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Chapter 30
Operational Amplifiers
Introduction
• Characteristics
– High input impedance
– Low output impedance
– High open-loop gain
– Two inputs
– One output
– Usually + and – dc power supplies
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Introduction
• Ideal Characteristics
– zin (inverting) ≈ ∞
– zin (non-inverting) ≈ ∞
– zout ≈ 0
– Av ≈ ∞
Inverting
Input
V+
-
Output
+
Non-Inverting
Input
V-
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Introduction
• Uses
– Comparators
– Voltage amplifiers
– Oscillators
– Active filters
– Instrumentation
amplifiers
Inverting
Input
V+
-
Output
+
Non-Inverting
Input
V-
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Introduction
• Single-ended amplifier
– One input grounded
– Signal at other input
• Double-ended
amplifier/Differential
amplifier
Inverting
Input
V+
-
Output
+
Non-Inverting
VInput
– Signals at both inputs
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Differential Amplifier and
Common-Mode Signals
• Basic differential amplifier
– Q1 identical to Q2
– RC1 = RC2
–
IC1 = IC2 and emitter currents equal
– Also, IC ≈ IE for high β
– and VBE ≈ 0.7 V
• Similar calculation of Bias

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Differential Amplifier and
Common-Mode Signals
◦
IC1
VCC
RC1
RC2
Q1
__
_
IE
Q2
◦
IC2
__
_
-
RE
–VEE
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Differential Amplifier and CommonMode Signals
• Apply same signal to
both Bases
Vout = Vout1 – Vout2 ≈ 0
– Eliminates commonmode signals
– 60 Hz
– Noise
◦ VCC
IC1
RC1
Q1
__
_
-
RC2
IC2
Q2
IE
RE
__
_
-
◦
–VEE
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Differential Amplifier and CommonMode Signals
• Apply sinusoids to
both bases:
– Same amplitude,
180° difference in
phase,
 if Vin1 = –Vin2
Vout = 2Vin
◦ VCC
IC1
RC1
Q1
__
_
-
RC2
IC2
Q2
IE
RE
__
_
-
◦
–VEE
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Differential Amplifier and CommonMode Signals
• Common-mode signals
– Differential voltage gain
vout
Avd 
vd
also called open-loop voltage gain
20,000 ≤ Av ≤ 200,000
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Differential Amplifier and CommonMode Signals
• Common-mode signals
– Common-mode voltage gain
vout
Avc 
vc
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Differential Amplifier and CommonMode Signals
• Common-mode rejection ratio (CMRR)
– Equations
Avd
CMRR 
Avc
[CMRR]db  20 log10 (CMRR)
– Values
70db  CMRR  90db
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Differential Amplifier and
Common-Mode Signals
• Noise
– Static in audio signal
– Increases as signal is
amplified
– Common mode signal
– Significantly reduced
by differential amplifier
vnoise
vin
__
_
- __
_
-
+
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Negative Feedback
• Op-amp
– Large differential, open-loop voltage gain
• Avol ≈ 100,000
– Small input yields saturated output (VCC or
VEE)
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Negative Feedback
• Negative feedback
– Returns a portion of output signal to the input
– Open-loop voltage gain decreased
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Negative Feedback
• Input impedance still
high
• Output impedance low
• Circuit voltage gain, Av
– Adjustable
– Stable
vout
Av 
vin
Negative
Feedback
+
vout
vin
__
_
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Inverting Amplifier
• Basic circuit
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Inverting Amplifier
• Output 180° out of phase with input
• Significant decrease in gain
– Gain now called closed-loop voltage gain
• Output impedance ≈ 0
• vd ≈ 0
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Inverting Amplifier
• Inverting input at virtual
ground, vin(-) ≈ 0
• iin to op-amp ≈ 0
• Input current only
dependent on vin and R1
• Avcl only dependent on
input resistor and
feedback resistor
vin
iin 
R1
vout
iin RF
Avcl 

vin
iin R1
RF
Avcl  
R1
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Inverting Amplifier
• Model
vd ≈ 0
Rin ≈ ∞
iin = if
zin ≈ R1
RF
R1
i=0
+
i
vin in
if
+
vd Rin
+
-
__
_
-
Rout
Avolvd internal +__
_
vout(OC)
-
-
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Inverting Amplifier
• Low output
impedance
zout 
zout
RF
vout (OC )
iout ( SC )
 Rout 
 (1  Avcl ) 

