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
Operational Amplifiers
13
∞→oV
0 =iV
A ⇒∞→=iV
oVInfinite gain !!!
Transfer characteristic
Vi [V]Vi [V]
Operational Amplifiers
14
Vi [V]
Vu [mV]
Vi [V]
Vu [mV]
Ideal transfer characteristics
Vo [V]
Operational Amplifiers
15
Vi [mV] t[ms]
Operational Amplifiers
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
Operational Amplifiers
17
iAVRR
RoV
Lo
L
+= 0 ⇒=oR
A ∞→i
)( LfoV R≠
Vo
0
iAV=
Output
Two input ports
Symbol
Noninverting input
Inverting input
Operational Amplifiers
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
Operational Amplifiers
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:
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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)
Operational Amplifiers
Biasing of OpAmp
23
How to use a component
with infinite gain?
Never alone – always with feedback
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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)
Operational Amplifiers
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)
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
33
)(1
)(2
)(
)(
sZ
sZ
sgV
soVA −==
Vi
+ vC -
vg
i1
i2
ii=0
vg
A differentiator – f domain
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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)
Operational Amplifiers
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)
Operational Amplifiers
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
A integrator (time domain)
Operational Amplifiers
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
A integrator (time domain)
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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*)
Operational Amplifiers
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
Operational Amplifiers
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
Operational Amplifiers
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.