analog electronic circuits - leda.elfak.ni.ac.rsleda.elfak.ni.ac.rs/education/analogna...

Faculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic Engineering

University of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, Serbia

Analog Electronic CircuitsAnalog Electronic Circuits

Prof. dr Predrag Petković

E-mail: [email protected] phone: 529207

Dr Srdjan Djordjević

E-mail: [email protected] phone: 529336

Faculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic EngineeringFaculty of Electronic Engineering

University of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, SerbiaUniversity of Nis, Serbia

Day 1Day 1

Introduction

�The aim of this course is to provide the student with

a broad knowledge of the main types of integrated

circuits involved in analog signal and mixed signal

acquisition and processing.

Aims of the cours

3

�By the end of the course you should be able to:

–Analyse the operation of analog systems

–Design basic analog systems to meet a

specification

–Design analog system through the use of

ORCAD

�This course follows on from the second year Basic

electronic course and Analog electronics course.

Prior skills

4

�The course assumes basic concepts of:

• amplification,

• analog circuit analysis and transistor modeling,

• circuit simulation environments such as

Cadence or Spice.

Lecture plan

� OP-AMP

• Basic Op-Amp circuits

• Static Op Amp Limitations

• Dynamic Op-Amp Limitations

5

� SPECIAL-PURPOSE AMPLIFIERS

• Instrumentation amplifiers

• Isolation amplifiers

• Operational Transconductance amplifiers (OTAs)

• Current-feedback amplifiers (CFAs)

Lecture plan

� DATA CONVERSION CIRCUITS

� Sample-and-Hold Amplifiers

� Digital-to-Analog Conversion

� Analog-to-Digital Conversion

� Voltage-to-Frequency Converters

6

� Voltage-to-Frequency Converters

� Frequency-to-Voltage Converters

� MEASUREMENT AND CONTROL CIRCUITS

� RMS-to-DC Converters

� Strain-, Pressure-, Temperature-Measuring circuits

� Auto-Zero Amplifiers

� Chopper Amplifiers

� Lock-in Amplifiers

Lecture plan

� COMUNICATIONS CIRCUITS

� The Phase-Locked Loop (PLL)

� The applications of the PLL

7

� NOISE

� Noise properties

� Sources of Noise

� BJT and MOSFET Noise

�Teaching materials are available on the course

webpage:

http://leda.elfak.ni.ac.rs/?page=education/Analogna

%20elektronska%20kola/

Teaching materials

8

%20elektronska%20kola/

• I will be updating the notes, the laboratory

instructions and tutorial problem sheets each week

after the lectures.

• Grading

- Answer test of the lectures 30

- Partial examination through the laboratory

Grading

9

exercies and classes 20

- Two project works 2X25

Summary:

Analog integrated circuits - Introduction

• Brief review of op-amp topologies and limitations

• The op-amp as a control loop - Stability criteria

10

• The op-amp as a control loop - Stability criteria

• Error Budget analysis S

• Specialist amplification techniques

Content

Operational amplifiers (OpAmp)

a. Ideal OpAmp

b. Biasing

c. Model

d. Applications

11

d. Applications

e. Real OpAmps

Ideal OpAmp behaves similarly to ideal voltage amplifier:

Voltage: Vi Vo

IdealIi IoRo

; [V/V] ∞=

= iRoVA

Operational Amplifiers

12

Vi VoRi

0 ; [V/V]

=

∞==

o

i

R

R

iV

oVA

0 =iVVi

Ii

Vo

Io

Ri

Ro

0 ;

=

∞=∞→=

o

i

R

R

iV

oVA


13

∞→oV

0 =iV

A ⇒∞→=iV

oVInfinite gain !!!

Transfer characteristic

Vi [V]Vi [V]


14

Vi [V]

Vu [mV]

Vi [V]

Vu [mV]

Ideal transfer characteristics

Vo [V]


15

Vi [mV] t[ms]


Vi

Ii

Vo

Io

Ri

Ro

0 ;

=

∞=∞→=

o

i

R

R

iV

oVA

16

Amplifiers with infinite input resistance

A0 =iI ⇒∞→iRdoes not attenuate input signal: Ri/(Rs+Ri)=1

Does not load previous stage!!!

oiV

Vi

Ii

Vo

Io

Ri

Ro

Output of voltage amplifiers with zero

output resistance does not depend on

load

RL0

[V/V] A

0 =

∞==

= o

i

IR

R

iV

oV

iVo


17

iAVRR

RoV

Lo

L

+= 0 ⇒=oR

A ∞→i

)( LfoV R≠

Vo

0

iAV=

Output

Two input ports

Symbol

Noninverting input

Inverting input


18

Two input ports

noninverting “+”

and inverting “–” input

One output port

What does OpAmp amplifies when it has two inputs?

