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Introduction to Electronic Hardware
Operational AmplifiersELE00001C
Jeremy Everard
1©2015 University of York
Syllabus• The properties of an ideal operational amplifier
– infinite input impedance, zero output impedance and infinite voltage gain and
– these properties in real (non-ideal) operational amplifiers • Ideal model of an operational amplifier using:
– virtual voltage sources and – the Virtual Earth Model
• Analysis and design of:– Inverting and non-inverting amplifier configurations– Differential Amplifiers– Summing Amplifiers applicable to audio mixer desks and Digital
to Analogue convertors• Gain Bandwidth Product• General model for feedback and in particular negative
feedback and how this applies in operational amplifier circuits
• Comparators and active rectifiers2©2015 University of York
On completion of this course you are expected to be able to:• Understand the main characteristics of an ideal
op amp– Understand the key limitations
• Analyse and design fundamental op amp circuits– Use equivalent circuit models to analyse op amp
circuits• Brief introduction to the gain bandwith product• Understand the principles of feedback in relation
to op amp circuits• Appreciate the practical issues around op amp
circuits
3©2015 University of York
Timetable: 7 lectures, 2 workshops & Labs
• Lectures: Wk 6 & 7– Monday 14:00 P/L/001– Friday 14:00 P/L/001
• Lectures: Wks 8, 9 & 10– Monday: 14:00 P/L/001
• Workshops: Weeks 8 & 10– Group B, Monday: 09:00 D/L047– Group A, Thursday 09:00 D/L047
• Labs: Wks: 8 & 9 in mornings on 4th floor - D Pearce– Group A: Monday/Tuesday– Group B: Wednesday/Thursday
4©2015 University of York
Operational Amplifier
5
• High gain directly coupled building block
• Two Voltage inputs– Non-inverting (+)– Inverting (−)– Amplifier with very high
open loop voltage gain (without feedback)
– voltage gain 105 to 106 at lower frequencies
• Output– low output impedance– ≈75Ω
=©2015 University of York
Operational AmplifiersSometimes a different notation
6
Note: =
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Operational Amplifiers: key uses• Inverting Amplifier
• The output (red) is a larger copy of the input (green). The multiplying factor is called Voltage Gain
• The output is inverted with respect to the input, ie 180 degrees out of phase
• Use resistors (R1 and RF) to set the final (closed loop) gain
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Time/uSecs 50uSecs/div
250 300 350 400 450 500 550
mV
-200
-100
0
100
200
300
Guess Voltage Gain ??
Operational Amplifiers: key uses• Non Inverting Amplifier
• The output (red) is a larger copy of the input (green). The multiplying factor is called Voltage Gain
• The output is in phase with the input©2015 University of York 8
Time/mSecs 200uSecs/div
0 0.2 0.4 0.6 0.8 1 1.2
V
-1.5
-1
-0.5
0
0.5
1
1.5
2
Guess Voltage Gain ??
Look at the different resistor topologies• Inverting Amplifier
• Non inverting Amplifier
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Time/uSecs 50uSecs/div
250 300 350 400 450 500 550
mV
-200
-100
0
100
200
300
Time/mSecs 200uSecs/div
0 0.2 0.4 0.6 0.8 1 1.2
V
-1.5
-1
-0.5
0
0.5
1
1.5
2
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Operational Amplifiers: key uses
• Differential Amplifier
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Operational Amplifiers:
• Summing Amp– Mixer desk
• D to A
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Inverting amp with extra resistors on the input
Switch in resistors ofdifferent values for
different bits
Operational Amplifiers:
• Active Rectifier
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Operational Amplifiers(not covered in this course)
• Integrator
• Differentiator
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Operational Amplifiers• Course Materials available from web link at module information
– Set of lecture slides– Tutorials and indicative answers
• Recommended texts:• Fundamentals of Electric Circuits (chapter 5 on Operational Amplifiers)
– By Charles K Alexander and Mathew N.O Sadiku, – Published by McGraw-Hill– Fourth Edition, – ISBN 978–0–07–352955–4
• Additional Texts– Stanley, W.D., Operational Amplifiers with Linear Integrated Circuits (3rd ed)
(Library catalogue number U 7.534 STA)– Dostal, J., Operational Amplfiers (2nd ed), Butterworth-Heinemann, 1993
(Library catalogue number U7.534 DOS)– Franco, S., Design with Operational Amplifiers and Analog Integrated Circuits
(3rd ed), McGraw-Hill, 2002 (Library catalogue number U 7.534 FRA)– Hambley, Allan R., Electrical Engineering Principles and Applications, Sixth
edition, published by Pearson
• And many, many more in the library
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Op Amps - History• 1930’s:origin as differential amplifiers
– (long tailed pair) using pairs of valves • audio amplification, filtering, mixing...
