 180o out of phase with regards to the input signal.

The additional 180o phase shift require for oscillation is achieved by the fact that the

two capacitors are connected together in series but in parallel with the inductive coil

resulting in overall phase shift of the circuit being zero or 360o.

Resistors R1, R2, R3, and R4 provide the usual stabilizing DC bias for the

transistor in the normal manner while the capacitor acts as DC-blocking capacitors.

6.1 Calculating Frequency using Formulae

The formulae to calculate the frequency of Colpitts Oscillator is:

Thus, plugging values in the above mentioned formula of frequency using our

Capacitor values:

� =1

2��

�� + ��

=1

2 ∗ 3.14�(27 ∗ 10��) �(. 013 ∗ 10��) ∗ (.001 ∗ 10��)(.013 ∗ 10��) + (.001 ∗ 10��)

�

≈ 1��

Approximately the same result was interpreted using PSPICE i.e. Figure 3, 4.

Chapter 7

Formulating Colpitts Oscillator using PCB

We had designed our Colpitts Oscillator on Printed Circuit Board (PCB). Figure 5.

shows our circuit that we had designed using PCB and figure 6. shows the artwork

format of our project.

7.1 Calculating Frequency of hardware Now, we had calculated the frequency of our colpitts oscillator that we’ve formulated on

PCB sheet.

Number of horizontal boxes=2.2

Time per division= 0.5µs/boxes

Time period =T= (Number of horizontal boxes)*(Time per

division)

T=2.2* 0.5µs=1.1 µs

�� = � =1

�=

1

1.1μs= .9090�� ≈ 1��

Chapter 8

Conclusions

We had found the frequency of our Colpitts Oscillator using following methods:

1. Using theoretical formula of Tank circuit i.e. using values of capacitors and

resistors.

2. Using voltage-time graph i.e. dividing the time period with 1.

3. Using voltage-frequency graph i.e. Fourier Transform of voltage-time graph

4. By formulating the circuit on a bread board.

5. By formulating the circuit on PCB Sheet.

And hence still getting almost the same results.

Figure 2: Artwork

colpitts oscillator by rasikh tariq

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