Inverting

input

Output

IT should amplify

voltage difference

between

noninverting “+” and


19

Noninverting input

noninverting “+” and

inverting “–” portCommon

ground

12 vvdviv −==

∞→−

=12 vv

ovA 012

=− vv 12vv =

Should NOT amplify

common mode input signal

)(1

vvv += Meaning:


20

)12(2

1vvicmv += If v2 and v1 have DC

component + sinewave signal

with the same frequency and

opposite phases:

)sin(2

);sin(1 00

tVVvtVVv uu ωω +=−=

)sin(212 tVvvidv u ωωωω=−= ;)12(21

0Vvvicmv =+=

,0

)12(2

1=

+===

vv

ov

icmv

ov

cmAA

Meaning:

Output should not have DC component


21

122

∞⇒−

===12 vv

ov

dv

ov

dAA

and difference should be amplified

Common Mode Rejection Ratio: CMRR

012

=− vv 12 vv =

∞⇒=cmA

dACMRR

Characteristics of IDEAL OpAmp

0 [V/V]

0

0=

=

∞==

=

cm

o

i

Ii

A

R

R

iV

oVA


22

Zero output resistance

Infinite gain of differential signal

Infinite input resistance

Vi=0; V+=V-

Vo≠ f(RL)

Does tot amplifies common mode Acm=0

Infinite bandwidth ideal f charact.

Ii=0; Vi≠ f(Rs)


Biasing of OpAmp

23

How to use a component

with infinite gain?

Never alone – always with feedback


24

Never alone – always with feedback

(to be seen later)

Therefore we have talked about OpAmp as

open loop amplifier and the gain we have talked about is

Open loop gain = infinite

Examples of use

Always looking for CLOSED LOOP GAIN

A=Vo/Vs

Good to know closed loop


25

Good to know closed loop

input resistance Ri(cl) and

output resistance Ro(cl)

Inverting amplifier*

i1

i2

ii=0

v2=0V

v2 –v1=0V

v1 =v2=0V

vg vo


26

v2=0V

ii=i1+i2=0A => i1=-i2

i1=

1

1

R

vgv −

i2=

2

1

R

vov −1R

gv

=

2R

ov=

12 R

gv

R

ov −=

gvR

R

ov

1

2−=0V

0V

1

2

R

R

gv

ovA −==

Input resistance ig=i1

i2

ii=0

v2 –v1=0V

i =i

vg vo

Ri(cl)

?)( ==gi

gv

cliR

Ri(cl)


27

ig=i1

i1=1

1

R

vgv −

1R

gv

= 1)(R

gi

gv

cliR ==0V

If needed big Ri(cl), R1 has to be big!

High gain (Ad=R2/R1) requires bigger R2

cont

Output resistance

ig=i1

i2

iu=0

v –v =0V

ii

Ro(cl)


28

v2 –v1=0Vvg vi

Ω=== 02)( oRRoRcloRRo(cl)

Less than Ro of the open loop OpAmp!

Noninverting amplifier

i1

i2

ii=0

v =v

v2 –v1=0V

v1 =vg

vgvo


29

v2=vg

ii=i1+i2=0A => i1=-i2

i1=

1R

gv−0

i2=

2R

gvov −1R

gv

−=

12 R

gv

R

gvov=

−gvR

R

ov

+=

1

21

vg

+==

1

2

R

R

gv

ovA 1

Noninverting unit gain amplifier

Voltage Follower - BUFFER

gVgVR

R

oV

R

R=

+=

∞→

=2 01

21ii=0


30

R ∞→1vg

vi

vivo1 x vi

;)( ∞→cliRii=0

0)( =cloR

Weighted Summer

vg1

vov =0V

vg2

vgn

i1

i2

in

i

i

ii=0

+++=+++=

===

n

gnggn

n

gnn

gg

R

v

R

v

R

viiii

R

vi

R

vi

R

vi

... ...

