final report.docx

OTA BASED OSCILLATOR

A minor project report submittedIn partial Fulfillment of the Requirements

For the award of the degree of

BACHELOR OF TECHNOLOGYIn

Electronics and Communication Engineeringby

TARUN KR. SWARAN(04796402812)

AMAN KUMAR(05296402812)

VIKAS KR. MISHRA(01496402812)

Under the Supervision of

Mr. UMESH CHANDRA SINGH , Assistant Professor

to

MAHARAJA AGRASEN INSTITUTE OF TECHNOLOGY

SECTOR 22, ROHINI, DELHIAffiliated to

GGSIP University, Dwarka, Delhi

November, 2015

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CERTIFICATE

It is certified that TARUN KR. SWRARAN (enrollment no. 04796402812) , AMAN KUMAR

(enrollment no.05296402812) and VIKAS KR. MISHRA (enrollment no. 01496402812) have

carried out the minor project work presented in this report entitled “OTA BASED

OSCILLATOR” for the award of Bachelor of Technology in Electronics and

Communication Engineering from Maharaja Agrasen Institute of Technology affiliated to

GGSIP University, Delhi under my supervision. The report embodies results of original work

and studies as carried out by the students themselves and the contents of the report do not form

the basis for the award of any other degree or to anybody else from this or any other

university/institution to the best of my knowledge and belief.

Mr.UMESH CHANDRA SINGH

Assistant Professor, ECE

Date:

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ACKNOWLEDGEMENTS

Firstly, we thank our advisor Mr.UMESH CHANDRA SINGH, for his continuous support and

guidance to complete this project. He was always there to listen and to give advice. He showed

us different ways to approach a problem and the need to be persistent to accomplish any goal.

Without his encouragement and constant guidance we could not have finished this project.

We are using this opportunity to express our deepest gratitude and special thanks to Head of

Electronics Department DR. Neelam Sharma ma’am who in spite of being extraordinarily busy

with her duties, took time out to hear, guide and keep us on the correct path and allowing us to

carry out our project.

It is our radiant sentiment to place on record our best regards, deepest sense of gratitude to all the

teachers of Maharaja Agrasen Institute of Technology for their careful and precious guidance

throughout our academics and helped us in being a well learned and disciplined individuals. We

would also like to thank our parents and family members for providing eminent support all the

time and making sure that our studies do not suffer due to any reasons whatsoever. Last but not

the least, we would like to thank the almighty God, who has been the source of everything and

with whom great things are possible. To him all the glory is given for the achievement of this

project.

TARUN KR. SWARAN VIKAS KR. MISHRA AMAN KUMAR

(Roll No. 01896402812) (Roll No. 01896402812) (Roll No. 00596402812)

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ABSTRACT

In recent years Operational Transconductance Amplifier based integrated circuits, filters and

analog circuits have been widely investigated At present, operational-transconductance-amplifier

(OTA)-based oscillators are receiving considerable attention. This is attributed mainly to their

electronic tunability over a wide-range, the use of a relatively small number of active and passive

components, the feasibility of obtaining relatively high-frequencies of oscillation, and finally

their suitability for integration in CMOS and bipolar technology. Although the literature contains

a large number of attractive OTA-based oscillator circuits, the proposed circuits are analyzed

assuming ideal OTAs, that is, the OTA is acting as an ideal voltage-controlled current-source

(VCCS). OTAs are, however, non-ideal in many respects. Of particular interest here is the output

conductance, the output and input capacitances and the frequency dependence of the

transconductance. The usefulness of OTAs over conventional OP-Amps in the design of both

first order and second order active filters are well documented. Operational amplifiers are

important building blocks for analog circuit design.

Unfortunately, their limited performance such as bandwidth, slew-rate etc. leads the analog

designer to search other possibilites and other building blocks. As a result, new current-mode

active building blocks such as operational transconductance amplifiers (OTA), second generation

current conveyors (CCII), current-feedback op-amps (CFOA), four terminal floating nullors

(FTFN), differential voltage current conveyor (DVCC), differential difference current conveyor

(DDCC), third-generation current-conveyor (CCIII), dual X current conveyors (DXCCII),

current controlled current conveyors (CCCII) etc. received considerable attention due to their

larger dynamic range and wider bandwidth. Employing these new active elements for analog

design and using CMOS technology for implementation the circuit designers obtained new

possibilities to solve their problems.

In this project using a general oscillator structure, oscillator circuit is systematically derived.

This oscillator circuit uses operational transconductance amplifiers (OTAs) and externally

connected passive element, exploiting the inherent zeros of the OTAs to advantage. The

feasibility of obtaining oscillation using OTAs without externally connected passive elements is

investigated. Experimental results are included.

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TABLE OF CONTENTS

Page No.

Certificate 2

Acknowledgements 3

Abstract 4

Table of Contents 5

List of figures 7

CHAPTER 1 : OPERATIONAL TRANSCONDUCTANCE AMPLIFIER 8 -14

1.1 INTRODUCTION 8

1.2 CIRCUIT AND OPERATION OF OTA 9

1.3 ANALYSIS OF SCHEMATIC CIRCUIT OF OTA 12

1.4 CHARACTERISTICS OF OTA 15

CHAPTER 2 Operational Amplifiers 16-19

2.1 INTRODUCTION 16

2.2 CHARACTERISTICS OF IDEAL OP AMP 17

2.3 CHARACTERISTICS OF PRACTICAL OP AMP 18

2.4 INVERTING AMPLIFIER 19

2.5 NON- INVERTING AMPLIFIER 19

CHAPTER 3 : Current Mirrors and differential amplifiers 21-26

3.1 CURRENT MIRRORS 21

3.2 SUMMING AMPLIFIERS 25

3.3 DIFFERENTIAL AMPLIFIERS 25

3.4 APPLICATIONS 26

CHAPTER 4 : OSCILLATORS 27-39

4.1 INTRODUCTION 27

4.2 BASIC OSCILLTOR FEEDBACK CIRCUIT 28

4.3 BARKHAUSEN STABILITY CRITERION 29

4.4 TYPE OF OSCILLATOR 30

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4.5 OSCILLATOR RESONANCE 30

4.6 THE RC OSCILLATOR 33

4.7 OTA BASED OSCILLATOR 37

4.8 DIFF. OTA OSCILLATOR CIRCUITS 38

CHAPTER 5 CIRCUIT SIMULATIONS AND RESULTS 40-42

5.1 OTA CIRCUIT 40

5.2 OTA OSCILLATOR CIRCUIT 40

5.3 OSCILLATOR OUTPUT 41

CHAPTER 6 SUMMARY & CONCLUSION 42-43 REFERENCES 44-45

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LIST OF FIGURES

Page No.

