Post on 22-Dec-2015
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
Ideal Op Amp
1) 0 vv A v v
The open-loop gain, Av, is very large, approaching infinity.
2) 0i i The current into the inputs are zero.
+
-
i
ov
v
vi
DDV
SSV
0SS DDV v V
Ideal Op Amp with Negative Feedback+
-ov
v
v
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
+
-
1R2R
iv ovv
v oF
i
vA
v
2
1
1oF
i
v RA
v R
1
1 2i o
Rv v v v
R R
Closed-loop voltage 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
Unity-Gain Buffer
+
-ov
v
viv
oF
i
vA
v
1oF
i
vA
v
i ov v v v
Closed-loop voltage gain
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
0v v
1 1
0i ii
v vi
R R
Current into op amp is zero
+
-
1R
2R
iv ovv
vii ii
0 0
2 2
0i
v vi
R R
2
1
oF
i
v RA
v R
0
1 2
iv v
R R
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
v v
11
1
v vi
R
Current into op amp is zero
01
2
v vi
R
+
-1R
2R
1vovv
v1i
1i
2v1R
2R
22
1 2
Rv v
R R
01
1 2
v vv v
R R
2 21 2 2 0
1 2 1 2
1 2
R Rv v v v
R R R R
R R
Differential Amplifier
+
-1R
2R
1vovv
v1i
1i
2v1R
2R
2 21 2 2 0
1 2 1 2
1 2
R Rv v v v
R R R R
R R
2
2 2 20 1 2 2
1 1 2 1 1 2
R R Rv v v v
R R R R R R
2 2 20 1 2
1 1 2 1
1R R R
v v vR R R R
20 2 1
1
Rv v v
R
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
i fi i
0v v
00 f Fv i R
0 i Fv i R
0Transresistance i Fv i R
+
-ov
v
vii
FR fi
Photodiode Circuit25 A per milliwatt of incident radiationii
650 25 10 1.25mAii
Assume 3.2kFR
3 30 1.25 10 3.2 10 4Vi Fv i R
+
-ov
v
vii
FR fi
h At 50 mW
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)• Finite slew rate• Input bias currents• Input bias current offset• Input offset voltage• Finite common mode rejection ratio (CMRR)
0slew rate ( ) MAXdv t dt