• 1940’s:op amps used in analogue computing– capable of performing mathematical operations:
• origin of name• 1950‘s: transistor op amps using discrete
transistors• 1960s: IC opamps
– 1964, μA702 - the first mass produced IC op amp– 1965, μA709
• Improved gain from a ~3000 up to up to 25,000 to 70,000
• Today: Very important analogue ICs– take a look at RS and Farnell catalogues!
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Fairchild μA702 (1964)• First mass produced IC
– Nominal resistor values– Equivalent circuit from
Fairchild data sheet
Pin numbers for metal can only
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Fairchild μA709, year after μA702 (1965)
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• Equivalent circuit from data sheet
• Higher gains– Up to 70,000
• Complementary output stage PNP & NPN
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Same structure as previous circuitbut drawn slightly differently
Input stage and block diagram
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Difference or differential Amplifier
Amplifies the differenceBetween the I/P voltages
Additionalgain block
Buffer andOutput stage
• Interesting to note that:• In IC design, resistors are rather large• so use transistors as active loads instead !!!!• In fact they have many other advantages as
well
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Low cost LM324 Quad Op Amp
AlarmSensor
Differential Amplifer
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Current Mirrors& Active Loads
O/Pstage
Buffer/emitterfollower &Additional gain
Diff Amp
CurrentMirrors
Diff Amp Active Load
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Look at Datasheets
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Circuit I developed – can you guess what it is?
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Simulation is a very useful tool for checking designs
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Simulation: use Simetrix. This can analyse circuits under both small signal and large signal operation. It has a large number of accurate models for devices.
This is a very useful tool for electronics design engineers - use to check design before building it
Described in Dave Pearce’sLabs under module information for second year course on semiconductor Devices.
A number of videos can be found at:
http://www.elec.york.ac.uk/internal_web/meng/yr2/labs/SemiconductorDevices/Simetrix/Simetrix.html
15V2
X1-out
100k
R3
1k
R2
0 AC 1 0 Sine(0 400m 10k 0 0)V1
1KR4X1
uA741
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Definition: A very high gain, direct coupled linear voltage difference amplifier that uses external feedback components to define circuit operation.
Perhaps the most important linear (analogue) integrating circuit
What is an operational amplifier
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Inverting input
Non Inverting input
+VCC
−VCC
The ideal linear voltage amplifier
O/P voltage proportional to I/P voltage
Constant of proportionality is
constant (according to application), stable and independent of time/frequency
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The op amp: ideal linear voltage difference amplifierOpen loop characteristics (limited by power supply)
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+VCC
−VCC
Max I/P beforesaturation
The ideal linear voltage amplifier: VCVSVoltage Controlled Voltage Source
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The ideal operational amplifierIdeal operational amplifier: Ideal linear differential voltage amplifier
1. input impedance is infinite2. output impedance is zero3. open loop gain is infinite
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Effect of finite input impedance (potential divider rule)
The ideal linear voltage amplifier: i/p impedance
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Effect of non-zero output impedance (potential divider rule)
The ideal linear voltage amplifier: o/p impedance
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Effect of finite input impedance and non-zero output impedance
The ideal linear voltage amplifier: loading
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The ideal operational amplifier
Infinite input impedanceNo current into or out of either input terminal
Infinite open loop gainNegative Feedback forces the voltages at the input terminals to become identical!!!Or: Differential voltage to be zero
;
Zero output impedanceOutput voltage is independent of the load resistance
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The ideal/non ideal operational amplifierMaximum input voltage before saturation
Infinite open loop gainThe voltages at the input terminals are identicalOr: Differential voltage is zero
33
In reality, If A =
= = 1510 = 150Maximum peak input voltage beforesaturation at low frequencies if the supply voltage is + VCC = + 15V:
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Analyse the Inverting Amplifier
• Use the virtual earth model
• Use the voltage controlled voltage source model which is more flexible but less simple
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The inverting voltage amplifierVirtual earth model
Single op amp circuit that provides voltage amplification with a gain controlled by feedback resistor network
Inverting: 180o phase shift between input and output signalsi.e. output inverted with respect to input
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The current intoR1 and RF are the
Same!!
