11 op amps
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Announcements
Assignment 3 due now, or by tomorrow
5pm in my mailbox
Assignment 4 posted, due next week
Thursday in class, or Friday 5pm in my
mailbox
mid-term: Thursday, October 27th
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Lecture 11 Overview
Amplifier impedance
The operational amplifier
Ideal op-amp Negative feedback
Applications
Amplifiers Summing/ subtracting circuits
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Attach an input - a source voltage VS plus source impedance RS
Impedances
RIN
ROUT
VINAV
IN
VOUT
Note the voltage divider RS + RIN.
VIN
=VS(R
IN/(R
IN+R
S)
We want VIN = VS regardless of source impedance
So want RIN to be large.
The ideal amplifier has an infinite input impedance
VS
RS
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Attach a load - an output circuit with a resistance RL
Impedances
Note the voltage divider ROUT + RL.
VOUT
=AVIN
(RL/(R
L+R
OUT))
Want VOUT=AVIN regardless of load
We want ROUT to be small.
The ideal amplifier has zero output impedance
RIN
ROUT
VINAV
IN
VOUTVS
RS
RL
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Operational Amplifier
An op amp is a high voltage gain, DC amplifier with high input
impedance, low output impedance, and differential inputs. Positive input at the non-inverting input produces positive output,
positive input at the inverting input produces negative output.
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Operational Amplifier
An op amp is a high voltage gain, DC amplifier with high input
impedance, low output impedance, and differential inputs. Positive input at the non-inverting input produces positive output,
positive input at the inverting input produces negative output.
Can model any amplifier as a "black-box" with a parallel input
impedance Rin, and a voltage source with gain Av in series with an
output impedance Rout.
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Ideal op-amp Place a source and a load on the model
Infinite internal resistance Rin(so vin=vs). Zero output resistance Rout(so vout=Avvin).
"A" very large
iin=0; no current flow into op-amp
-
+
vout
RL
RS
So the equivalent circuit of an
ideal op-amp looks like this:
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Many Applications e.g.
Amplifiers
Adders and subtractors
Integrators and differentiators
Clock generators
Active Filters
Digital-to-analog converters
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ApplicationsOriginally developed for use in analog computers:
http://www.youtube.com/watch?v=PBILL8UypHA
http://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHA -
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ApplicationsOriginally developed for use in analog computers:
http://www.youtube.com/watch?v=PBILL8UypHA
http://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHA -
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Using op-amps
Power the op-amp and apply a voltage
Works as an amplifier, but:
No flexibility (A~105-6
) Exact gain is unreliable (depends on chip, frequency and temp)
Saturates at very low input voltages (Max vout=power supply voltage)
To operate as an amp, v+-v-
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Noninverting Amplifier
21
2
)(
RR
RvvAv
vvAv
OINO
O
INOAv
RR
ARv
21
21
21
21RR
ARAvv IN
O
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When A is very large:
Take A=106, R1=9R, R2=R
10
10
1101
10
9101
10
6
6
6
6
INO
IN
O
IN
O
vv
vv
RRR
vv
2
21
21
2
21
21
R
RR
vv
RR
RA
Avv
RR
AR
Avv
INO
INO
IN
O
Gain now determined only by resistance ratio
Doesnt depend on A, (or temperature,
frequency, variations in fabrication)
>>1
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Negative feedback:
How did we get to stable operation in the linear
amplification region??? Feed a portion of the output signal back into the input
(feeding it back into the inverting input = negative feedback)
This cancels most of the input
Maintains (very) small differential signal at input
Reduces the gain, but if the open loop gain is ~, who
cares?
Good discussion of negative feedback here:
http://www.allaboutcircuits.com/vol_3/chpt_8/4.html
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Why use Negative feedback?:
Helps to overcome distortion and non-linearity
Improves the frequency response
Makes properties predictable - independent of
temperature, manufacturing differences or other
properties of the opamp
Circuit properties only depend upon the
external feedback network and so can be easily
controlled
Simplifies circuit design - can concentrate on
circuit function (as opposed to details of
operating points, biasing etc.)
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More insight
Under negative feedback:
vv
A
vR
RR
A
vvv
IN
O 01
21
We also know
i+ 0
i- 0 Helpful for analysis (under negative feedback)
Two "Golden Rules"
1) No current flows into the op-amp
2) v+ v-
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More insight
Allows us to label almost every point in circuit terms of vIN!
1) No current flows into the op-amp
2) v+ v-
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Op amp circuit 1: Voltage follower
So vO=vIN
or, using equations
2
21
R
RRvvINO
2
10
R
R
What's the gain of this circuit?
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Op amp circuit 1: Voltage follower
So vO=vIN
or, using equations
2
21
R
RRvvINO
2
10
R
R
What's the application of this circuit?
Buffer
voltage gain = 1
input impedance=
output impedance=0
Useful interface between different circuits:
Has minimum effect on previous and next
circuit in signal chain
RIN
ROUT
VINAVIN VOUTVS
RS
RL
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Op amp circuit 2: Inverting Amplifier
S
S
F
out
F
out
S
S
F
out
S
S
FS
inFS
vR
Rv
R
v
R
v
R
vv
R
vv
ii
iii
00
0
Signal and feedback resistor,
connected to inverting (-) input.
v+=v- connected to ground
S
F
S
out
R
R
v
vGain
0 vvv+ grounded, so:
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Op amp circuit 3: Summing Amplifier
SN
SN
F
S
S
F
S
S
F
out
F
out
SN
SN
S
S
S
S
FN
vR
Rv
R
Rv
R
Rv
R
v
R
v
R
v
R
v
iiii
.....
.....
.....
2
2
1
1
2
2
1
1
21
Same as previous, but add more
voltage sources
)...(21 SNSS
S
F
outvvv
R
Rv
SSNSSRRRR
...If21
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Summing Amplifier Applications
Applications - audio mixer
Adds signals from a number of waveforms
http://wiredworld.tripod.com/tronics/mixer.html
Can use unequal resistors to get a weighted sum
For example - could make a 4 bit binary - decimal converter
4 inputs, each of which is +1V or zero
Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)
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Op amp circuit 4: Another non-inverting amplifier
Feedback resistor still to inverting input,
but no voltage source on inverting input
(note change of current flow) Input voltage to non-inverting input
vv FS ii
S
in
vvv
i
and0since F
out
S R
vv
R
v
0
S
F
S
out
S
S
F
out
S
F
out
R
R
v
v
vR
Rv
vR
Rv
1Gain
1
1
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Op amp circuit 5: Differential Amplifier (subtractor)
021 ii
)(12
1
2
2
21
2
21
1
vvR
Rv
vvRR
Rv
vv
R
vv
R
vv
out
out
Useful terms:
if both inputs change together, this is a common-modeinput change
if they change independently, this is a normal-modechange
A good differential amp has a high common-mode rejection ratio (CMMR)
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Differential Amplifier applications Very useful if you have two inputs corrupted with the same noise
Subtract one from the other to remove noise, remainder is signal
Many Applications : e.g. an electrocardiagram measures the
potential difference between two points on the body
The AD624AD is an instrumentationamplifier - this is a high gain, dc
coupled differential amplifier with a high input impedance and high CMRR
(the chip actually contains a few opamps)
http://www.picotech.com/applications/ecg.html
http://www.picotech.com/applications/graphics/ecg_circuit_big.gif
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