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EMT 212
Analog Electronic IIChapter 1- Operational Amplifier
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1.0 Operational Amplifier
1.1 Introduction1.2 Ideal Op-Amp
1.3 Op-amp input modes
1.4 Op-amp Parameters
1.5 Operation
Single-mode
Differential-mode
Common-mode operation
1.6 Op-Amps basics
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1.1 Introduction
Uses of Op-Amp To provide voltage amplitude changes
(amplitude and polarity)
Comparators
Oscillators
Filter circuits
Instrumentation circuits
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1.1 Introduction
Definition: The operational amplifier or op-amp is an
integrated circuit that amplifies the differencebetween two input voltages and produces a
single output. A typical op-amp is powered by two dc voltages
and has an inverting(-) and a non-inverting input
(+) and an output. Op-amps were used to model the basic
mathematical operations; addition, subtraction,integration, differentiation, etc, in electronic
analog computers.
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1.1 Introduction
Stages of an Op-ampINPUTSTAGE OUTPUT
STAGE
GAINSTAGE
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1.1 Introduction
Two Power Supply Inverting input
Non-inverting input
One Output Terminal
Two Input Terminal
+V : Positive PS
-V : Negative PS
Op-amp schematicsymbol
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1.2 Ideal Op-Amp
Practical Op-Amp
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1.2 Ideal Op-Amp
Ideal Op-Amp
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1.2 Ideal Op-Amp
Infinite input impedance
Zero output impedance Infinite open-loop gain
Infinite bandwidth
Zero noise contribution
Zero DC output offset Both differential inputs stick
together
Ideal Op-AmpPractical Op-Amp
input impedance 500k-2M
output impedance 20-100 open-loop gain (20k to 200k)
Bandwidth limited (a few kHz)
noise contribution
Non-zero DC output offset
Properties
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1.2 Ideal Op-Amp
Infinite Input Impedance Input impedance is measured across the input
terminals
It is the Thevenin resistance of the internalconnection between the two input terminals.
Input impedance is the ratio of input voltage toinput current
in
in
in
I
VZ
Iin
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1.2 Ideal Op-Amp
Infinite Input Impedance When Zi is infinite, the input current is zero.
the op amp will neither supply current to acircuit nor will it accept current from any
external circuit.
In real, the resistance is 500k to 2M
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1.2 Ideal Op-Amp
Zero Output Impedance Looking back into the output terminal, we see
voltage sourcewith an internal resistance
Iin
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1.2 Ideal Op-Amp
Zero Output Impedance The internal resistance of the op-amp is op-amp
output impedance, Zout.
This internal resistance is in series with the load,
reducing the output voltage available to the load Real op-amps have output impedance in the range
20-100 .
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1.2 Ideal Op-Amp
Infinite Open-Loop Gain
Open-Loop Gain, A is the gain of the op-amp without
feedback In the ideal op-amp, A is infinite
In real op-amp is (20k to 200k)
invout VAV
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1.2 Ideal Op-Amp
Infinite Bandwidth The ideal op-amp will amplify all signals from DC to
the highest AC frequencies
In real op-amps, the bandwidth is rather limited
This limitation is specified by the Gain-Bandwidthproduct, which is equal to the frequency where theamplifier gain becomes unity
Some op-amps, such as 741 family, have very limited
bandwidth up to a few kHz
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1.2 Ideal Op-Amp
Zero Noise Contribution in an ideal op amp, all noise voltages produced are
external to the op amp. Thus any noise in the outputsignal must have been in the input signal as well
the ideal op amp contributes nothing extra to theoutput noise
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1.2 Ideal Op-Amp
Zero Output Offset The output offset voltage of any amplifier is the
output voltage that exists when it should be zero
The voltage amplifier sees zero input voltage when
both inputs are grounded. This connection shouldproduce a zero output voltage
If the output is not zero then there is said to be anoutput voltage present
In the ideal op amp this offset voltage is zero volts,but in practical op amps the output offset voltage isnonzero
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1.2 Ideal Op-Amp
Both Differential Inputs Stick Together this means that a voltage applied to one inverting
inputs also appears at the other non-inverting inputs
If we apply a voltage to the inverting input and then
connect a voltmeter between the non-inverting inputand the power supply common, then the voltmeterwill read the same potential on non-inverting as onthe inverting input
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1.3 Op-Amp input Modes
Single-Ended input mode input signal is connected to one input and the other
input is grounded.