Fig. 1.1 Basic Equivalent Circuit of OTA 12

Fig. 1.2 Circuit of Operational Transconductance Amplifier 13

Fig. 1.3 Simplified Diagram of OTA 14

Fig. 1.4 Waveform of Phase margin 15

Fig. 1.5 Waveform of Gain Margin 16

Fig. 1.6 Waveform of DC Analysis 16

Fig. 1.8 Voltage Transfer Characteristic of OTA 17

Fig. 1.9 Timing Characteristic of OTA 17

Fig 2.1 Op-amp IC & diagram 18

Fig 2.2 Ideal Op-amp 19

Fig 2.3 Inverting amplifier Equivalent circuit of inverting op-amp 21

Fig 2.4 Non inverting amplifier 21

Fig 3.1 Constant VBE gives constant IB, constant IE, and constant IC. 24Fig 3.2 Diode junction 0.7 V 24

Fig 3.3 Currentmirrors 25

Fig 3.4 Multiple current mirrors. 26

Fg 3.5 Summing Amplifier 27

Fg 3.6 Differential Amplifier 27

Fig 4.1 Basic Oscillator Feedback Circuit 30

Fig 4.2 LC Oscillator Tank Circuit 33

Fig 4.4 Rc Phase shift Network 35

Fig 4.5 Stage Networks 37

Fig4.6 OTA-C oscillator structures: (a) 20TA3C, 40- 41

(b) 30TA2C,

(c) 40TA2C,

(d) quadrature,

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CHAPTER 1

OPERATIONAL TRANSCONDUCTANCE AMPLIFIERS(OTA)

1. INTRODUCTION

OTA-C structures have attracted considerable attention in recent years because they offer several

advantages over conventional op-amp based circuits as well as providing the evaluation of fully

integrated circuits inVLSI design with CMOS technology. It is well-known that OTAs provide

highly linear electronic tunability of their transconductance (gm) and require just a few or even

no resistors for their internal circuitry and have more reliable high frequency performance

because of the current mode operation which has been established as art important topic in

analogue signal processing owing to ils advantage over the voltage mode, particularly for higher

frequency of operation. Because of these features, the OTAs are increasingly replacing

operational amplifiers and in the past few years, a number of OTA-C based filters and oscillators

have been reported . The rapid increasing use of battery-operated portable equipment in

application areas such as telecommunications and medical electronics imposes the use of low-

power and small-sized circuits realized with VLSI (very large scale integrated) technologies.

CMOS (complementary metal–oxide semiconductor) circuits operating in the subthreshold

(weakinversion) region introduce a versatile solution for the realization of low-power VLSI

building blocks. Circuits needed for processing of biological signals are a typical and good

example of low-power and small-sized building blocks. The main features of biological signals

are their low amplitude and low frequency range. In the late sixties, RCA, then one of the major

leaders in linear semiconductors, came out with the Operational Transconductance Amplifier,

hereafter called OTA. The name means essentially a controllable resistance amplifier. The

control input is a current. Like an operational amplifier, there are differential inputs. These inputs

are used to modulate the control current. Unlike an op amp, the output of the OTA is a current!

Unlike an op amp, there is not a single resistor in the OTA circuit.

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An OTA is a voltage controlled current source, more specifically the term “operational” comes

from the fact that it takes the difference of two voltages as the input for the current conversion.

The ideal transfer characteristic is therefore

Iout = gm (Vin+ − Vin-)

or, by taking the pre-computed difference as the input,

Iout = gmVin

with the ideally constant transconductance gm as the proportionality factor between the two

voltages. An OTA is basically an op-amp without any output buffer, preventing it from driving

resistive or large capacitive loads. They are preferred over op-amps mainly because of their

smaller size and simplicity. The OTA is based on a differential amplifier at the input. If the

inputs are equal, the transistors in the differential pair conduct equal currents. The purpose of an

OTA is to generate a current proportional to an input voltage difference.

2. CIRCUIT AND OPERATION OF OTAThe OTA is similar in generic form to conventional operational amplifier, but differ sufficiently

to justify an explanation of their unique characteristics . This new class of operational amplifier

not only includes the usual input terminals, but also contains an additional control terminal

which enhances the device’s flexibility for use in a broad spectrum of applications. The amplifier

incorporated in these devices is referred to as in Operational Transconductance Amplifier

(OTA), because its output signal is best described in terms of the output-current that it can

Supply The amplifier’s output-current is proportional to the voltage difference at its differential

input terminals. Figure 1 shows the equivalent circuit for the OTA. The output signal is a current

which is proportional to the transconductance (gM) of the OTA established by the amplifier bias

current (Iabc) and the differential input voltage (eIN). The OTA can either source or sink current

at the output terminal, depending on the polarity of the input signal. The availability of the

amplifier bias current (IABC) terminal significantly increase the flexibility of the OTA and

permits the circuit designer to exercise his creativity in the utilization of this device in many

unique applications not possible with the conventional operational amplifier

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Fig. 1.1 Basic Equivalent Circuit of OTA

The figure 1.1 is shows complete schematic diagram of the OTA. The OTA employs only active

device (transistors and diodes). Current applied to the amplifier-bias-current terminal, IABC,

establishes the emitter current of the input differential amplifier M1 and M2. Hence, effective

control of the differential transconductance (gM) is achieved. Here, there are 4 current mirror is

used where M9 & M10 forms one current mirror than M7 & M8, M3 & M5, M4 & M6 are forms

a current mirror circuit. OTA has 8 pin structures in which 6 pins is used. 6 pins are given as

below.

