discussion #17 - operational amplifiersbmazzeo/ecen_301_f08/fall2008/slides...ecen 301 discussion...
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ECEN 301 Discussion #17 – Operational Amplifiers 1
Date Day Class
No.
Title Chapters HW
Due date
Lab
Due date
Exam
29 Oct Wed 17 Operational Amplifiers 8.1 – 8.2
30 Oct Thu
31 Oct Fri Recitation HW 7
1 Nov Sat
2 Nov Sun
3 Nov Mon 18 Operational Amplifiers 8.3 – 8.4
LAB 6
4 Nov Tue
5 Nov Wed 19 Binary Numbers 13.1 – 13.2
Schedule…
ECEN 301 Discussion #17 – Operational Amplifiers 2
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 3
Lecture 17 – Operational Amplifiers
ECEN 301 Discussion #17 – Operational Amplifiers 4
Ideal Amplifiers
Amplifier: a device for increasing the power of a signal.
Power increase is called gain (A)
vS(t) +
–
RS
Gain A
+
vL
–
RL
Source Amplifier Load
0:21CD
Source Amplifier Load
)()( tAvtv SL
ECEN 301 Discussion #17 – Operational Amplifiers 5
Ideal Amplifiers
Simplified Amplifier Model:The source ―sees‖ and equivalent load (Rin)
The load ―sees‖ and equivalent source (Avin)
vS(t) +
–
RS
Gain A
+
vL
–
RL
Source Amplifier Load
NB: Thévenin
equivalentNB: equivalent
resistance
vS(t) +
–
RS
+
vL
–
RLRin
+–
Rout
Avin
+
vin
–
ECEN 301 Discussion #17 – Operational Amplifiers 6
Ideal Amplifiers
The gain is dependent on the source and load (i.e. is different for different sources and loads)
Lout
LinL
RR
RAvv
vS(t) +
–
RS
+
vL
–
RLRin
+–
Rout
Avin
+
vin
–
inS
inSin
RR
Rvv
S
Lout
L
inS
inL v
RR
R
RR
RAv
NB: expression for vL depends on the source (RS) and the load (RL)
ECEN 301 Discussion #17 – Operational Amplifiers 7
Ideal Amplifiers
The gain can be made to be almost independent of the source (RS) and the load (RL)
Let Rin → ∞
Let Rout → 0
in
Lout
LinL
Av
RR
RAvv
0 R if out
vS(t) +
–
RS
+
vL
–
RLRin
+–
Rout
Avin
+
vin
– S
inS
inSin
v
RR
Rvv
: R if in
SL Avv
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 8
Op-Amps
Operational Amplifier: originally designed (late 1960’s) to perform mathematical operations (analog computer) Addition
Subtraction
Integration
differentiation
–
+
Positive power supply (usually +15V)
Negative power supply (usually –15V)
Output
Inverting Input
Noninverting Input
VS+
VS–
NB: the power supplies (VS+
and VS–) are often omitted in
drawings – they are implicit
ECEN 301 Discussion #17 – Operational Amplifiers 9
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)
–
++
v+
–
+
v–
–
+
vo
–
io
i2
i1
–vin
+
–
+
+–
RoutRin
i1
AOLvin
+
vo
–
–
vin
+
v–
v+
NB: op-amps have near-infinite input resistance (Rin) and very small output resistance (Rout)
)( vvA
vAv
OL
inOLoAOL – open-loop voltage gain
i2
ECEN 301 Discussion #17 – Operational Amplifiers 10
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)
–
++
v+
–
+
v–
–
+
vo
–
io
i2
i1
–vin
+ Ideally i1 = i2 = 0
(since Rin → ∞)
021 ii
ECEN 301 Discussion #17 – Operational Amplifiers 11
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)
What? No input current??