Inverting amplifier: Virtual earth modelIdeal operational amplifier:1. input impedance is infinite: No current flows into inverting input2. open loop gain is infinite:
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Inverting amplifier: Virtual earth model
(virtual earth means input voltage dropped across R1)
(current into op amp is zero)
(virtual earth means output voltage is voltage across Rf)
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Input impedance of the inverting amplifierInverting amplifier: Virtual earth model
N.B. R1 is the input impedance of the inverting amplifier circuit NOT the input impedance of the op amp which is infinite 38©2015 University of York
Virtual Earth – in words• The I/P impedance of the op amp is infinite in the
ideal case so no current flows into the op amp.• All the current flowing in R1 flows into RF
• The gain of the op amp is infinite in the ideal case.
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Virtual Earth (in words)• The output voltage of the amplifier adjusts
itself to force the input voltage to zero (virtual earth) via the feedback network. – If you put a perturbation (of voltage) on the
output (in either direction) away from where it should be, the feedback at the input will try and push it back to the correct position.
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You can check this bylooking at the model.
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Virtual Earth (in words)• As the current into R1 is the same as the
current into Rf (and Ve is zero) then the voltage gain is -Rf/R1.
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Test question 1.a & b on the inverting voltage amplifier
Example(a) What is closed loop gain?(b) What is the output voltage when
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(c) Determine the op amp output current with a 2kΩ load and
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Test question 1.c on the inverting voltage amplifier
Example(c) Determine the op amp output current with a 2kΩ load and
Remember the current through R1
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R1
Operational amplifiers: Summary 1Open loop characteristics
Infinite input impedanceNo current into op amp
Zero output impedanceOutput voltage independent of load
Infinite open loop gainDifferential voltage is zero
Ideal operational amplifier: assumptions
44©2015 University of York
Operational amplifiers: Summary 2Inverting amplifier: virtual earth model
Output 180o out of phase with input (Inverting amplifier)
Closed loop gain: determined by ratio of resistances only45©2015 University of York
Quiz: The inverting amplifiera) Design an inverting amplifier with closed loop gain of -12 and an input impedance of 1kΩ.
b) What is the maximum input voltage allowed for linear operation? (assume saturation voltages of ±13V)
c) For an input voltage of 500mV, calculate the current through a 2kΩ load resistor?
d) what is the actual circuit gain when connected to an input source (e.g. microphone) with an impedance of 50Ω
46©2015 University of York
And now...The VCVS model for circuit analysisClosed loop gain for inverting amplifier using ideal VCVS model
The non-inverting voltage amplifierClosed loop gain and input impedanceSpecial case: the voltage follower
Closed loop op amp circuits: Design considerationsGood practice in the design of operational amplifier circuits
The open loop differential amplifier: CMRR47©2015 University of York
The inverting voltage amplifier: VCVS model
48One method is to use the superposition principle to find νo as a function of νi . Remember it is a linear system ©2015 University of York
Superposition reminderApplies to LINEAR Circuits1. Set all sources, except
one, to zero2. Solve the new circuit for
unknown currents and voltages
3. Repeat 1 and 2 until each source has been allowed to drive the circuit on its own
4. The overall voltages and currents are the sum of voltages and currents due to each source
• Short out νi and work out ν d in terms of νo