1. Inverting Input

2. Non Inverting Input

3. Vss

4. Vdd

5. Iabc

6. Output

The OTA used as a final design is shown in figure 1.2. Input and output pins represent

connections to nodes in the circuit. A differential pair used to sense the input voltage difference.

If the pair is operation in saturation, when one transistor is turned on, the other will turn off . The

current through one leg will be sourced to the output while the other leg will sink current from

the load, the input transistors were sized with a very large W/L ratio to provide the high

transconductance required to quickly move charge into the test capacitors. Special care must be

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taken to ensure that the input differential pair is operating in saturation and not in the triode

region. Operation in the triode region will caused the behavior of the OTA to be nonlinear and

will result in poor transient response as well as a loss in DC gain. The telescopic architecture

differs from other approaches because it requires the common node of the input to be different

pair to be in saturation and operate linearly. This will have to be taken into consideration before

the telescopic design is used in a larger circuit. If the outputs are to be used as inputs to another

OTA, their common mode must first be adjusted.

Fig. 1.2 Circuit of Operational Transconductance Amplifier

The OTA is based on a differential amplifier at the input. If the inputs are equal, the transistors in

the differential pair conduct equal currents. The purpose of an OTA is to generate a current

proportional to an input voltage difference. The difference in the output currents should be

proportional to the difference in the input voltages The simplified diagram of the OTA is shown

in figure 1.3 which are given clear idea of operation. A current Iabc is given to M9, and is pulled

via mirror W from the input differential pair. Let the supply voltages be +5 and -5. The current

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defined by Iabc is now divided equally between M1 and M2. As we will see shortly, the output of

the amplifier is a current. Assume that the amplifier bias current I, is 1mA. Half the current I, is

pulled via M1 from current mirror Y whose output pushed an equal current into current mirror X,

which pulls an equal current from the output. Half the current I, is pulled via M2 from current

mirror Z, which pushed an equal current into the output. Thus, current mirror X is pulling 1mA,

and current mirror Z is pushing 1mA, and the net current into the output is zero . The voltage at

the output is zero. For getting output at output pin we required to give input voltage at the

differential pair. According to difference getting over the differential pair we get output in the

form of current at the output pin

Fig. 1.3 Simplified Diagram of OTA

3. ANALYSIS OF SCHEMATIC CIRCUIT OF OTAThe analysis of schematic circuit of OTA used in Tanner EDA Tools. Apply different input

source and get parameter likes Gain Margin, Phase Margin, Transient Time, Noise Spectral

Density, CMMR, PSRR and slew rate arrangement for Ac analysis, it requires AC source at the

input terminal of the circuit. Iabc current require for converting voltage in to the current. Figure

1.4 shows the waveform of AC analysis which is helpful for derive voltage gain of the circuit.

Here DC source is applied for biasing or in other words it shift dc level according to applied

voltage arrangement for DC analysis, reducing the input signal Vin1 and Vin2 to zero.

Waveform of DC analysis is shown in figure 1.6. Dc analysis shows the DC behavior of DC

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circuit of OTA. The common-mode rejection ratio (CMRR) is defined in several essentially

equivalent ways by various manufacturers. Generally, the common-mode rejection ratio (CMRR)

is defined as the ration of the differential voltage gain (Ad) to the common-mode voltage gain

(Acm). CMRR is expressed in decibels (dB); that is

In this analysis, the Differential Voltage Gain Ad is get to 5V and Common Mode Voltage Gain

Acm is get to 500μV. So value of CMRR for OTA is given in below

The figure 1.7 shows the schematic diagram of Noise analysisof OTA. The electrical noise is

random in nature; it is expressed as a root-mean square value. Standard industry practice is to

express the noise as a power density. The equivalent input noise voltage is, therefore, expressed

as square voltage (v2/z) and the equivalent input noise current as square current. Using input

noise voltage and input noise current versus frequency curves given in figure10. For all analysis

we take W=22μ and L=2μ for all MOS transistor.

Fig. 1.4 Waveform of Phase Margin

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Fig. 1.5 Waveform of Gain Margin

Fig. 1.6 Waveform of DC Analysis

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4. Characteristic of OTA

Fig. 1.8 Voltage Transfer Characteristic of OTA

Fig. 1.9 Timing Characteristic of OTA

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Chapter 2: Operational Amplifiers

1. INTRODUCTIONAn operational amplifier is a high-gain direct-coupled amplifier that is normally used in

feedback connections. An op amp is an active circuit element designed to perform

mathematicaloperations of addition, subtraction, multiplication, division, differentiation, and

integration. The op amp is an electronic device consisting of a complexarrangement of resistors,

transistors, capacitors, and diodes Op amps are commercially available in integrated circuit

packagesin several forms. A typicalone is the eight-pin dual in-line package (or DIP), Pin or

terminal 8 is unused, and terminals 1 and 5 are of little concern to us. The five important

terminals are:

1. The inverting input, pin 2.

2. The non-inverting input, pin 3.

3. The output, pin 6.

4. The positive power supply V+, pin 7.

5. The negative power supply V-, pin 4.

Fig 2.1: Op-amp IC & diagram

The inputs are marked with minus (-) and plus (+) to specify inverting and non-inverting inputs,

respectively. An input applied to the non-inverting terminalwill appear with the same polarity at

the output, while an inputapplied to the inverting terminal will appear inverted at the output.

The equivalent circuit model of an op amp is shown. The output section consists of a voltage-

controlled source in series with the output resistance Ro. It is evident that the input resistance

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Riis the Thevenin equivalent resistance seen at the input terminals, while the output resistance Ro

is the Thevenin equivalent resistance seen at the output. The differential input voltage Vdis given

by

Vd= V2-V1

Where

V1 is the voltage between the inverting terminal and ground and

V2 is the voltage between the non-inverting terminal and ground.

