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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
Lecture 11 Overview
• Amplifier impedance
• The operational amplifier
• Ideal op-amp
• Negative feedback
• Applications– Amplifiers– Summing/ subtracting circuits
• Why do we care about the input and output impedance?
• Simplest "black box" amplifier model:
Impedances
RIN
ROUT
VIN AVINVOUT
• The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A
• This voltage generator, in series with the output resistance ROUT, is connected to the output port.
• A should be a constant (i.e. gain is linear)
• Attach an input - a source voltage VS plus source impedance RS
Impedances
RIN
ROUT
VINAVIN
VOUT
• Note the voltage divider RS + RIN.
• VIN=VS(RIN/(RIN+RS)
• We want VIN = VS regardless of source impedance
• So want RIN to be large.
• The ideal amplifier has an infinite input impedance
VS
RS
• Attach a load - an output circuit with a resistance RL
Impedances
• Note the voltage divider ROUT + RL.
• VOUT=AVIN(RL/(RL+ROUT))
• Want VOUT=AVIN regardless of load
• We want ROUT to be small.
• The ideal amplifier has zero output impedance
RIN
ROUT
VINAVIN VOUTVS
RS
RL
Operational Amplifier
• Integrated circuit containing ~20 transistors, multiple amplifier stages
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.
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.
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
-
+
voutRL
RS
So the equivalent circuit of an ideal op-amp looks like this:
Many Applications e.g.
• Amplifiers• Adders and subtractors• Integrators and differentiators• Clock generators• Active Filters• Digital-to-analog converters
ApplicationsOriginally developed for use in analog computers:
http://www.youtube.com/watch?v=PBILL8UypHA
ApplicationsOriginally developed for use in analog computers:
http://www.youtube.com/watch?v=PBILL8UypHA
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-<VS/A=12/105 so v+≈v-
• In the ideal case, when an op-amp is functioning properly in the active region, the voltage difference between the inverting and non-inverting inputs≈0
Noninverting Amplifier
21
2
)(
RR
RvvAv
vvAv
OINO
O
INO AvRR
ARv
21
21
21
21 RRARAv
v INO
When A is very large:
Take A=106, R1=9R, R2=R
10101
101
10
9101
10
6
6
6
6
INO
INO
INO
vv
vv
RRR
vv
2
21
21
2
21
21
R
RRvv
RRR
A
Avv
RRARAv
v
INO
INO
INO
• Gain now determined only by resistance ratio• Doesn’t depend on A, (or temperature, frequency, variations in fabrication)
>>1
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
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.)
More insight
• Under negative feedback:
vv
A
vRRR
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-amp2) v+ ≈ v-
More insight
• Allows us to label almost every point in circuit terms of vIN!
1) No current flows into the op-amp2) v+ ≈ v-
Op amp circuit 1: Voltage follower
• So vO=vIN
•or, using equations
2
21
R
RRvv INO
2
1 0
R
R
• What's the gain of this circuit?
Op amp circuit 1: Voltage follower
• So vO=vIN
•or, using equations
2
21
R
RRvv INO
2
1 0
R
R
• What's the application of this circuit?•Buffer
voltage gain = 1input 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
Op amp circuit 2: Inverting Amplifier
SS
Fout
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:
Op amp circuit 3: Summing Amplifier
SNSN
FS
S
FS
S
Fout
F
out
SN
SN
S
S
S
S
FN
vR
Rv
R
Rv
R
Rv
R
v
R
v
R
v
R
v
iiii
.....
.....
.....
22
11
2
2
1
1
21
• Same as previous, but add more voltage sources
)...( 21 SNSSS
Fout vvv
R
Rv
SSNSS RRRR ... If 21
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)
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
and
0 sinceF
out
S R
vv
R
v
0
S
F
S
out
SS
Fout
S
Fout
R
R
v
v
vR
Rv
vR
Rv
1Gain
1
1
Op amp circuit 5: Differential Amplifier (subtractor)
021 ii
)( 121
2
221
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-mode input change• if they change independently, this is a normal-mode change • A good differential amp has a high common-mode rejection ratio (CMMR)
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 instrumentation amplifier - 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