ASP

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ANALOG SIGNAL PROCESSING

A SUMMER INTERN PROJECT REPORT

Submitted by

Mohit Lamba

Roll No. 06514802812

in fulfillment of Summer Internship for the award of the degree of

BACHELOR OF TECHNOLOGY

in

ELECTRONICS AND COMMUNICATION ENGINEERING

Maharaja Agrasen Institute of Technology

Guru Gobind Singh Indraprastha University, Delhi

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Maharaja Agrasen Institute of Technology

To Whom It May Concern I Mohit Lamba, Enrolment No. 06514802812 from a student of Bachelor of Technology

(ECE), a class of 2012-16, Maharaja Agrasen Institute of Technology, Delhi hereby

declare that the Summer Training entitled ANALOG SIGNAL PROCESSING at

Radiance Edutech is an original work and the same has not been submitted to any other

Institute for the award of any other degree.

Date: Signature of the Student

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Abstract

Although the world is today moving vastly towards digitisation of everything,

the signals actually present around us are analog in nature. Furthermore our five

senses also perceive analog signals only.

Hence Analog signal Processing is an integral part of complete design. My

report gives many convincing reasons for understanding well analog signal

processing and some of their techniques.

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CONTENTS

1. Title page i

2. Certificate by the Supervisor ii

3. Acknowledgement iii

4. Abstract iv

5. List of figures v

6. Introduction 5

7. A universal filter using OTA 8

8. Wien bridge oscillator using OTA 12

9. Wien bridge oscillator using op-amp 16

10. An oscillator using CFOA 20

11. Amplitude modulator using OTA 23

12. Translinear circuits 26

13. Redesign of a OTA 30

14. References 35

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Since all natural signals are analog, the analog circuits and techniques to process them arc unavoidable in spite of almost everything going digital. In particular, several analog functions/circuits such as amplification, rectification, continuous-time liltering, analog-to-digital (A/D) and digital-to-analog (D/A) conversion are impossible to be performed by digital circuits regardless of the advances made in the digital circuits and techniques. Thus, analog circuits arc indispensable in many applications. Further some applications like image processing and speech recognition are better carried out by analog VLSI or mixed signal VLSIs than digital circuits.

The Ubiquitous Op-amp

In the world of analog circuits, it is widely believed that almost any function can be performed using the classical voltage-mode op-amp (VOA). Thus, on one hand, one can realize using op-amps, all linear circuits such as the four controlled sources (VCVS, VCCS, CCVS and CCCS), integrators, differentiators, summing and differencing amplifiers, variable-gain differential/instrumentation amplifiers, filters, oscillators etc. On the other hand, op-amps can also be used to realize a variety of non-linear functional circuits such as comparators, Schmitt trigger, sample and hold circuits, precision rectifiers, multivibrators, log-antilog amplifiers and a variety of relaxation oscillators.

Short comings of Op-amp

1. Matched Impedances and not minimum number of passive components

Consider Iwo well-known VCCS configurations

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A straight forward analysis of the circuit shows that the relation between the output current and input voltage (assuming ideal op-amp) for the circuit is given by

From the above, it may be seen that to realize a VCCS. the op-amp circuits not only require more than the minimum number of resistances necessary' but also require that all the four resistors should have either a relationship R1 = R2R4/R3 or else all the four resistors be equal-valued and matched so that the output current becomes independent of the output voltage and depends only on the input voltage, as required. Thus, any mismatch in resistor values from the intended ones would degrade the performance of the circuit.

2. The Gain-Bandwidth Conflict

The gain and the bandwidth cannot be set independent of each other i.e. there is a gain-bandwidth conflict.

3. Slew-Rate Based Limitations

At large input voltages or high frequencies or a combination of the two, the output voltage fails to respond with the same speed as the input (due to finite maximum SR) and this results in slew-induced distortion. Conversely, to avoid slew-induced distortion, the input voltages and their frequencies are constrained to be kept small. Thus, the finite slew rate affects both the dynamic range of the op-amp circuits as well as the maximum frequency of the input signal which can be applied without causing noticeable distortion in the output waveform.

ADVANTAGES OF OTA

1. Less Passive components count

2. Also full active active circuits can be made as resistors, inductors and

capacitors all can be simulated using OTA

3. So fully integrated IC components can be made

4. Electronically controllable

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However when larger circuit design became even difficult with OTA, current conveyors proposed by Sedra and Smith in 1968 gained a lot of popularity especially since 2000s.