The Op amp senses the difference between the two inputs, multiplies it bythe gain A, and causes

the resulting voltage to appear at the output.Thus, the output Vois given by

V0 =A*Vd = A*(V2-V1)

A is called the open-loop voltage gain because it is the gain of the Op-amp without any external

feedback from output to input

2. Characteristics of Ideal Op AmpAn op amp is ideal if it has the following characteristics

Infinite input impedance

Zero output impedance

Zero common-mode gain or, equivalently, infinite common-mode rejection

Infinite open-loop gain A

Infinite bandwidth

Zero offset i.e. if V1 = 0; V2 = 0 then V0 = 0

Slew rate is infinite.

Fig 2.2 Ideal Op-amp

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Although assuming an ideal op amp provides only an approximateanalysis, most modern

amplifiers have such large gains and input impedances that the approximate analysis is a good

one. Unless stated otherwise, we will assume from now on that every op amp is ideal. For circuit

analysis, the ideal op amp is illustrated in Fig which is derived from the non-ideal model. Two

important characteristics of the ideal op amp are:

1. The currents into both input terminals are zero:

i1=0; i2=0

This is due to infinite input resistance. An infinite resistancebetween the

input terminals implies that an open circuit exists thereand current cannot enter the op

amp. But the output current is notnecessarily zero

2. The voltage across the input terminals is equal to zero; i.e.

Vd=V1-V2

Or

V1 = V2=0

Thus, an ideal op amp has zero current into its two input terminalsand the voltage

between the two input terminals is equal to zero.

3. Characteristics of the practical Op Am1. Input impedance is of order 1MΩ to 2MΩ.

2. Output impedance is of order 50Ω to 100Ω.

3. Common mode rejection ratio is 106 or 120dB.

4. Open loop gain is 106

5. Open loop band width is 5Hz.

6. Non zero offset.

7. Slew rate is 0.5 to 1 volt/µsec.

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4. Inverting Amplifier

Fig 2.3 Inverting amplifier Equivalent circuit of inverting op-amp

In this circuit, the non-inverting input is grounded, viisconnected to the inverting input through

R1, and the feedback resistor Rfis connected between the inverting input and output. Our goal is

to obtain the relationship between the input voltage viand the output voltage vo. Applying KCL at

node 1

i1= i2= (vi-v1)/R1 = (v1-v0)/Rf

But v1=v2= 0 for an ideal op amp, since the non-inverting terminal is grounded. Hence,

Vi/R1 = -v0 /Rf

v0= (R1/Rf)*vi

An inverting amplifier reverses the polarity of the input signal while amplifying it.

5. Non-inverting Amplifier

Fig 2.4 Non inverting amplifier

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In non-inverting amplifier, the input voltage viis applieddirectly at the non-inverting input

terminal, and resistor R1 is connectedbetween the ground and the inverting terminal. We are

interested in the output voltage and the voltage gain. Application of KCL at the inverting

terminal gives

i1= i2 = (0-v1)/R1= (v0-v1)/Rf

But v1=v2=vi.

Above equation become

-v/R = (v0-v1)/Rf

Or

vo= (1+Rf/R1)vi

The voltage gain is Av =vo/vi=1 –Rf/R1, which does not have a negative sign. Thus, the output

has the same polarity as the input.

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CHAPTER 3 :

Current Mirrors and differential amplifiers

1. CURRENT MIRRORS:

An often-used circuit applying the bipolar junction transistor is the so-called current mirror,

which serves as a simple current regulator, supplying nearly constant current to a load over a

wide range of load resistances. We know that in a transistor operating in its active mode,

collector current is equal to base current multiplied by the ratio β. We also know that the ratio

between collector current and emitter current is called α. Because collector current is equal to

base current multiplied by β, and emitter current is the sum of the base and collector currents,

α should be mathematically derivable from β. If you do the algebra, you’ll find that α =

β/(β+1) for any transistor.. Well, the α ratio works similarly: if emitter current is held constant,

collector current will remain at a stable, regulated value so long as the transistor has enough

collector-to-emitter voltage drop to maintain it in its active mode. Therefore, if we have a way

of holding emitter current constant through a transistor, the transistor will work to regulate

collector current at a constant value. Remember that the base-emitter junction of a BJT is

nothing more than a PN junction, just like a diode, and that the “diode equation” specifies how

much current will go through a PN junction given forward

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If both junction voltage and temperature are held constant, then the PN junction current will be

constant. Following this rationale, if we were to hold the base-emitter voltage of a transistor

constant, then its emitter current will be constant, given a constant temperature. (Figure below)

Fig 3.1 Constant VBE gives constant IB, constant IE, and constant IC.

This constant emitter current, multiplied by a constant α ratio, gives a constant collector

current through Rload, if enough battery voltage is available to keep the transistor in its active

mode for any change in Rload‘s resistance. To maintain a constant voltage across the transistor’s

base-emitter junction use a forward-biased diode to establish a constant voltage of

approximately 0.7 volts, and connect it in parallel with the base-emitter junction as in

Figure below.

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Fig 3.2 Diode junction 0.7 V maintains constant base voltage, and constant base current.

The voltage dropped across the diode probably won’t be 0.7 volts exactly. The exact amount

of forward voltage dropped across it depends on the current through the diode, and the diode’s

temperature, all in accordance with the diode equation. If diode current is increased (say, by

reducing the resistance of Rbias), its voltage drop will increase slightly, increasing the voltage

drop across the transistor’s base-emitter junction, which will increase the emitter current by

the same proportion, assuming the diode’s PN junction and the transistor’s base-emitter

junction are well-matched to each other. In other words, transistor emitter current will closely

equal diode current at any given time. If you change the diode current by changing the

resistance value of Rbias, then the transistor’s emitter current will follow suit, because the

emitter current is described by the same equation as the diode’s, and both PN junctions

experience the same voltage drop.