... ; ;

2

2

1

121

2

22

1

11

fo iRv −= 0


31

v2=0Vfo

+++−= gn

n

fg

fg

fo v

R

Rv

R

Rv

R

Rv ... 2

21

1

Find the output voltage

Exercise 1 of day 1

32

44

33

22

11

vR

Rv

R

Rv

R

R

R

Rv

R

R

R

Rv cc

b

ca

b

cao −−+=

The inverting configuration with general impedances in

the feedback and the feed-in paths

ViVg


33

)(1

)(2

)(

)(

sZ

sZ

sgV

soVA −==

Vi

+ vC -

vg

i1

i2

ii=0

vg

A differentiator – f domain


34

gvsCCj

gv

Z

gvi

C

⋅==−

=ωωωω/1

)0(

1

R

ov

gsCv −= gvCRsiv ⋅⋅⋅−=R

v

R

vi oo −=

−=

02

21 ii =

o

sCRs

gv

ovsAωωωω

−=⋅⋅−==)(

20log(Vo/Vg)o

ssRC

gv

ovsAωωωω

−=−==)(

RCsA ωωωω=)(

A differentiator – f domain


35

ω ω ω ω (log scale)

Behaves as HF filter with infinite bandwidth

RCsA ωωωω=)(

2/0

)}(Re{

)}(Im{

ππππωωωω

ϕϕϕϕ

−=

−=

=

=

RCarctg

sA

sAarctg

+ vC -

vg

i1

i2

ii=0

A differentiator

time domain


36

dt

tdvCti

dt

tvdC

dt

tdvCti

g

gC

)()(

)0)(()()(

1

1

=

−==

R

tov

dt

tgdvC

)()(−=

dt

tgdvRCtov

)()( −=

R

tvti o

)(0)(2

−=

)()( 21 titi =

dt

gdvRCiv −=

Determine output waveform of

Exercise 2 of day 1

37

vi(t)

-10V

1ms 2mst

Determine output waveform of

the differentiator with R=10k i

C=10nF if excited with triangular

signal:

A integrator (f –domain)

R

gv

R

gvi =

−=

)0(

1

vo

+ vC -

vg

i1

i2

iu=0


38

RRi ==1

osCvR

gv−=

gvRCsov

1−=ooo

C

o sCvCvjCj

v

Z

vi −=−=−=

−= ωωωω

ωωωω/10

2

21 ii =

ssRCgv

ivsA oωωωω

−=−==1

)(

20log(Vo/Vg)

RCsA

ωωωω1

)( =

ωωωωωωωω

ωωωωωωωωωωωω ooo jjssRC

sA =−=−=−=1

)(

A integrator (f –domain)


39

ω ω ω ω (log scale)

Behaves as LP filter with zero corner frequency

2/0

/1

)}(Re{

)}(Im{

ππππωωωω

ϕϕϕϕ

=

=

=

=

RCarctg

sA

sAarctg

vi

+ vC -

vg

i1

i2

iu=0

tgvtgv )(0)(=

−=

A integrator (time domain)


40

dt

todvCti

dt

tovdCdt

tCdvCti

)()(

))(0()()(

2

2

−=

−==

R

tgv

R

tgvti

)(0)()(1 =

−=

dt

todvCR

tgv )()(−=

∫−= dttgvRCtiv )(

1)(

)()( 21 titi =

vo

+ vC -

vg

∫−= dtuvRCiv1

vg(t)

1V

-1V

1ms

t

2ms

vo(t) 1ms 2mst



41

vovg

R=10k, C=10nF

∫∫=

−=−=

msT

dttvdttvRCo

v2

0g84g

)(1010

1)(

1

-10V

−⋅−= ∫∫

=

=

= msT

msT

msT

dtdtov2

012/

12/

0

4 V110

v

+ vC -

v

∫−= dtgvRCiv1

vi



42

vivg

vivg

vi

Characteristics of IDEAL OpAmp

0 [V/V]

0

0=

=

∞==

=

cm

o

i

Ii

A

R

R

iV

oVA

Operational Amplifiers To recall

43

Zero output resistance

Infinite gain of differential signal

Infinite input resistance

Vo≠ f(RL)

Does tot amplifies common mode Acm=0

Infinite bandwidth ideal f charact.