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Circuit Diagram

Pspice Code

*hpf

x1 2 1 5 3 4 6 ota14

x2 7 6 5 3 4 2 ota14

x3 0 2 5 3 4 7 ota14

vcc 3 0 dc 9V

vee 0 4 dc 9V

Ib1 5 0 dc 100ua

c1 6 9 3nf

c2 2 10 10nf

v1 1 0 AC 0mv

v2 9 0 AC 0mv

v3 10 0 AC 30mv

r1 7 0 15k

.include ota14.cir

.probe

.AC DEC 1000 10Hz 10MegHz

.end

*lpf

x1 2 1 5 3 4 6 ota14

x2 7 6 5 3 4 2 ota14

x3 0 2 5 3 4 7 ota14

vcc 3 0 dc 9V

vee 0 4 dc 9V

Ib1 5 0 dc 100ua

c1 6 9 3nf

c2 2 10 10nf

v1 1 0 AC 30mv

v2 9 0 AC 0mv

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v3 10 0 AC 0mv

r1 7 0 15k

.include ota14.cir

.probe

.AC DEC 1000 10Hz 10MegHz

.end

*bpf

x1 2 1 5 3 4 6 ota14

x2 7 6 5 3 4 2 ota14

x3 0 2 5 3 4 7 ota14

vcc 3 0 dc 9V

vee 0 4 dc 9V

Ib1 5 0 dc 100ua

c1 6 9 3nf

c2 2 10 10nf

v1 1 0 AC 0mv

v2 9 0 AC 30mv

v3 10 0 AC 0mv

r1 7 0 4.86k

.include ota14.cir

.probe

.AC DEC 1000 10Hz 10MegHz

.end

*apf

x1 2 1 5 3 4 6 ota14

x2 7 6 5 3 4 2 ota14

x3 0 2 5 3 4 7 ota14

vcc 3 0 dc 9V

vee 0 4 dc 9V

Ib1 5 0 dc 100ua

c1 6 9 3nf

c2 2 10 10nf

v1 1 0 AC 30mv

v2 0 9 AC 30mv

v3 10 0 AC 30mv

r1 7 0 4.86k

.include ota14.cir

.probe

.AC DEC 1000 10Hz 10MegHz

.end

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So from the charachterestic equation following conditions are obtained:

1. Low pass filter when Vc = Vb = 0 2. High pass filter when Vb = Va = 0 3. Bandpass filter when Vc = Va = 0 4. All pass filter when all are applied

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Output

Frequency

10Hz

30Hz

100Hz

300Hz

1.0KHz

3.0KHz

10KHz

30KHz

100KHz

300KHz

1.0MHz

3.0MHz

10MHz

V(2)

0V

10mV

20mV

30mV

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Circuit Diagram :

Pspice Code :

X1 1 2 4 1 ota

X2 0 1 5 1 ota

X3 1 0 3 2 ota

c1 2 0 0.1uf

c2 1 0 0.1uf

Ib1 4 0 122.5ua

.param val=117ua

*Ib2 5 0 119.3ua

Ib2 5 0 {val}

Ib3 3 0 100ua

.include ota.cir

.four 3.38khz 11 v(1)

*.step param val 117ua 120ua 1ua

.tran 1ms 500ms 0.01ms 0.01ms

.probe

.end

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Transient Response :

Time

10.0ms

20.0ms

30.0ms

40.0ms

50.0ms

60.0ms

70.0ms

80.0ms

90.0ms

100.0ms

0.8msV(1)

-20mV

-10mV

0V

10mV

20mV

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Steady State Response (10x Zoom)

Time

60.600ms

60.800ms

61.000ms

61.200ms

61.400ms

61.600ms

61.800ms

62.000ms

62.200ms

62.400ms

62.600ms

62.800ms

60.428ms

V(1)

-10.0mV

0V

10.0mV

20.0mV

-19.9mV

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Fourier Transform

Theoretical Frequency :

= 3.38 KHz

Total Harmonic Distortion: 1.311593E+01 PERCENT

Frequency

0Hz 5KHz 10KHz 15KHz 20KHz 25KHz 30KHz 35KHz 40KHz 45KHz 50KHz 55KHz 60KHz 65KHz 70KHz

V(1)

10nV

1.0uV

100uV

10mV

1.0nV

100mV

3.1 K

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Circuit Diagram :

Pspice Code : x1 1 5 3 4 2 ua741

r1 1 0 1k

c1 1 0 0.01uf

r2 1 6 1k

c2 6 2 0.01uf

ra 5 2 10.29k

rb 5 0 5k

vcc 3 0 dc 50

vee 4 0 dc -50

.include opamp.cir

.tran 0 50ms 0.01ms 0.01ms

.four 15.19khz 11 v(2)

.probe v(2)

.end

Charachteristic Equation :

S2C2R2 + SCR(3-k)+1 = 0, where k= 1 +

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Transient Response :

Time

2.00ms

4.00ms

6.00ms

8.00ms

10.00ms

12.00ms

14.00ms

16.00ms

18.00ms

20.00ms

22.00ms

24.00ms

0.04ms

V(2)