Remember, the transistor’s collector current is almost equal to its emitter current, as the α ratio

of a typical transistor is almost unity . If we have control over the transistor’s emitter current

by setting diode current with a simple resistor adjustment, then we likewise have control over

the transistor’s collector current. In other words, collector current mimics, or mirrors, diode

current. Current through resistor Rload is therefore a function of current set by the bias resistor,

the two being nearly equal. This is the function of the current mirror circuit: to regulate current

through the load resistor by conveniently adjusting the value of Rbias. Current through the diode

is described by a simple equation: power supply voltage minus diode voltage (almost a

constant value), divided by the resistance of Rbias. To better match the characteristics of the two

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PN junctions (the diode junction and the transistor baseemitter junction), a transistor may be

used in place of a regular diode, as in Figure below .

Fig 3.3 Current mirrors

Because temperature is a factor in the “diode equation,” and we want the two PN junctions to

behave identically under all operating conditions, we should maintain the two transistors at

exactly the same temperature. This is easily done using discrete components by gluing the two

transistor cases back-to-back. If the transistors are manufactured together on a single chip of

silicon (as a so-called integrated circuit, or IC), the designers should locate the two transistors

close to one another to facilitate heat transfer between them.

The current mirror circuit shown with two NPN transistors in Figure above is sometimes

called a current-sinking type, because the regulating transistor conducts current to the

load from ground (“sinking” current), rather than from the positive side of the

battery (“sourcing” current). If we wish to have a grounded load, and a current sourcing mirror

circuit, we may use PNP transistors like Figure above

While resistors can be manufactured in ICs, it is easier to fabricate transistors. IC designers

avoid some resistors by replacing load resistors with current sources. A circuit like an

operational amplifier built from discrete components will have a few transistors and many

resistors. An integrated circuit version will have many transistors and a few resistors. In

Figure below One voltage reference, Q1, drives multiple current sources: Q2, Q3, and Q4. If

Q2 and Q3 are equal area transistors the load currents I load will be equal. If we need a 2·Iload,

parallel Q2 and Q3. Better yet fabricate one transistor, say Q3 with twice the area of Q2.

Current I3 will then be twice I2. In other words, load current scales with transistor area.

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Fig 3.4 Multiple current mirrors may be slaved from a single (Q1 - Rbias) voltage source.

Note that it is customary to draw the base voltage line right through the transistor symbols for

multiple current mirrors! Or in the case of Q4 in Figure above, two current sources are

associated with a single transistor symbol. The load resistors are drawn almost invisible to

emphasize the fact that these do not exist in most cases.

2. Summing Amplifier Besides amplification, the op amp can perform addition and subtraction.

Fg 3.5 Summing Amplifier

The summing amplifier, shown is a variation of the inverting amplifier. It takes advantage of the

fact that the inverting configuration can handle many inputs at the same time. We keep in

mindthat the current entering each op amp input is zero. Applying KCL at node a gives

i=i1+i2=i3

i1=(v1-va)/R1, i2=(v2-va)/R2, i3=(v3-va)/R3

we know that va= 0

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v0=-Rf(v1/R1+v2/R2+v3/R3)

3. Differential Amplifier

FiG 3.6 Differential Amplifier

Difference (or differential) amplifiers are used in various applicationswhere there is a need to

amplify the difference between two input signals.

They are first cousins of the instrumentation amplifier, the mostuseful and popular

amplifier.Applying KCL to node a

Since a difference amplifier must reject a signal common to the two inputs, the amplifier must

have the property that vo=0 when v1 = v2.

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Thus, when the op amp circuit is a difference amplifier, Equation becomes

If R2 =R1 and R3 =R4, the difference amplifier becomes a subtractor, with the output

vo= v2- v1

Applications1. Digital-to-Analog Converter

2 .Instrumentation Amplifiers

3. Differentiator

4. Integrator

5. Used as an oscillator

6. Low pass, Band pass filter, High pass filter

8. Half wave rectifier, Full wave rectifier

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CHAPTER 4: OSCILLATORS1. INTRODUCTION:

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.

A clock pendulum is a simple type of mechanical oscillator. The most accurate timepiece in the

world, the atomic clock, keeps time according to the oscillation within atoms. Electronic

oscillators are used to generatesignals in computers, wireless receivers and transmitters, and

audio-frequency equipment, particularly music synthesizers. There are many types of electronic

oscillators, but they all operate according to the same basic principle: an oscillator always

employs a sensitive amplifier whose output is fed back to the input in phase. Thus, the signal

regenerates and sustains itself. This is known as positive feedback. It is the same process that

sometimes causes unwanted "howling" in public-address systems.The frequency at which an

oscillator works is usually determined by a quartz crystal. When a direct current is applied to

such a crystal, it vibrates at a frequency that depends on its thickness, and on the manner in

which it is cut from the original mineral rock. Some oscillators employ combinations of

inductors, resistors, and/or capacitors to determine the frequency. However, the best stability

(constancy of frequency) is obtained in oscillators that use quartz crystals.

In a computer, a specialized oscillator, called the clock, serves as a sort of pacemaker for the

microprocessor. The clock frequency (or clock speed) is usually specified in megahertz (MHz),

and is an important factor in determining the rate at which a computer can perform instructions.

Oscillators are used in many electronic circuits and systems providing the central “clock” signal

that controls the sequential operation of the entire system. Oscillators convert a DC input (the

supply voltage) into an AC output (the waveform), which can have a wide range of different

wave shapes and frequencies that can be either complicated in nature or simple sine waves

depending upon the application.

Oscillators are also used in many pieces of test equipment producing either sinusoidal sine

waves, square, sawtooth or triangular shaped waveforms or just a train of pulses of a variable or

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constant width. LC Oscillators are commonly used in radio-frequency circuits because of their

good phase noise characteristics and their ease of implementation. An Oscillator is basically

an Amplifier with “Positive Feedback”, or regenerative feedback (in-phase) and one of the many

problems in electronic circuit design is stopping amplifiers from oscillating while trying to get

oscillators to oscillate.