• Short out νo and work out ν d in terms of νi
• Add the values of ν dtogether
49©2015 University of York
as
The inverting voltage amplifier: VCVS modelUsing superposition
50
then - 1 =
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Multiply both sides by −A and place vo components on LHS and vi on RHS
The inverting voltage amplifier: VCVS model
Advantage of VCVS over virtual earth model
Amenable to analysis of non-ideal op amp behaviour
e.g. finite input impedance/ non-zero output impedance
finite open loop gain
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An alternative method
Calculate the effect of finite gain on the closed loop gain wherethe I/P impedance is infinite
R1
R2
A.VeVout
Vin
Ve
_
+
i1
i2
dout AVV −=
Assuming no input current
i i1 2 0− =
01
=−+−
f
doutdin
RVV
RVV
νd
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i2
+=+
fd
F
outin
RRV
RV
RV 11
11
As AVVd out−=
+−=+
f
out
f
outin
RRAV
RV
RV 11
11
11
1111RV
RRARV in
ffout −=
++
11
111RV
RR
ARV inf
f
out −=
++
++
−=111
1
1
1
RR
ARR
VV
f
f
in
out
For R2 >> R1the error is
approximately
Closed loop gainOp Amp open loop gain
Ideal
Ratio =
Useful to calculate gain in terms of the ideal equation and an error term
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Remembering Binomial Series Expansion
......11
1 5432 xxxxxx
−+−+−=+
Check accuracy of this for x = 0.1
For x2 < 1
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Op amp: current controlled voltage source
Current controlled voltage source or
Transimpedance amplifier wheretransimpedance (or transresistance) is
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This type of amplifier is often usedWith photodiodes
for optical receivers
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Photodiode & Amplifier
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Now apply similar technique to virtual earth model to the
Non-inverting amplifier
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Amplifier where output voltage is in phase with input voltageNon-inverting voltage amplifier
so
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Similar technique to virtual earth model
Example
Example(a) What is closed loop gain?(b) What is the output voltage when
(c) Determine the op amp output current when 59©2015 University of York
Example(c) Determine the op amp output current when
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Special case of non-inverting amplifierVoltage follower
Closed loop gain of non-inverting amplifier
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Design considerationsQuestion: Design an inverting amplifier with a closed loop gain -10.
Design guidelines:
1. Resistor values in range 1kΩ to 100kΩ used typicallyLow R: high current drain and loading of op ampHigh R: input current no longer assumed to be zero
increase noise
Also resistors have tolerances:Example with 5% tolerance resistorsand Rf = 100kΩ; R1 = 10kΩ
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Design considerations
2. Input impedanceinverting amplifier: ensure sufficient input impedance to minimise loading of sourcenon-inverting amplifier: input impedance is infinite
5. Frequency response
3. Sufficient dynamic range for desired output voltage rangei.e. Avoid saturation: Many op amps only achieve ~70% of supply voltage
4. Keep closed loop gain much smaller than open loop gain‘ideal’ op amp assumptions breaks down as ACL approaches op amp open loop gain
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Frequency response• It has been assumed, so far, that the gain of
the amplifier is constant with increasing frequency– In real life this is not the case
• Many basic components and circuits such as transistors and operational amplifiers have a frequency response which rolls off at higher frequencies.
• This can often be modelled using a simple Resistor Capacitor network (RC network)
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RC lowpass network
• An RC network is now shown and the frequency response calculated and simulated.