-4.00V

0V

4.00V

-7.34V

7.27V

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Steady State Response (10x Zoom) :

Time

19.40ms

19.50ms

19.60ms

19.70ms

19.80ms

19.90ms

20.00ms

20.10ms

20.20ms

20.27ms

V(2)

-4.00V

0V

4.00V

-7.55V

7.38V

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Fourier Transform

Condition of Oscillation:

3 = K => 2RB = RA

Theoretical Frequency

= 15.19K Hz

Total Harmonic Distortion: 2.947749E+01 PERCENT

Frequency

0Hz 20KHz 40KHz 60KHz 80KHz 100KHz 120KHz 140KHz 160KHz 180KHz

V(2)

100uV

10mV

1.0V

10uV

10V

13K

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Circuit Diagram :

Pspice Code :

x1 1 3 5 6 4 2 AD844/AD

.param val=2.64k

.param vall=1uf

r3 1 0 {val}

c6 1 2 {vall} ic=1ua

*r10 1 2 11k

r4 3 0 1k

c 2 0 .8uf ic=1ua

*r11 2 0 11k

r2 3 4 1k

vcc 5 0 dc 10v

vee 6 0 dc -10v

.tran 30ms 250ms 0.01ms 0.01ms uic

*.step param vall .79uf .81uf 0.001uf

.probe v(4)

.four 0.109khz 11 v(4)

.include cfoa.cir

.end

Charachteristic Equation : S2[R2R3R4C0C6] + S[-R2R3C6+R2R4C0+C6R2R4] + R4 = 0

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TOTAL RESPONSE (NO ZOOM) :

Time

0s

20ms

40ms

60ms

80ms

100ms

120ms

140ms

160ms

180ms

200ms

220ms

240ms

260ms

V(4)

-8.0V

-4.0V

0V

4.0V

8.0V

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Fourier Transform :

Condition of Oscillation:

Theoretical Frequency

= 109 Hz

Total Harmonic Distortion: 8.625649E+00 PERCENT

Frequency

0Hz 0.1KHz 0.2KHz 0.3KHz 0.4KHz 0.5KHz 0.6KHz 0.7KHz 0.8KHz 0.9KHz 1.0KHz

V(4)

1.0mV

10mV

100mV

1.0V

10V

104Hz

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Circuit Diagram :

Pspice Code :

X1 3 2 5 60 70 6 ota14

.param val=100k

R1 3 0 51

R2 2 0 51

R3 2 7 47k

R4 6 0 5.1k

R5 5 1 {val}

v 7 0 dc 1v

V1 1 0 sin(0 1v 5khz)

V2 3 0 sin(0 .5v 10khz)

vcc 60 0 dc 3V

vee 70 0 dc -3V

.include ota14.cir

*.step param val 90k 100k 5k

.tran 0 100ms .1ms .1ms

.probe

.end

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Under Modulation

Time

0s

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

V(1)

V(6)

0V

1.0V

-1.2V

SEL>>

V(5)

-200mV

0V

200mV

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Over Modulation (DISTORTION IS CLEARLY SEEN)

Time

0s

1ms

2ms

3ms

4ms

5ms

6ms

7ms

8ms

9ms

10ms

V(1)

V(6)

-2.0V

0V

2.0V

V(5)

-400mV

0V

400mV

SEL>>

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History and Background A translinear circuit is a circuit that carries out its function using the translinear principle. These are current-mode circuits that can be made using transistors that obey anexponential current-voltage characteristic—this includes BJTs and CMOS transistors in weak inversion. The word translinear (TL) was invented by Barrie Gilbert in 1975[1] to describe circuits that used the exponential current-voltage relation of BJTs.[2][3] By using this exponential relationship, this class of circuits can implement multiplication, amplification and power-law relationships. When Barrie Gilbert described this class of circuits he also described the translinear principle (TLP) which made the analysis of these circuits possible in a way that the simplified view of BJTs as linear current amplifiers did not allow. TLP was later extended to include other elements that obey an exponential current-voltage relationship (such as CMOS transistors in weak inversion).

Usage in electronics today The TLP has been used in a variety of circuits including vector arithmetic circuits,[6] current conveyors, current-mode operational amplifiers, and RMS-DC converters.[7] It has been in use since the 1960s (by Gilbert), but was not formalized until 1975.[1] In the 1980s, Evert Seevinck's work helped to create a systematic process for translinear circuit design. In 1990 Seevinck invented a circuit he called a companding current-mode integrator[8] that was effectively a first-order log-domain filter. A version of this was generalized in 1993 by Douglas Frey and the connection between this class of filters and TL circuits was made most explicit in the late 90s work of Jan Mulder et al. where they describe thedynamic translinear principle. More work by Seevinck led to synthesis techniques for extremely low-power TL circuits.[9] More recent work in the field has led to the voltage-translinear principle, multiple-input translinear element networks, and field-programmable analog arrays (FPAAs).