Oscillators work because they overcome the losses of their feedback resonator circuit either in

the form of a capacitor, inductor or both in the same circuit by applying DC energy at the

required frequency into this resonator circuit. In other words, an oscillator is a an amplifier

which uses positive feedback that generates an output frequency without the use of an input

signal. It is self sustaining. Then an oscillator has a small signal feedback amplifier with an open-

loop gain equal too or slightly greater than one for oscillations to start but to continue oscillations

the average loop gain must return to unity. In addition to these reactive components, an

amplifying device such as anOperational Amplifier or Bipolar Transistor is required. Unlike an

amplifier there is no external AC input required to cause the Oscillator to work as the DC supply

energy is converted by the oscillator into AC energy at the required frequency.

2 . Basic Oscillator Feedback Circuit

Fig 4.1 Basic Oscillator Feedback Circuit

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Oscillator Gain Without Feedback

Oscillator Gain With Feedback

3 .Barkhausen stability criterion: In electronics, the Barkhausen stability criterion is a mathematical condition to determine when a

linear electronic circuit will oscillate. It was put forth in 1921 by German physicist Heinrich

Georg Barkhausen (1881–1956). It is widely used in the design of electronic oscillators, and also

in the design of general negative feedback circuits such as op amps, to prevent them from

oscillating.

Criterion:

It states that if A is the gain of the amplifying element in the circuit and β(jω) is the transfer

function of the feedback path, so βA is theloop gain around the feedback loop of the circuit, the

circuit will sustain steady-state oscillations only at frequencies for which:

1. The loop gain is equal to unity in absolute magnitude, that is, and

2. The phase shift around the loop is zero or an integer multiple of

2π:

Barkhausen's criterion is a necessary condition for oscillation but not a sufficient condition: some circuits satisfy the criterion but do not oscillate. Similarly, the Nyquist stability criterion also indicates instability but is silent about oscillation. Apparently there is not a compact formulation of an oscillation criterion that is both necessary and sufficient

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LimitationsBarkhausen's criterion applies to linear circuits with a feedback loop. Therefore it cannot be

applied to one port negative resistance active elements like tunnel diode oscillators.

4. TYPES OF OSCILLATORS

1. Sinusoidal Oscillators – these are known as Harmonic Oscillators and are generally

a “LC Tuned-feedback” or “RC tuned-feedback” type Oscillator that generates a purely

sinusoidal waveform which is of constant amplitude and frequency.

2. Non-Sinusoidal Oscillators – these are known as Relaxation Oscillators and generate

complex non-sinusoidal waveforms that changes very quickly from one condition of

stability to another such as “Square-wave”, “Triangular-wave” or “Sawtoothed-wave”

type waveforms.

5. Oscillator Resonance

When a constant voltage but of varying frequency is applied to a circuit consisting of an

inductor, capacitor and resistor the reactance of both the Capacitor/Resistor and

Inductor/Resistor circuits is to change both the amplitude and the phase of the output signal as

compared to the input signal due to the reactance of the components used.

At high frequencies the reactance of a capacitor is very low acting as a short circuit while the

reactance of the inductor is high acting as an open circuit. At low frequencies the reverse is true,

the reactance of the capacitor acts as an open circuit and the reactance of the inductor acts as a

short circuit. Between these two extremes the combination of the inductor and capacitor

produces a “Tuned” or “Resonant” circuit that has a Resonant Frequency, ( ƒr ) in which the

capacitive and inductive reactance’s are equal and cancel out each other, leaving only the

resistance of the circuit to oppose the flow of current. This means that there is no phase shift as

the current is in phase with the voltage. Consider the circuit below.

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Basic LC Oscillator Tank Circuit

Fig 4.2 LC Oscillator Tank Circuit

Tthe circuit consists of an inductive coil, L and a capacitor, C. The capacitor stores energy in the

form of an electrostatic field and which produces a potential (static voltage) across its plates,

while the inductive coil stores its energy in the form of an electromagnetic field. The capacitor is

charged up to the DC supply voltage, V by putting the switch in position A. When the capacitor

is fully charged the switch changes to position B.

The charged capacitor is now connected in parallel across the inductive coil so the capacitor

begins to discharge itself through the coil. The voltage across C starts falling as the current

through the coil begins to rise. This rising current sets up an electromagnetic field around the coil

which resists this flow of current. When the capacitor, C is completely discharged the energy that

was originally stored in the capacitor, C as an electrostatic field is now stored in the inductive

coil, L as an electromagnetic field around the coils windings.As there is now no external voltage

in the circuit to maintain the current within the coil, it starts to fall as the electromagnetic field

begins to collapse. A back emf is induced in the coil (e = -Ldi/dt) keeping the current flowing in

the original direction.This current charges up capacitor, C with the opposite polarity to its

original charge. C continues to charge up until the current reduces to zero and the

electromagnetic field of the coil has collapsed completely.. The capacitor now starts to discharge

again back through the coil and the whole process is repeated. The polarity of the voltage

changes as the energy is passed back and forth between the capacitor and inductor producing an

AC type sinusoidal voltage and current waveform.

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This process then forms the basis of an LC oscillators tank circuit and theoretically this cycling

back and forth will continue indefinitely. However, things are not perfect and every time energy

is transferred from the capacitor, C to inductor, L and back from L to C some energy losses occur

which decay the oscillations to zero over time.This oscillatory action of passing energy back and

forth between the capacitor, C to the inductor, Lwould continue indefinitely if it was not for

energy losses within the circuit..Then in a practical LC circuit the amplitude of the oscillatory

voltage decreases at each half cycle of oscillation and will eventually die away to zero. The

oscillations are then said to be “damped” with the amount of damping being determined by the

quality or Q-factor of the circuit.

Damped Oscillations

Fig 4.3 Damped Oscillations

The frequency of the oscillatory voltage depends upon the value of the inductance and

capacitance in the LC tank circuit. We now know that for resonance to occur in the tank circuit,

there must be a frequency point were the value of XC, the capacitive reactance is the same as the

value of XL, the inductive reactance ( XL = XC ) and which will therefore cancel out each other

out leaving only the DC resistance in the circuit to oppose the flow of current. If we now place

the curve for inductive reactance of the inductor on top of the curve for capacitive reactance of

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the capacitor so that both curves are on the same frequency axes, the point of intersection will

give us the resonance frequency point, ( ƒr or ωr ) as shown below.