 Avol 
R1
i=0
+
i
vin in
if
+
vd Rin
-
__
_
-
Rout
-
Avolvd
internal+__
_
-
i1
iout(sc)
__
_
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Non-Inverting Amplifier
• Circuit
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The Non-Inverting Amplifier
•
•
•
•
Very high input impedance
Voltage gain related to the two resistors
Very low output impedance
Excellent buffer
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Non-Inverting Amplifier
• Differential voltage
– vd ≈ 0
• Input current to op-amp
–i=0
• Closed-loop voltage gain (Avcl) is a resistor
ratio
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Non-Inverting Amplifier
vout
Av 
vin
RF iF  R1iF
Av 
R1iF
Avcl
RF

1
R1
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Non-Inverting Amplifier
• Model
• Input impedance
vd
iin 
Rin
 Avol 
zin  1 
 Rin
 Avcl 
vin
iin
zin
+
vd Rin
-
+
R1
-
__
_
-
-
vout
Rout
Avolvd
internal __
_
+ - +
RF
if
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Non-Inverting Amplifier
• Model
• Output impedance
iout ( sc )  i2  i f
zout
 Avcl

 Avol

 Rout

iin
-
+
R1
-
__
_
-
i2
+
vd Rin
-
Rout
Avolvd
internal __
_
+ - +
RF
if
__
_
-
iout(sc)
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Non-Inverting Amplifier
•
•
•
•
•
Very high zin
Very low zout
Good buffer circuit
Also called voltage follower (gain = 1)
Or adjustable gain > 1
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Non-Inverting Amplifier
• Voltage Follower Buffer Circuit
– Gain = 1
– High impedance source drives low impedance
load
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Op-Amp Specifications
• LM 741 series
– Inexpensive
– Widely used
– Good general specifications
– Characteristic of all op-amp specifications
• Provide Minimum, Typical, and Maximum
ratings
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Op-Amp Specifications
• Input Offset Voltage, Vio
– LM741C, Vio typical is 2 millivolts
– Model is voltage source with value, Vio in
series with + input
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Op-Amp Specifications
• Input Offset Voltage, Vio
– Without feedback this would saturate output
with no input
– With negative feedback, output due to Vio is
closed-loop gain times Vio
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Op-Amp Specifications
• Input Offset Current, Ios
• Ios = Difference between bias currents at +
and – inputs of op-amp
• 741C typical Ios is 20 nanoamps
• Multiplying resistor used to measure Ios
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Op-Amp Specifications
• Input Resistance
– 741C: minimum = .3 MΩ, typical = 2 MΩ
• Open-Loop Voltage gain (Avol)
– 741C: Avol = Large Signal Voltage Gain
• minimum = 20,000, typical = 200,000
– Closely related to Bandwidth, BW
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Op-Amp Specifications
• Gain-bandwidth product
– 741C = 1,000,000 = 106 MHz
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Op-Amp
Specifications
• Gain versus
frequency curve
for op-amp
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Op-Amp Specifications
• Slew rate
– Maximum rate of change of output voltage
V
Slew Rate 
t
• 741C maximum slew rate = 0.5 V/μsec
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Op-Amp Specifications
• Fastest time for output to go from 0 to 10
volts is 20 μsec
• Can distort waveforms that have too fast
a rise time
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Op-Amp Specifications
• Slew rate required for
Sinusoid with frequency
f and amplitude A
• Maximum amplitude of
a sine wave with
frequency f for a given
slew rate
v  A sin(t )
dv
  A cos(t )
dt
slew rate  2 fA
slew rate
f max 
2 A
slew rate
Amax 
2 f
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Op-Amp Specifications
• Bias
Compensation: use
RC = R1||RF
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Troubleshooting an Op-Amp Circuit
• Problems occur when circuit is first built
• Most important
– Correct connection of dual power supply
• Connecting a – supply to a + input (or vice
versa) can burn out an op-amp
• Single earth ground
• Short connecting wires
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