Download Discussion #17 - Operational Amplifiers

Schedule…
Date
Day
Class
No.
Title
Chapters
29 Oct
Wed
17
Operational Amplifiers
8.1 – 8.2
30 Oct
Thu
31 Oct
Fri
1 Nov
Sat
2 Nov
Sun
3 Nov
Mon
Recitation
18
Operational Amplifiers
HW
Due date
Lab
Due date
Exam
HW 7
8.3 – 8.4
LAB 6
4 Nov
Tue
5 Nov
Wed
ECEN 301
19
Binary Numbers
13.1 – 13.2
Discussion #17 – Operational Amplifiers
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Increase
Helaman 12:2
2 Yea, and we may see at the very time when he doth prosper his
people, yea, in the increase of their fields, their flocks and their
herds, and in gold, and in silver, and in all manner of precious
things of every kind and art; sparing their lives, and delivering
them out of the hands of their enemies; softening the hearts of
their enemies that they should not declare wars against them;
yea, and in fine, doing all things for the welfare and happiness
of his people; yea, then is the time that they do harden their
hearts, and do forget the Lord their God, and do trample under
their feet the Holy One—yea, and this because of their ease,
and their exceedingly great prosperity.
ECEN 301
Discussion #17 – Operational Amplifiers
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Lecture 17 – Operational Amplifiers
ECEN 301
Discussion #17 – Operational Amplifiers
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Ideal Amplifiers
Amplifier: a device for increasing the power of a signal.
 Power increase is called gain (A)
RS
+
0:21
vS(t) +
Gain A
–
CD
RL
vL
–
Source
Amplifier
Load
Source
Amplifier
Load
vL (t )  AvS (t )
ECEN 301
Discussion #17 – Operational Amplifiers
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Ideal Amplifiers
Simplified Amplifier Model:
The source “sees” and equivalent load (Rin)
The load “sees” and equivalent source (Avin)
RS
Rout
RS
+
vS(t) +
Gain A
–
RL
vL
–
Source
NB: Thévenin
equivalent
ECEN 301
Amplifier
+
vS(t) +
–
vin
–
Avin
Rin
+
+
–
RL
vL
–
Load
NB: equivalent
resistance
Discussion #17 – Operational Amplifiers
5
Ideal Amplifiers
The gain is dependent on the source and load (i.e. is
different for different sources and loads)
Rout
RS
+
vS(t) +
–
vin
–
Avin
Rin
+
+
–
RL
vL
–
Rin
vin  vS
RS  Rin
RL
vL  Avin
Rout  RL

Rin
RL 
vS
vL   A
 RS  Rin Rout  RL 
NB: expression for vL depends on the source (RS) and the load (RL)
ECEN 301
Discussion #17 – Operational Amplifiers
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Ideal Amplifiers
The gain can be made to be almost independent of the source (RS)
and the load (RL)
 Let Rin → ∞
 Let Rout → 0
Rout
RS
+
vS(t)
+
–
vin
–
Avin
Rin
+
+
–
RL
vL
if R in   :
vin  vS
–
Rin
RS  Rin
 vS
if R out  0
vL  Avin
RL
Rout  RL
 Avin
vL  AvS
NB: it is desirable for an amplifier to have:
• a very large input impedance
• a very small output impedance
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps
Operational Amplifier: originally designed (late 1960’s)
to perform mathematical operations (analog computer)
 Addition
 Subtraction
 Integration
 differentiation
Positive power supply (usually +15V)
VS+
Inverting Input
–
Output
Noninverting Input
+
NB: the power supplies (VS+
and VS–) are often omitted in
drawings – they are implicit
VS–
Negative power supply (usually –15V)
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Open-Loop Mode
Open-Loop Model: an ideal op-amp acts like a difference amplifier (a
device that amplifies the difference between two input voltages)
i1
i1
+
vin
+
+
v–
v+
–
–
–
–
+
i2
v–
io
–
–
Rin
+
Rout
vin
+
vo
AOLvin–
+
–
+
v+
+
vo
–
i2
NB: op-amps have near-infinite input resistance (Rin) and very small output resistance (Rout)
vo  AOLvin


