NO DESCRIPTION

1. EECE 311: Electronic Circuits
Part 4

2. OPERATIONAL AMPLIFIER
2

3.  Ideal Op-Amp
 
3 2 1
v A v v
 
 Infinite input impedance
 Zero output impedance
 Infinite open-loop gain
 Infinite bandwidth
…
 …
Open loop gain

4.  Inverting Amplifier Configuration
1 2
2
1 2 1
1
0
O
I
I O
O
I
v
I
i
I
o
v
v
i i
R R
v
v R
A
R R R
v
R R
i
R
 
    
 

 Input and output signals out of
phase
 Trade-off between a large input
resistance and a large gain

5.  Effect of Finite Open-Loop Gain
 
2 1
2 1
if is not :
0 /
o
O
A
A v v v
v v v A

 
   
2
1
lim v
A
R
A
R

 
 
1
1 1
2
2
1
/
/
I O
I
I
o
o I I O
v v A
v v
i
R R
v R
v i R v v A
A R


 
     
2 1
2 1
/
1 /
1
o
v
I
v R R
A
R R
v
A

  

 
  
 

6.  Summing Amplifier

7.  Non-Inverting Amplifier Configuration
2 1
2
1
1
i
O I I
O
v
I
R
v v v
R R
v R
A
v R
 


   
2 1
2 1
Finite :
1 /
1 /
1
v
A
R R
A
R R
A




 Infinite input resistance
 Input and output signals in-phase

8.  Voltage Follower
 Infinite input resistance
 Zero output resistance
 Input and output signals are equal

9.  Difference Amplifier: Amplify the difference of two signals
1
2
I
I
v
v
Two input signals:
 
2 1
1 2
1
2
Id I I
Icm I I
v v v
v v v
 
 
let
Difference signal
Common-mode
1
2
2
2
Id
I Icm
Id
I Icm
v
v v
v
v v
 
 


10.  Difference Amplifier: Amplify the difference of two signals
1
2
I
I
v
v
Two input signals:
vo = A1vI1 + A2vI 2
= A1 vIcm -
vId
2
æ
è
ç
ö
ø
÷ + A2 vIcm +
vId
2
æ
è
ç
ö
ø
÷
= A1 + A2
( )vIcm +
A2 - A1
2
æ
è
ç
ö
ø
÷ vId
= AcmvIcm + AdvId
Ad = differential gain =
vo
vId vIcm =0ÞvI 2 =-vI1=
vId
2
Acm = common-mode gain =
vo
vIcm vId =0ÞvI 2 =vI1

11. Common-Mode Rejection Ratio
11
common-mode rejection ratio
20log d
cm
CMRR
A
A


In a differential amplifier, Acm is ideally zero and CMRR is ideally infinite

12. Op-Amp Difference Amplifier Circuit
12

13. By superposition:
2
1
1
o I
R
v v
R
  2 2 4
2
1 1 3 4
1 1
o I
R R R
v v v
R R R R

 
   
     
   

    
 
2 2 4
1 2
1 1 3 4
4 2 2
2 1
3 1 1
1
with = :
o I I
o I I
R R R
v v v
R R R R
R R R
v v v
R R R
 
 
      
 

  
 
d
A Id
v

14. vo = -
R2
R1
vI1 + 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷ vI 2
= -
R2
R1
vIcm -
vId
2
æ
è
ç
ö
ø
÷ + 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷ vIcm +
vId
2
æ
è
ç
ö
ø
÷
=
1
2
R2
R1
+ 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷
æ
è
ç
ö
ø
÷ vId + 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷ -
R2
R1
æ
è
ç
ö
ø
÷ vIcm
Ad Acm

15. vo =
1
2
R2
R1
+ 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷
æ
è
ç
ö
ø
÷ vId + 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷ -
R2
R1
æ
è
ç
ö
ø
÷ vIcm
= AdvId + AcmvIcm
For the difference amplifier, the output should be a function of vID only.
Acm = 1+
R2
R1
æ
è
ç
ö
ø
÷
R4
R3 + R4
æ
è
ç
ö
ø
÷ -
R2
R1
æ
è
ç
ö
ø
÷ =
R1R4 - R2R3
R1 R3 + R4
( )
For the difference amplifier, Acm should be zero:
R1R4 - R2R3
R1 R3 + R4
( )
= 0 Þ
R1
R2
=
R3
R4
=
R2
R1
vId

16.  Effect of Finite Bandwidth
 fb = f3dB is made very low to
stabilize the op-amp
3
3
( )
1
M
dB
t M dB
A
A s
s
A

 


 

17.  Frequency Response of the Inverting Op-Amp
 
2 1 2 1
2 1 2
1 2 1
( ) / /
1 /
( ) 1
1 1 1
( ) / 1 /
O
I
M t
V s R R R R
R R
V s R s
A s A R R R

 
 
  
   
 

 
1

2 1
/
( )
1
O
I
p
V R R
s
s
V


 
 2
1
1
t
p
R
R

 


18.  Frequency Response of the Inverting Op-Amp
 Example: R2/R1 = 10

19.  Large-Signal Operation of Op-Amps
 Output Voltage Saturation
The op-amp output voltage saturates within 1V of the power supplies
voltages (rail-to-rail op-amps reach to within a few mV)
 Output Current Limits
Output current limited to a few mA (or few tens of mA, usually
20mA) in either direction (source or sink)

20.  Slew Rate
There is a maximum rate of change possible at the output of the op-amp.
max
o
dv
SR
dt


21.  Slew Rate
1
1
o
i
t
V
s
V



For a step input V:
 
( ) ( ) 1
1
tt
o o
t
V
V s v t e V
s
s



   
 

 
 
For a voltage follower:
1 2 3 4
0.2
0.4
0.6
0.8
1.0
Slew-rate distortion if dvo/dt > SR

22.  Full-Power Bandwidth
The output of the op-amp can be slew rate limited or frequency limited.
It is slew rate limited when (for a sinusoidal input):
max
max
max
for
FPB:
2
o
o o
M o
M
o
V SR
V V
V SR
SR
f
V



 

 
 

Frequency at which op amp stops
behaving linearly
 Example:
 
max
1 V/ s
10 V
1 V/ s
15.9 KHz
10 V 2
o
M
SR
V
f





   2 V
2 80 KHz
o
SR
V

 

at around 80 KHz,
in order to get linear operation (not SR limited)

23.  Op-Amp Integrator and Differentiator
1
2
resistor
capacitor
1
1
o
i
o
i
V a
V s
Z
Z
V sC
V R RCs



 
Integrator:
1
2
.
capacitor
resistor
1
o
i
o
i
V
a s
V
Z
Z
V R
RCs
V
sC

  

Differentiator:

24.  Op-Amp Integrator
0
1
1
(0)
1
C O
I
R C
O
I
t
O I C
o
i
dv dv
v
i i C C
R dt dt
dv
v
dt RC
v v dt v
RC
V
V RCs
    



 



integrator time constant
1
integrator frequency
RC
RC


1 1
90
o
i
V
V j RC RC
 


  

25.  Op-Amp Differentiator

26. Simple CMOS Op-Amp