Principle

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Here each BJT is considered to be identical with large β. So,

ICO1 = ICO2 = ICO3 = ICO4 and ic = Ico eVBE/ηVT

=> VBE = ηVT ln (ic / ICO) Now applying KVL,

VBE1 + VBE2 = VBE3 + VBE4 ...2

So using 1 and 2 we get

ic1 * ic2 = ic3 * ic4 The next section shows an application of this principle

... 1

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Circuit Diagram :

Pspice Code :

vx 1 0 sin(0 .5v 10khz)

rx 1 2 1k

q1 2 0 3 n

x1 0 2 3 ua741

*vy 9 0 sin(1.5 1v 8khz 0 0 0DEG)

vy 9 0 pulse(0 1 0 0 0 1ms 2ms)

ry 9 4 1k

x2 0 4 5 ua741

q2 4 3 5 n

ro 11 6 1k

x3 0 6 11 ua741

q3 6 7 5 n

q4 8 0 7 n

x4 0 8 7 ua741

vw 10 0 dc 1v

rw 10 8 1k

.include opampvcc.cir

.MODEL n NPN(BF=300 VJE=0.7V)

.tran 0.1ms 4ms 0.01ms 0.01ms

.probe v(1) v(9) v(11) v(10)

.end

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Output Example :

Time

0s

0.4ms

0.8ms

1.2ms

1.6ms

2.0ms

2.4ms

2.8ms

3.2ms

3.6ms

4.0ms

V(1)

V(9)

-0.5V

0V

0.5V

1.0V

V(11)

250mV

500mV

-50mV

SEL>>

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Internal architecture of an OTA

Scope of Improvement The above architecture of OTA is made basically by cascading 4 SIMPLE CURRENT MIRRORs and a differential amplifier. But for very accurate results I replaced the the simple current mirrors with much better WILSON CURRENT MIRROR (shown below)

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My modified INTERNAL STRUCTURE of OTA now looks as below

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Pspice Code * current_source out down

.subckt wilsoncurrp 1 3 4

q1 1 2 4 p

q2 2 2 4 p

q3 3 1 2 p

.model p PNP

.ends wilsoncurrp

.subckt wilsoncurrn 11 13 14

q1 11 12 14 n

q2 12 12 14 n

q3 13 11 12 n

.model n NPN

.ends wilsoncurrn

*V- V+ Ib Vcc Vee op

.subckt ota14 1 2 3 8 5 10

x1 3 4 5 wilsoncurrn

x2 7 10 5 wilsoncurrn

x3 6 7 8 wilsoncurrp

x4 9 10 8 wilsoncurrp

q1 6 1 4 n

q2 9 2 4 n

.model n NPN

.ends ota14

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TESTING THE DEVICE :

1. Testing the current mirrors used

Pspice Test Code

x1 1 3 4 wilsoncurrn

vin 1 0 dc 1a

v2 3 10 dc 0

r1 10 0 1k

r2 4 0 1000mega

x2 11 13 14 wilsoncurrp

vinn 11 0 dc -1a

v22 13 110 dc 0

r11 110 0 1k

r22 14 0 1000mega

.include wilson_current.cir

.end

A section of the output file

2. Testing the overall device

Pspice code for integrator

* inverting noninverting ib Vcc Vee o/p

x1 1 0 3 8 5 10 ota14

v1 1 0 PULSE(-1mv 1mv 1s 0 0 1s 2s)

ib 3 0 dc 920ua

vcc 8 0 dc 3

vee 5 0 dc -3

c 10 11 1uf ic=100ua

r 11 0 1000

.include ota14.cir

.tran 0.1s 20s 0.01s 0.01s uic

.probe .end

Note : All the currents are equal.

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Integrator Output

Time

0s

2s

4s

6s

8s

10s

12s

14s

16s

18s

20s

1

V(10)

2

V(1)

-3.0V

-2.0V

-1.0V

-0.0V

1.0V

2.0V

3.0V

1

-1.0mV

-0.5mV

0V

0.5mV

1.0mV

2

>>

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1. Current Feedback Operational Amplifiers and Their Applications By Raj Senani, Data Bhaskar, A. K. Singh, V. K. Singh.

2. Current Conveyors: Variants, Applications and Hardware Implementations By Raj Senani, D. R. Bhaskar, A. K. Singh

3. Op-amps and Linear Integrated Circuits by Ramakant A. Gayakwad.

4. Spice For Circuits And Electronics Using Pspice by Rashid Muhammad H