6. The RC Oscillator

In our series of tutorials about Amplifiers , we saw that a single stage amplifier will produce

180o of phase shift between its output and input signals when connected in a class-A type

configuration. For an oscillator to sustain oscillations indefinitely, sufficient feedback of the

correct phase, ie, “Positive Feedback” must be provided with the amplifier being used as one

inverting stage to achieve this. In an RC Oscillator circuit the input is shifted 180o through the

amplifier stage and 180o again through a second inverting stage giving us “180o + 180o = 360o”

of phase shift which is effectively the same as 0o thereby giving us the required positive

feedback. In other words, the phase shift of the feedback loop should be “0”.In a Resistance-

Capacitance Oscillator or simply an RC Oscillator, we make use of the fact that a phase shift

occurs between the input to a RC network and the output from the same network by using RC

elements in the feedback branch, for example

RC Phase-Shift Network

Fig 4.4 Rc Phase shift Network

The circuit on the left shows a single Resistor-Capacitor Network whose output voltage “leads”

the input voltage by some angle less than 90o. An ideal single-pole RC circuit would produce a

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phase shift of exactly 90o, and because 180o of phase shift is required for oscillation, at least two

single-poles must be used in an RC oscillator design.However in reality it is difficult to obtain

exactly 90o of phase shift so more stages are used. The amount of actual phase shift in the circuit

depends upon the values of the resistor and the capacitor, and the chosen frequency of

oscillations with the phase angle ( Φ ) being given as:

RC Phase Angle

n our simple example above, the values of R and C have been chosen so that at the required

frequency the output voltage leads the input voltage by an angle of about 60o. Then the phase

angle between each successive RC section increases by another 60o giving a phase difference

between the input and output of 180o (3 x 60o) as shown by the following vector diagram

Vector Diagram

Then by connecting together three such RC networks in series we can produce a total phase shift

in the circuit of 180o at the chosen frequency and this forms the bases of a “phase shift oscillator”

otherwise known as a RC Oscillator circuit.

We know that in an amplifier circuit either using a Bipolar Transistor or an Operational

Amplifier, it will produce a phase-shift of 180o between its input and output. If a three-stage RC

35

phase-shift network is connected between this input and output of the amplifier, the total phase

shift necessary for regenerative feedback will become 3 x 60o + 180o = 360o as shown.

Fig 4.5 Stage Networks

Basic RC Oscillator Circuit

The basic RC Oscillator which is also known as a Phase-shift Oscillator, produces a sine wave

output signal using regenerative feedback obtained from the resistor-capacitor combination. This

regenerative feedback from the RC network is due to the ability of the capacitor to store an

electric charge, (similar to the LC tank circuit).

This resistor-capacitor feedback network can be connected as shown above to produce a leading

phase shift (phase advance network) or interchanged to produce a lagging phase shift (phase

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retard network) the outcome is still the same as the sine wave oscillations only occur at the

frequency at which the overall phase-shift is 360o.

By varying one or more of the resistors or capacitors in the phase-shift network, the frequency

can be varied and generally this is done by keeping the resistors the same and using a 3-ganged

variable capacitor.

If all the resistors, R and the capacitors, C in the phase shift network are equal in value, then the

frequency of oscillations produced by the RC oscillator is given as:

Where:

ƒr is the Output Frequency in Hertz

R is the Resistance in Ohms

C is the Capacitance in Farads

N is the number of RC stages. (N = 3)

Since the resistor-capacitor combination in the RC Oscillator circuit also acts as an attenuator

producing an attenuation of -1/29th ( Vo/Vi = β ) per stage, the gain of the amplifier must be

sufficient to overcome the circuit losses. Therefore, in our three stage RC network above the

amplifier gain must be greater than 29.

The loading effect of the amplifier on the feedback network has an effect on the frequency of

oscillations and can cause the oscillator frequency to be up to 25% higher than calculated. Then

the feedback network should be driven from a high impedance output source and fed into a low

impedance load such as a common emitter transistor amplifier but better still is to use an

Operational Amplifier as it satisfies these conditions perfectly.

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7. OPERATIONAL TRANSCONDUCTANCE AMPLIFIERS(OTA) BASED OSCILLATORS :

THE USE OF circuits composed of operational transconductance amplifiers and capacitors

(OTA-C’S) has been demonstrated to be potentially advantageous for the synthesis of high-

frequency continuous-time monolithic analog operators, either linear or nonlinear . One basic

reason for the high-frequency potential of these circuits comes from the fact that the OTA is used

in a local openloop. It means that no additional constraints are imposed on. the frequency

response due to local feedback-induced pole displacements Another advantage of open-loop

OTAbased circuits is that the transconductance gain of the OTA is used as a design parameter. In

a typical OTA architecture this gain can be adjusted either by changing the tail current of a

differential pair (fine adjustment) or by using digitally controlled current mirrors (coarse

adjustment) . Programmability is hence an inherent property of OTA-C circuits. Based upon the

previous considerations, it may be expected that the transconductance amplifier–capacitor

oscillators (TACO’s) overcome the limitations in frequency and tunability of conventional op-

amp-based RC-active oscillators. TACO’s could then be applied for the design of highfrequency

voltage-controlled sinusoidal oscillators (VCO’S) with potential application in communication

systems and in the tuning of active filters . In a companion paper the authors have explored the

synthesis of TACO’s from classical oscillator models, namely quadrature and bandpassbased.