1. Inverting () terminal is grounded and input
signal is applied to the non-inverting (+)terminal
In this configuration, the resultant output signal is inphase with the input signal
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1.3 Op-Amp input Modes
2. The non-inverting (+) terminal is grounded andinput signal is applied to the inverting ()terminal
In this configuration, the resultant output signal is in
anti-phase with the input signal
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1.3 Op-Amp input Modes
Differential mode input two out-of-phase signals are applied with the
difference of the two amplified and produced at theoutput
21 inind
ddout
VVV
VAV
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1.3 Op-Amp input Modes
Common mode input two signals of same phase, frequency, and amplitude
are applied to the inputs which results in no output(signals cancel).
Practically, a small output signal will result. This iscalled common-mode rejection. This type of modeis used for removal of unwanted noise signals
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1.4 Op-Amp Parameters
Common-Mode Rejection Ratio (CMRR) The ability of amplifier to reject the common-mode
signals.
Ratio of open-loop gain to common-mode gain.
The higher the CMRR, the better
open-loop gain is high and common-mode gain is low.
cm
ol
A
ACMRR
dBlog20
cm
ol
A
ACMRR
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1.4 Op-Amp Parameters
ExampleA certain op-amp has an open-loop differentialvoltage gain of 100, 000 and a common-modegain of 0.2.
Determine the CMRR and express it in decibels.
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1.4 Op-Amp Parameters
Common-Mode Input Voltage The range of input voltages which, when
applied to both inputs, will not cause clipping orother output distortion.
Input Offset Voltage
The differential dc voltage required between
the inputs to force the output to zero volts. Range between 2 mV.
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1.4 Op-Amp Parameters
Input Bias Current The dc current required by the inputs of the amplifier
to properly operate the first stage.
Is the average of both input currents.
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1.4 Op-Amp Parameters
Input Impedance Is the total resistance between the inverting and
non-inverting inputs.
1. Differential input impedance is measured by the
changes of differential input voltage over changes ofbias current:
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1.4 Op-Amp Parameters
2. Common-mode input impedance is measured bythe changes of common-mode input voltage overchanges of bias current
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1.4 Op-Amp Parameters
Input Offset Current The difference in the input bias currents:
21 IIIos
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1.4 Op-Amp Parameters
Input Offset Current The difference in the input bias currents
offset voltage:
inininos RIIRIRIV 2121
inosos RIV
inosverrorout RIAV )(
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1.4 Op-Amp Parameters
Output Impedance The resistance viewed from the output terminal of the
op-amp.
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1.4 Op-Amp Parameters
Slew Rate The maximum rate of change of the output voltage in
response to a step input voltage.
Test circuit
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1.4 Op-Amp Parameters
Slew Rate
t
VSlewRate out
)( maxmax VVVout
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1.4 Op-Amp Parameters
Example:
Determine the slew rate:
t
VSlewRate out
sVs
VVSlewRate
/181
)9(9
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1.4 Op-Amp Parameters
Example:When a pulse is applied to an op-amp, the outputvoltage goes from -8 V to +7 V in 0.75 s.
What is the slew rate?
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1.5 Operation - Differential Amplifier Circuit
Basic differential amplifier circuit
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1.5 Operation
If an input signal isapplied to either inputwith the other input isconnected to ground,the operation isreferred to as single-ended.
The input signal is applied to input 1
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1.5 Operation
If an input signal isapplied to either inputwith the other input isconnected to ground,the operation is referredto as single-ended.
The input signal is applied to input 2
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1.5 Operation
If two opposite-polarity input signals are applied, theoperation is referred to as double-ended:
Vi1 and Vi2 are
in oppositepolarity
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1.5 Operation
If the same input isapplied to both inputs,the operation is calledcommon-mode.
Viis sometimes
known as Vcm
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1.5 Operation - Differential Amplifier Circuit
The differential amplifier
is a circuit that has twoseparate inputs andproduces two separateoutputs where theemitters are connectedtogether.
It amplifies the differencevoltage between the twoinput (Vdiff).
There are threeoperations can be done ina differential amplifiercircuit; dc bias, acoperationand common
mode operation.
Figure: The basic differential amplifier.
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1.5 Operation - Differential Amplifier Circuit
DC bias of differentialamplifier circuit.