 AOL (v  v )
ECEN 301
AOL – open-loop voltage gain
Discussion #17 – Operational Amplifiers
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Op-Amps – Open-Loop Mode
Open-Loop Model: an ideal op-amp acts like a difference amplifier (a
device that amplifies the difference between two input voltages)
i1
–
–
+
vin
+
+
v–
+
i2
v+
–
io
+
Ideally i1 = i2 = 0
(since Rin → ∞)
vo
–
–
i1  i2  0
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Open-Loop Mode
Open-Loop Model: an ideal op-amp acts like a difference amplifier (a
device that amplifies the difference between two input voltages)
i1  i2  0
ECEN 301
What? No input current??
In reality there is a small current
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
i2
+
+
vo
–
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
Feedback current: current from the output
is fed back into the input of the op-amp
Node a
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
+
+
vo
–
vS  v 
iS 
RS
vo  v 
iF 
RF
i1  0
KCL at Node a :
iS  iF  i1  0
iS  iF
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
From Open - Loop Model :
iF
RS
iS
vS(t) +
–
vo  AOL (v   v  )
v–
–
 AOL (0  v  )
i1
v+
+
vo
–
ECEN 301
  AOLv 
+
vo
v 
AOL

Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
iS  iF
vS  v 
vo  v 

RS
RF
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
+
+
vo
–
ECEN 301
vS   vo / AOL 
vo   vo / AOL 

 

RS 
RS
R
R
F
F



vS
v
v
v
 S  o  o
RS
RS AOL RF AOL RS
 1
1
1 

vS  vo 


 RF / RS AOL RF / RS AOL 
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
 1
1
1 


vS  vo 


 RF / RS AOL RF / RS AOL 
iF
RS
iS
vS(t)
+
–
v–
–
NB: if AOL is very large these terms → 0
i1
v+
+
+
vo
–
Closed - Loop Gain :
A CL 
vo
vS

ECEN 301
Discussion #17 – Operational Amplifiers
RF
RS
16
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
From Open - Loop Model :
v
v    out
AOL
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
+
+
vo
–
NB: as AOL → ∞ v– → 0
As AOL  

v v
ECEN 301
Discussion #17 – Operational Amplifiers

17
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified
is connected to the inverting terminal
RF
NB: two important results for an ideal
op-amp with negative feedback
iF
v–
RS
iS
vS(t) +
–
–
i1
v+
i2
+
+
vo
–
ECEN 301
i1  i2  0

v v
Discussion #17 – Operational Amplifiers

18
Op-Amps – Closed-Loop Mode
Example1: determine AOL and vo
RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s
RF
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
+
+
vo
–
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
Example1: determine AOL and vo
RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s
RF
A CL 
iF
RS
iS
vS(t) +
–
v–
vo  
–
i1
v+
+
R
vo
 F
vS
RS
+
vo
RF
vS
RS
10 4
  3 0.015 cos(t )
10
 0.15 cos(t )
–
A CL
RF

RS
 10
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
Example1: determine AOL and vo
RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s
RF
iF
iS
vS(t) +
–
0.10
–
i1
v+
+
+
vo
–
Voltage (V)
RS
0.15
v–
0.05
vs(t)
0.00
vo(t)
-0.05
-0.10
-0.15
0.0
0.2
0.4
0.6
0.8
1.0
time (s)
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
Example2: What is the min/max gain, and gain uncertainty if 5%
tolerance resistors are used?
RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s
RF
A CL nom  10
iF
RS
iS
vS(t) +
–
v–
–
i1
v+
+
+
vo
A CL min  
RF min
RS max
A CL max  
RF max
RS min
9500