In reality there is a small current021 ii
ECEN 301 Discussion #17 – Operational Amplifiers 12
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
–
+ +
vo
–
i1
RF
RS
vS(t) +
–
v+
v–
iF
iS
i2
ECEN 301 Discussion #17 – Operational Amplifiers 13
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
S
SS
R
vvi
–
+ +
vo
–
i1
Feedback current: current from the output
is fed back into the input of the op-amp
RF
RS
vS(t) +
–
v+
v–
iF
iS
Node a
FS
FS
ii
iii 0
:a deNoat KCL
1
F
oF
R
vvi 01i
ECEN 301 Discussion #17 – Operational Amplifiers 14
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
–
+ +
vo
–
i1
RF
RS
vS(t) +
–
v+
v–
iF
iS
OL
o
OL
OL
OLo
A
vv
vA
vA
vvAv
)0(
)(
:Model Loop-Open From
ECEN 301 Discussion #17 – Operational Amplifiers 15
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
RF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
OLSFOLSF
oS
SOL
o
FOL
o
S
S
S
S
F
OLo
F
o
S
OLo
S
S
F
o
S
S
FS
ARRARRvv
RA
v
RA
v
R
v
R
v
R
Av
R
v
R
Av
R
v
R
vv
R
vv
ii
1
/
1
/
1
//
ECEN 301 Discussion #17 – Operational Amplifiers 16
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
OLSFOLSF
oSARRARR
vv1
/
1
/
1RF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iSNB: if AOL is very large these terms → 0
S
F
S
o
R
R
v
vCLA
:Gain Loop-Closed
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
OL
out
A
vv
:Model Loop-Open FromRF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
NB: as AOL → ∞ v– → 0
vv
AOL As
ECEN 301 Discussion #17 – Operational Amplifiers 18
Op-Amps – Closed-Loop Mode
The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal
vv
ii 021
RF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
NB: two important results for an ideal
op-amp with negative feedback
i2
ECEN 301 Discussion #17 – Operational Amplifiers 19
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
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
ECEN 301 Discussion #17 – Operational Amplifiers 20
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
)cos(15.0
)cos(015.010
10
A
3
4
CL
t
t
vR
Rv
R
R
v
v
S
S
Fo
S
F
S
oRF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
10
ACL
S
F
R
R
ECEN 301 Discussion #17 – Operational Amplifiers 21
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
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.0 0.2 0.4 0.6 0.8 1.0
time (s)
Vo
lta
ge
(V
)
vs(t)
vo(t)
ECEN 301 Discussion #17 – Operational Amplifiers 22
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
10A nomCL
RF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS
05.9
1050
9500
Amax
min
minCL
S
F
R
R
05.11
950
10500
Amin
max
maxCL
S
F
R
R
NB: nominal gain
ECEN 301 Discussion #17 – Operational Amplifiers 23
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/sRF
–
+ +
vo
–
i1
RS
vS(t) +
–
v+
v–
iF
iS%5.9
10
9.0510100
A
AA100
:Error % Max
nomCL
minCLnomCL
%5.10
10
11.0510100
A
AA100
:Error % Min
nomCL
maxCLnomCL
ECEN 301 Discussion #17 – Operational Amplifiers 24
Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
–
+ +
vo
–
RF
RS1
vS1(t)+
–v+
v– iF
i1
RS2
vS2(t)+
–i2
RSN
vSN(t) +
–iN
ECEN 301 Discussion #17 – Operational Amplifiers 25
Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
–
+ +
vo
–
RF
RS1
vS1(t)+
–v+
v– iF
i1
RS2
vS2(t)+
–i2
RSN
vSN(t) +
–iN
Node a
N , 2, 1, nR
vi
Sn
nSn
FN iiii 21
:a deNoat KCL
F
oF
R
vi
NB: v– = v+ = 0
ECEN 301 Discussion #17 – Operational Amplifiers 26
Op-Amps – Closed-Loop Mode
The Summing Amplifier: sources are summed together
independently of load and source impedances
–
+ +
vo
–
RF
RS1
vS1(t)+
–v+
v– iF
i1
RS2
vS2(t)+
–i2
RSN
vSN(t) +
–iN
Node a
N
n
sn
sn
Fo
F
oN
n sn
sn
vR
Rv
R
v
R
v
1
1
ECEN 301 Discussion #17 – Operational Amplifiers 27
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal
–
+ +
vo
–
i1
RF
R
vS(t) +
–
v+
v–
iF
RS
iS
i1
ECEN 301 Discussion #17 – Operational Amplifiers 28
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal
–
+ +
vo
–
i1
RF
R
vS(t) +
–
v+
v–
iF
RS
iS
i1
S
SS
R
vi
FS
FS
ii
iii 0
:a deNoat KCL
1
F
oF
R
vvi 01i
Node a
ECEN 301 Discussion #17 – Operational Amplifiers 29
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal
–
+ +
vo
–
i1
RF
R
vS(t) +
–
v+
v–
iF
RS
iS
i1
vvv
R
i
S
drop) voltageno rough current th no (i.e.
: 0 Since 1
S
F
S
o
S
S
F
So
SF
R
R
v
v
R
v
R
vv
ii
1
Node a
ECEN 301 Discussion #17 – Operational Amplifiers 30
Op-Amps – Closed-Loop Mode
The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal
–
+ +
vo
–
i1
RF
R
vS(t) +
–
v+
v–
iF
RS
iS
i1
Node a
S
F
S
o
R
R
v
v
1
A
:Gain Loop-Closed
CL
NB: always positive and greater than or equal to 1
ECEN 301 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
–
+ +
vo
–
i1
vS(t) +
–
v+
v–
i1
ECEN 301 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
svv
–
+ +
vo
–
i1
vS(t) +
–
v+
v–
i1
NB: an ideal op-amp with negative
feedback has the property
vv
ovv
So vv
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
Loading: changing the behaviour of one circuit by connecting another circuit to it
+
va
–
If va ≠ vb
ib is the load current
Circuit 1 Circuit 2
+
vb
–
ib
ECEN 301 Discussion #17 – Operational Amplifiers 34
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