The experimental results measured from discrete bipolar prototypes showed good potential of the

TACO’s for high-frequency VCO’S. Also, a 3-pm CMOS TACO including a limiting

mechanism for controlling the amplitude has been reported exhibiting a 1O-MHZ frequency and

THD down to 0.2%. In this paper we first present a number of new architectures that can be

systematically obtained from a general idealized TACO topology and then provide experimental

results for 2- and 3-~m CMOS prototypes up to 69 and 56 MHz, respectively. The results

demonstrate that it is possible to implement high-frequency monolithic VCO oscillators based on

simple OTA-C techniques and the modeling of the dominant OTA parasitic effects .Furthermore,

we show that based on a general TACO structure, conventional and unconventional structures

can be derived.

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8 . DIFFERENT OTA BASED OSCILLATORS CIRCUITS :

39

Fig. 4.6. OTA-C oscillator structures: (a) 20TA3C, (b) 30TA2C, (c) 40TA2C, (d) quadrature,

and (e) 40TA4C.

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CHAPTER 5: CIRCUIT SIMULATIONS AND

RESULTS 1. OPERATIONAL TRANSCONDUCTANCE AMPLIFIER:

2. OTA BASED OSCILLATOR:

41

3. OSCILLATOR OUTPUT :

42

CHAPTER 6 : SUMMARY & CONCLUSION

The OTA is similar in generic form to conventional operational amplifier, but differ sufficiently

to justify an explanation of their unique characteristics . This new class of operational amplifier

not only includes the usual input terminals, but also contains an additional control terminal

which enhances the device’s flexibility for use in a broad spectrum of applications. The amplifier

incorporated in these devices is referred to as in Operational Transconductance Amplifier

(OTA), because its output signal is best described in terms of the output-current that it can

Supply The amplifier’s output-current is proportional to the voltage difference at its differential

input terminals. Figure 1 shows the equivalent circuit for the OTA. The output signal is a current

which is proportional to the transconductance (gM) of the OTA established by the amplifier bias

current (Iabc) and the differential input voltage (eIN). The OTA can either source or sink current

at the output terminal, depending on the polarity of the input signal. The availability of the

amplifier bias current (IABC) terminal significantly increase the flexibility of the OTA and

permits the circuit designer to exercise his creativity in the utilization of this device in many

unique applications not possible with the conventional operational amplifier

The OTA is based on a differential amplifier at the input. If the inputs are equal, the transistors

in the differential pair conduct equal currents. The purpose of an OTA is to generate a current

proportional to an input voltage difference. The difference in the output currents should be

proportional to the difference in the input voltages The simplified diagram of the OTA is shown

in figure 1.3 which are given clear idea of operation. A current Iabc is given to M9, and is pulled

via mirror W from the input differential pair. Let the supply voltages be +5 and -5. The current

defined by Iabc is now divided equally between M1 and M2. As we will see shortly, the output of

the amplifier is a current. Assume that the amplifier bias current I, is 1mA. Half the current I, is

pulled via M1 from current mirror Y whose output pushed an equal current into current mirror X,

which pulls an equal current from the output. Half the current I, is pulled via M2 from current

mirror Z, which pushed an equal current into the output. Thus, current mirror X is pulling 1mA,

and current mirror Z is pushing 1mA, and the net current into the output is zero . The voltage at

the output is zero. For getting output at output pin we required to give input voltage at the

differential pair.

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We have researched about OTA , working of Oscillators , Oscillators using OTAs which

includes different circuits using OTA and their functioning . Different circuits like current mirros

,Differential amplifiers ,op-amps and ocsillators which are based on OTA and also conclude why

our proposed circuit is better than the pre-existing one .

And learned the properties and working of simple circuit of an oscillator using OTA on Tanner

Tool, which uses a lesser number of components and less power consumption .

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References

1] Edward K.F. Lee, “Low-Voltage Opamp Design Differential Difference Amplifier Design

using Linear Transconductance with Resistor Input”, IEEE TRANSACTIONS ON CIRCUITS

AND SYSTEMS-II, ANALOG AND DIGITAL SIGNAL PROCESSING, Vol. 47, No.8,

August 2000

[2] Erik McCarthy, “Design and Layout of Telescopic Operational Transconductance

Amplifier, May 9, 2003

[3] Nimisha Saini, “Design and Analysis of different orders of Active RC Butterworth Filter,

June 2006

[4] Peggy Alavi, ”Op-Amp Basics”, September 2003

[5] Rahul Madhusudanan, “Development of Digital and Mixed Signal Standard Cells CMOS

Process, September 2005

[6] W. Nye et al. DELIGTH.SPICE: An optimization-based system for the design of

integrated circuits. IEEE Transactions on Computer-Aided Design, 7:501-518; April 1988

. [7] R. Jacob Baker, Harry W. LI, David E. Boyce, “CMOS Circuit Design Layout and

Simulation”, Wiley-IEEE Press, 1st Edition, August 1997

8] Ramakant A. Gayakwad, “OP-AMPs and Linear Integrated Circuits”, Prentice-Hall of

India, Private Limited, New Delhi, 1997

[9] Mohammad Hekmat, “A two stage Fully Differential Operational Transconductance

Amplifier”, EE 214 Midterm Project Report, Stanford University, December 2005

[10] Prasant K. Mahapatra, Manjeet Singh, Neelsh Kumar, “ Relaization of Active filters using

OTA”, J. Instrum. Soc. India, 35(1) 1-9

[11] National Semiconductor, Application Note, LM 3600 Dual Operational

Transconductance Amplifiers with Linearzing Diodes and Buffers”, February 1995

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[12] R. L. Geiger and E. Sanchez-Sinencio, “Active Filter Design Using Operational

Transconductance Amplifiers: A Tutorial”, IEEE Circuits and Devices Magazine, Vol. 1, pp.

20-32, march 1985

[13] C. F. Wheatley, H. A. Wittlinger, “OTA obsoletes OPAMP”, Pant. Econ. Conf. pp. 152-

157, December 1969

[14] Erik McCarthy, “Design and Layout a Telescopic Operational Transconductance

Amplifier”, Department of Electrical and Computer Engineering, University of Maine, Orono,

Marine, May 2003

[15] www.google.co.in/homwork_7.html

[16] www.microwind.org for Micro wind Tool [17] www.penzar.com for Tanner EDA Tool

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