• The impedance of a capacitor can be shown to be:
• Where f
• The voltage transfer function (using potential divider rule) is therefore:
66
= =
Probe1-NODE
AC 1 0 Sine(0 400m 10k 0 0)V2
1K
R1
C115.915u
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Frequency Response of RCnetwork with 10Hz ‘cutoff’
67Frequency / Hertz
10m 100m 1 10 100 1k 10k 100k 1M
Pro
be1-
NO
DE /
V
20u
40u
100u
200u
400u
1m2m
4m
10m
20m
40m
100m
200m400m
1
-291.303m
999.9995m708.6967m
9.945389410.00000m 9.9553894
AREF
Probe1-NODE
AC 1 0 Sine(0 400m 10k 0 0)V2
1K
R1
C115.915u
©2015 University of York 68Time/mSecs 200uSecs/div
8.8 9 9.2 9.4 9.6 9.8 10
IPROBE1 / u
A
Y2
-400
-300
-200
-100
-0
100
200
300
Probe
1-NODE / mV
Y1
-1
0
1
2
3
4
5
6
IPROBE1
C115.915u
1K
R1
AC 1 0 Sine(0 400m 1k 0 0)V2
Probe1-NODE
VoltageCurrentNote 90 phase shift
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Time Domain Response
Op Amp Frequency Response
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Frequency / Hertz
10m 100m 1 10 100 1k 10k 100k 1M
X1-
out /
V
200m400m
124
102040
100200400
1k2k4k
10k20k40k
100k200k400k
1M15V2
X1-out
100k
R3
1k
R2
0 AC 1 0 Sine(0 400m 10k 0 0)V1
1KR4X1
uA741
15V3
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Op Amp Frequency Response
• Gain bandwidth product. It can be seen that: G×B is a constant
70
Frequency / Hertz
10m 100m 1 10 100 1k 10k 100k 1M
X1-
out /
V
200m400m
124
102040
100200400
1k2k4k
10k20k40k
100k200k400k
1M
15V2
X1-out
100k
R3
1k
R2
0 AC 1 0 Sine(0 400m 10k 0 0)V1
1KR4X1
uA741
15V3
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Op Amp Frequency Response
Frequency / Hertz
10m 100m 1 10 100 1k 10k 100k 1M
X1-
out /
V
200m400m
124
102040
100200400
1k2k4k
10k20k40k
100k200k400k
1M
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Simulator
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Closed loop differential amplifierDifferential amplifier: amplifies the difference between the voltages applied to two inputs with controlled weighting
Electrocardiography (ECG)Instrumentation Amplifier
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Closed loop differential amplifier
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Same as non inverting amplifier
Use superposition
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Using superposition add the terms for vo together
Closed loop differential amplifier
Special case:
N.B Input impedance of inputs differ
Instrumentation amplifier: typically includes voltage follower/ buffer on both inputs 74©2015 University of York
Common mode rejection ratioCommon mode rejection ratio (CMRR): Important measure that quantifies the ability of a differential amplifier to amplify the difference between inputs and reject common mode signals.
N.B. in ideal amplifier75©2015 University of York
Closed loop differential amplifier: CMRR
N.B. Resistor tolerances!
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Feedback
Feedback: a process for controlling the state of a system e.g. gain of an amplifier, by transferring a portion of the output signal back to the input
1927 Harold S. Black
77©2015 University of York
Fluid mechanics (toilets!)
Feedback
Mechanical EngineeringFly ball governor Biology
Homoeostasis
ANDControl EngineeringChemistryEconomicsClimate...
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FeedbackNegative feedback: Temperature regulation
Negative feedback: Voltage follower Negative feedback: non-inverting amp
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Two different examples
With gainHow much?
Fundamental feedbackrelationship
Feedback: Basic definitions
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Feedback: Basic definitions
1. Closed loop gain is open loop gain divided by
2. Without feedback (i.e. β=0)
3. if then i.e. independent of A
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Feedback: non-inverting amplifier
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Operational amplifiers with non-infinite gainFor ideal amplifier
What is the closed loop gain of the amplifier if A= 1000
(ideal case)
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Operational amplifiers with non-infinite gain
For ideal amplifier
In reality open loop gain is finite
10 5 1 0.99999 0.001
10 5 100 9.999 0.1
10 5 1,000 990.1 1
10 5 10,000 9091 9.0984©2015 University of York
Feedback: positive and negativeNegative feedback: feedback signal subtracted from input signal
Positive feedback: feedback signal added to input signalNegative feedback Positive feedback
85Eol_5_18_11_2013 ©2015 University of York
For positive feedbackVf is added to vi.
In an oscillator they add in phase andAβ tends to −1 so the gain is initially
infinite. The oscillation builds upuntil it hits the power supply !!!
Positive feedback:tends to cause system instability in amplifierscan be used to create oscillators
Negative feedback:1. reduce gain to a specified level below the open loop gain;2. reduce distortion;3. make the input impedance more ideal (increase);4. make the output impedance more ideal (decrease);5. improve the frequency response.
Feedback in operational amplifiers
86©2015 University of York
Review: feedback
Fundamental feedbackrelationship
Negative feedback: feedback signal subtracted from input signal
Positive feedback: feedback signal added to input signal87Eol5_wk9_24_11_2014 ©2015 University of York
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