Vi=0; V+=V-

Ii=0; Vi≠ f(Rs)

finite output resistance

finite gain

finite input resistance Ii ≠ 0, Vi=f(Rs)

V = f(R )

Vi=Vo/A

Characteristics of REAL OpAmp


44

finite output resistance Vo= f(RL)

amplifies common mode signal Acm≠0

finite bandwidth real f charact.

i1

i2

ii=0

v2=0V

v2 –v1=vo/A

v1 =-vo/A

vg vo

Finite gain effects on inverting amplifier


45

v2=0V

ii=i1+i2=0A => i1=-i2

i1=

1

1

R

vgv −

i2=

2

1

R

vov −1

)/(

R

Avgv o−−=

2

/

R

Aovov −=

ARR

RR

gv

ovAr/)1/21(1

1/2

++

−==

Consider the inverting amplifier with R1=1k, R2=100k that

uses OpAmp with open loop gain of A=60dB, A=80dB

i A=100dB. Find:

a) Closed loop gain

b) Drop of gain in percentage relative to the ideal

Exercise 3 of day 1

46

b) Drop of gain in percentage relative to the ideal

OpAmp.

Solution:

a)(90,83; 99,00; 99,90);

b)(-9,17%;-1,00%; -0,10%);

For inverting amplifier with R1=1k and R2=100k find in

percentages the change of closed loop gain when

open loop gain change from 100.000 to 50.000.

(-0,1%!!!)

Exercise 4 of day 1

47

(-0,1%!!!)

Finite bandwidth effects

Real amplitude characteristics of OpAmp 741

Internal compensation

(stability*)


48

(stability*)

Low 3dB frequency

Roll-off slope -20dB/dec

One dominant pole

Unity gain

f3dBf

1

dBdB j

A

s

AsA

33 /1

0

/1

0)(ωωωωωωωωωωωω +

=+

=

dBdB

j

AjA 3

3for 0)( ωωωωωωωω

ωωωω

ωωωωωωωω >>≈

Finite bandwidth effects


49

dBj

jA 3for )( ωωωωωωωωωωωωωωωω >>≈

dBdBA

jA 33

for 0)( ωωωωωωωωωωωω

ωωωωωωωω >>≈

( ) dBAjA 301for 0)(log20 ωωωωωωωωωωωω ==

f1=ωωωω1/2ππππ, Unity-Gain Bandwidth or

Gain Bandwidth Product (GB)

f3dBf1

)(/)/1(1

/

)(

)()(

12

12

sARR

RR

sV

sVsA

g

or ++

−==

Finite bandwidth effects on inverter amplifier


50

)/1/(1

/

)/1/()/1(

11

/

)(

)(

121

12

12112

0

12

RR

s

RR

RR

sRR

A

RR

sV

sV

g

o

++

−≈

++++

−=

ωωωωωωωω

12

13

/1 RRdB +

=ωωωω

ωωωω

• Characteristics of ideal OpAmp

• The meaning of infinite open loop voltage gain, input

resistance and zero output resistance.

• Inverting and noninverting amplifier with OpAmp

• Integrator

Summary of day 1

51

• Integrator

• Differentiator

• Weighted summer

• Characteristics of real OpAmp (Finite gain and

bandwidth)

What we have learned?

• Characteristics of ideal OpAmp

• The meaning of infinite open loop voltage gain,

input resistance and zero output resistance.

Questionary (Very important and Important

priority) for Day 1

52

input resistance and zero output resistance.

• Inverting amplifier with OpAmp (circuitry and

expression for gain)

• Nonverting amplifier with OpAmp (circuitry

and expression for gain)

1. What is CMRR?

2. How use infinite gain amplifiers?

3. Weighted sum circuit.

4. Differentiator.

Questionary (Advance priority) for Day 1

53

5. Integrator.

6. Effects of OpAmp’s finite gain to (non)inverting amplifier.

7. Effects of OpAmp’s finite bandwidth to (non)inverting

amplifier.

analog electronic circuits - leda.elfak.ni.ac.rsleda.elfak.ni.ac.rs/education/analogna...

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