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Operational Amplifiers (Op Amps)
Discussion D3.1
Operational Amplifiers (Op Amps)
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•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Ideal Op Amp
i
i
1)
v
v
VDD
VSS  v0  VDD
+
vo
-
VSS
v0  Av  v  v 
The open-loop gain, Av, is very large, approaching infinity.
2)
i  i  0
The current into the inputs are zero.
Ideal Op Amp with Negative Feedback
v
+
v
-
vo
Network
Golden Rules of Op Amps:
1. The output attempts to do whatever is necessary to
make the voltage difference between the inputs zero.
2. The inputs draw no current.
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Non-inverting Amplifier
v
vi
v
R1
+
vo
Closed-loop voltage gain
AF 
-
vo
vi
R2
vi  v  v 
R1
vo
R1  R2
vo
R2
AF   1 
vi
R1
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Unity-Gain Buffer
vi
v
v
+
-
Closed-loop voltage gain
vo
AF 
vo
vi
vi  v  v  vo
AF 
vo
1
vi
Used as a "line driver" that transforms a high input impedance
(resistance) to a low output impedance. Can provide substantial
current gain.
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Inverting Amplifier
R2
Current into op amp is zero
v  v  0
v  0 vi
ii  i

R1
R1
0  v0 v0
ii 

R2
R2
vi
ii
ii
R1
v
v
+
vi v0

R1 R2
AF 
vo
R
 2
vi
R1
vo
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Differential Amplifier
R2
Current into op amp is zero
v1
v  v
i1 
v2
v1  v
R1
R1
v
v
+
R1
R2
v  v0
i1 
R2
R2
v 
v2
R1  R2
i1
i1
v1  v v  v0

R1
R2
v1 
R2
R2
v2
v2  v0
R1  R2
R1  R2

R1
R2
vo
Differential Amplifier
R2
R2
R2
v1 
v2
v2  v0
R1  R2
R  R2
 1
R1
R2
v1
v2
2
2
R2
R2
R
v0   v1 
v2 
v2
R1
R1  R2
R1  R1  R2 
R2
R2  R2 
v0   v1 
1   v2
R1
R1  R2  R1 
i1
R1
v
v
i1
+
R1
R2
R2
v0 
 v2  v1 
R1
vo
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Current-to-Voltage Converter
v
v
ii
+
vo
-
RF
if
ii  i f
v  v  0
0  v0  i f RF
v0  ii RF
Transresistance  v0 ii   RF
Photodiode Circuit
ii  25 A per milliwatt of incident radiation
v
v
h
ii
+
vo
-
At 50 mW
RF
if
ii  50  25 106  1.25mA
Assume RF  3.2k
v0  ii RF  1.25 103  3.2  103  4V
Operational Amplifiers (Op Amps)
•
•
•
•
•
•
•
Ideal Op Amp
Non-inverting Amplifier
Unity-Gain Buffer
Inverting Amplifier
Differential Amplifier
Current-to-Voltage Converter
Non-ideal Op Amp
Non-ideal Op Amp
•
•
•
•
•
•
•
•
•
•
Output voltage is limited by supply voltage(s)
Finite gain (~105)
Limited frequency response
Finite input resistance (not infinite)
Finite output resistance (not zero)
slew rate  dv0 (t ) dtMAX
Finite slew rate
Input bias currents
Input bias current offset
Input offset voltage
Finite common mode rejection ratio (CMRR)