Chapter 30
Operational Amplifiers
2
Introduction
• Characteristics– High input impedance– Low output impedance– High open-loop gain– Two inputs– One output– Usually + and – dc power supplies
3
Introduction
• Ideal Characteristics– zin (inverting) ≈ ∞
– zin (non-inverting) ≈ ∞
– zout ≈ 0
– Av ≈ ∞
-
+
V-
V+
Output
InvertingInput
Non-InvertingInput
4
Introduction
• Uses– Comparators– Voltage amplifiers– Oscillators– Active filters– Instrumentation
amplifiers
-
+
V-
V+
Output
InvertingInput
Non-InvertingInput
5
Introduction• Single-ended amplifier
– One input grounded– Signal at other input
• Double-ended amplifier/Differential amplifier– Signals at both inputs
-
+
V-
V+
Output
InvertingInput
Non-InvertingInput
6
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
∴
7
Differential Amplifier and Common-Mode Signals
RE
–VEE
IE
___-
___-
RC2RC1IC1
IC2
VCC
Q1 Q2
8
RE
–VEE
IE
RC2RC1IC1
IC2
VCC
Q1 Q2
___-
___-
Differential Amplifier and Common-Mode Signals
• Apply same signal to both BasesVout = Vout1 – Vout2 ≈ 0– Eliminates common-
mode signals– 60 Hz– Noise
9
Differential Amplifier and Common-Mode Signals
• Apply sinusoids to both bases:– Same amplitude,
180° difference in phase,
if Vin1 = –Vin2
Vout = 2Vin
∴RE
–VEE
IE
Q1 Q2
___-
RC2RC1IC1
IC2
VCC
___-
10
Differential Amplifier and Common-Mode Signals
• Common-mode signals– Differential voltage gain
also called open-loop voltage gain
20,000 ≤ Av ≤ 200,000
outvd
d
vA
v=
11
Differential Amplifier and Common-Mode Signals
• Common-mode signals– Common-mode voltage gain
outvc
c
vA
v=
12
Differential Amplifier and Common-Mode Signals
• Common-mode rejection ratio (CMRR)– Equations
– Values
10[ ] 20log ( )
70 90
vd
vc
db
ACMRR
A
CMRR CMRR
db CMRR db
=
=
≤ ≤
13
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
14
Negative Feedback• Op-amp
– Large differential, open-loop voltage gain
• Avol ≈ 100,000
– Small input yields saturated output (VCC or VEE)
15
Negative Feedback• Negative feedback
– Returns a portion of output signal to the input– Open-loop voltage gain decreased
16
Negative Feedback• Input impedance still
high
• Output impedance low
• Circuit voltage gain, Av
– Adjustable– Stable
-+
NegativeFeedback
___-
vin
vout
outv
in
vA
v=
17
Inverting Amplifier• Basic circuit
18
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
19
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
1
1
1
inin
out in Fvcl
in in
Fvcl
vi
R
v i RA
v i R
RA
R
=
= =−
=−
20
Inverting Amplifier
-
+
___-
vout(OC)
vd+
-
Rin
RF
-+___
-
vin
R1
+
-
• Modelvd ≈ 0Rin ≈ ∞iin = if zin ≈ R1
i = 0
iin
if
Rout
Avolvdinternal
21
Inverting Amplifier
-
+
___-
iout(sc)
vd Rin
RF
-+___
-
vin
R1
+
-
i = 0
iin
if
Rout
i1
___-
Avolvdinternal
( )
( )
(1 )
out OCout
out SC
outout vcl
vol
vz
i
Rz A
A
=
⎛ ⎞= − ⎜ ⎟
⎝ ⎠
• Low output impedance
22
Non-Inverting Amplifier• Circuit
23
The Non-Inverting Amplifier
• Very high input impedance• Voltage gain related to the two resistors• Very low output impedance• Excellent buffer
24
Non-Inverting Amplifier
• Differential voltage– vd ≈ 0
• Input current to op-amp– i = 0
• Closed-loop voltage gain (Avcl) is a resistor ratio
25
Non-Inverting Amplifier
1
1
1
1
outv
in
F F Fv
F
Fvcl
vA
v
R i R iA
R i
RA
R
=
+=
= +
26
Non-Inverting Amplifier• Model
• Input impedance
-
+
___-
vout
vd Rin
RF
-
+___-
vin
R1
iin
if
Rout
Avolvdinternal
+
-- +
1
din
in
volin in
vcl
vi
R
Az R
A
=
⎛ ⎞= +⎜ ⎟⎝ ⎠
zin
27
Non-Inverting Amplifier• Model
• Output impedance
-
+
___-
vd Rin
RF
-
+___-
R1
iin
if
Rout
Avolvdinternal
+
-- +
___-iout(sc)
i2( ) 2out sc f
vclout out
vol
i i i
Az R
A
= +
⎛ ⎞=⎜ ⎟⎝ ⎠
28
Non-Inverting Amplifier• Very high zin
• Very low zout
• Good buffer circuit
• Also called voltage follower (gain = 1)
• Or adjustable gain > 1
29
Non-Inverting Amplifier• Voltage Follower Buffer Circuit
– Gain = 1– High impedance source drives low impedance
load
30
Op-Amp Specifications• LM 741 series
– Inexpensive– Widely used– Good general specifications– Characteristic of all op-amp specifications
• Provide Minimum, Typical, and Maximum ratings
31
Op-Amp Specifications• Input Offset Voltage, Vio
– LM741C, Vio typical is 2 millivolts
– Model is voltage source with value, Vio in series with + input
32
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
33
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
34
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
35
Op-Amp Specifications• Gain-bandwidth product
– 741C = 1,000,000 = 106 MHz
36
Op-Amp Specifications
• Gain versus frequency curve for op-amp
37
Op-Amp Specifications• Slew rate
– Maximum rate of change of output voltage
• 741C maximum slew rate = 0.5 V/μsec
VSlew Rate
t
Δ=
Δ
38
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
39
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
40
Op-Amp Specifications• Bias
Compensation: use RC = R1||RF
41
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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