1050
 9.05
10500

950
 11.05
Discussion #17 – Operational Amplifiers
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–
ECEN 301
NB: nominal gain
Op-Amps – Closed-Loop Mode
Example2: What is the min/max gain, and gain uncertainty if 5%
tolerance resistors are used?
RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt),
A=0.015, ω = 50 rads/s
RF
iF
RS
iS
vS(t) +
–
–
A CL nom
10  9.05
10
 9.5%
i1
+
100 
A CL nom  A CL min
 100 
v–
v+
Max % Error :
+
vo
–
Min % Error :
100 
A CL nom  A CL max
A CL nom
10  11.05
10
 10.5%
 100 
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
RF
RS1
vS1(t) +
–
–
–
i1
RS2
vS2(t) +
iF
v–
v+
+
+
vo
i2
–
RSN
vSN(t) +
–
ECEN 301
iN
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
RF
Node a
RS1
vS1(t) +
–
–
KCL at Node a :
–
i1
RS2
vS2(t) +
iF
v–
v+
+
+
i1  i2    iN  iF
vo
i2
–
NB: v– = v+ = 0
RSN
vSN(t) +
–
ECEN 301
iN
vSn
in 
RSn
n  1, 2, , N
Discussion #17 – Operational Amplifiers
vo
iF 
RF
25
Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
RF
Node a
RS1
vS1(t) +
–
–
ECEN 301
N
v+
+
+
vo
i2
RSN
vSN(t) +
–
i1
RS2
vS2(t) +
–
iF
v–
–
vsn
vo


RF
n 1 Rsn
N
RF
vo  
vsn
n 1 Rsn
iN
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be
amplified is connected to the noninverting terminal
RF
iF
RS
iS
vS(t) +
–
ECEN 301
R
v–
–
i1
v+ +
+
i1
vo
–
Discussion #17 – Operational Amplifiers
27
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be
amplified is connected to the noninverting terminal
RF
Node a
iF
RS
iS
vS(t) +
–
ECEN 301
R
v
iS  S
RS
v–
–
vo  v 
iF 
RF
i1  0
i1
v+ +
+
i1
vo
KCL at Node a :
 iS  iF  i1  0
–
Discussion #17 – Operational Amplifiers
iS  iF
28
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be
amplified is connected to the noninverting terminal
RF
Since i1  0 :
Node a
(i.e. no current th rough R  no voltage drop)
iF
RS
iS
vS(t)
+
–
R
v   vS  v 
v–
–
i1
v+ +
+
i1
vo
–
i F  iS
vo  v S v S

RF
RS
RF
vo
 1
vS
RS
ECEN 301
Discussion #17 – Operational Amplifiers
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Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be
amplified is connected to the noninverting terminal
RF
Node a
Closed - Loop Gain :
iF
RS
iS
vS(t) +
–
R
v–
A CL
–
i1
v+ +
+
i1
vo
–
vo

vS
RF
 1
RS
NB: always positive and greater than or equal to 1
ECEN 301
Discussion #17 – Operational Amplifiers
30
Op-Amps – Closed-Loop Mode
Voltage Follower: the voltage on the output of the
op-amp is equal to the source voltage
v–
–
i1
v+ +
+
i1
vS(t) +
–
ECEN 301
vo
–
Discussion #17 – Operational Amplifiers
31
Op-Amps – Closed-Loop Mode
Voltage Follower: the voltage on the output of the
op-amp is equal to the source voltage
NB: an ideal op-amp with negative
feedback has the property
v–

–
v v
i1
v+
+
+
i1
vS(t) +
–
ECEN 301

vo
–
v   vs
v   vo
vo  vS
Discussion #17 – Operational Amplifiers
32
Op-Amps – Closed-Loop Mode
Voltage Follower: the voltage on the output of the
op-amp is equal to the source voltage
ib
Circuit 1
+
va
–
Circuit 1
+
vb
–
Circuit 2
If va ≠ vb
ib is the load current
Loading: changing the behaviour of one circuit by connecting another circuit to it
ECEN 301
Discussion #17 – Operational Amplifiers
33
Op-Amps – Closed-Loop Mode
Voltage Follower: the voltage on the output of the
op-amp is equal to the source voltage
–
+
Circuit 1
Circuit 2
Voltage follower can be used to prevent loading
(ib = 0)
Loading: changing the behaviour of one circuit by connecting another circuit to it
ECEN 301
Discussion #17 – Operational Amplifiers
34