DC Analysis:
0 EEEEBE VRIV
E
BEEEE
R
VVI
221
Ecc
III
cE
cccccccc RI
VRIVVV221
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1.5 Operation - Differential Amplifier Circuit
Example
Calculate the dc voltagesand currents:
Solution
mA5.2k3.3
V7.0V9
E
BEEE
E
R
VVI
mA25.1
2
m5.2
221
EccI
II
ccccc RIVV
V1.4
)k9.3)(m25.1(9
VVc
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1.5 Operation - Differential Amplifier Circuit
AC Analysis:
For ac analysis, VCCand VEEmay beconsidered as ground.
AC connection of differentialamplifier
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1.5 Operation - Differential Amplifier Circuit
AC Analysis
AC equivalent of differential amplifiercircuit
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1.5 Operation - Differential Amplifier Circuit
AC Analysis
Single-Ended ACVoltage Gain
Single-ended ac
voltage gain iscalculated byconnecting one ofvoltage sources to oneinput and the otherconnected to ground.
1
1
1
i
o
v
V
VA
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1.5 Operation - Differential Amplifier Circuit
AC Analysis Single-Ended AC Voltage Gain
AC equivalentcircuit
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1.5 Operation - Differential Amplifier Circuit
AC Analysis
Single-Ended ACVoltage Gain
i
i
bcr
VII
2
1
01
ibibi rIrIVbbb III 21
iii rrr 21
21
i
i
br
VI
2
1
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1.5 Operation - Differential Amplifier Circuit
AC Analysis
Single-Ended ACVoltage Gain
where
1
1
2
2
1
i
e
c
c
i
i
cco
Vr
R
Rr
V
RIV
e
c
i
ov
r
R
V
VA
21
1 E
eI
mVr
26
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1.5 Operation - Differential Amplifier Circuit
Example:
Calculate the single-ended output voltageVo1.
Given that;
75
k20
21
21
ii rr
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1.5 Operation - Differential Amplifier Circuit
Solution
A193k43
V7.0V9
7.0
E
EE
E
R
VVI
V5.4
k47A5.969
ccccc RIVV
1.88)267(2
k47
2
e
cv
r
RA
V176.0
)mV2)(1.88(
ivo VAV
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1.5 Operation - Differential Amplifier Circuit
AC Analysis - Double ended
A similar analysis can be used to show that for thecondition of signals applied to both inputs, thedifferential voltage gain magnitude is:
where:
i
c
d
o
d
r
R
V
VA2
21 iid VVV
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1.5 Operation - Differential Amplifier Circuit
AC Analysis - Common-
mode To operate a differential
amplifier in a common-mode connection, thesame ac voltage sourceis applied to both inputs.
In most ac operation, adifferential amplifierprovides largeamplification, but in thisoperation it providessmall amplification.
Common-mode connection
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1.5 Operation - Differential Amplifier Circuit
AC Analysis - Common-mode
Ei
ib
Rr
VI
)1(2
i
Ebib
r
RIVI
)1(2
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1.5 Operation - Differential Amplifier Circuit
AC Analysis - Common-mode
Ei
c
i
ov
Rr
R
V
VA
)1(2
Ei
ci
cbccoRr
RVRIRIV
)1(2
1
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1.6 Op-Amp Basics
High input impedance
Low output impedance
Made using difference amplifiers having 2 inputsand at least 1 output
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1.6 Op-Amp Basics
AC equivalent circuit
Input impedance, Riis typically very high
Output voltage, Vois amplifier gain times input signaltaken through output impedance, Rowhich is typicallylow.
Ideal op-amp would have infinite input impedance, zerooutput impedance and infinite voltage gain.
IdealPractical
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1.6 Op-Amp Basics - constant-gain multiplier
Basic circuit connection
The input voltageV1 is applied to theinverting terminalthrough R1.
The output voltageVo is fed back to theinverting terminalthrough Rf.
The output voltage Vo is inantiphase with the input voltageVi
The non-invertingterminal isgrounded
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1.6 Op-Amp Basics - constant-gain multiplier
AC equivalent circuit
Practical op-amp
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1.6 Op-Amp Basics - constant-gain multiplier
AC equivalent circuit
Ideal op-amp Redrawn
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1.6 Op-Amp Basics - constant-gain multiplier
Using superposition theorem
i) V1 only (setAvVi= 0)
ii)AvVionly (set V1 = 0)
1
1
1 VRR
R
Vf
f
i
ivf
i VARR
RV
1
12
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1.6 Op-Amp Basics - constant-gain multiplier
Solving for Vi, gives us;
21 iii VVV
ivff
fVA
RR
RV
RR
R
1
11
1
f
ivf
RR
VARVR
1
11
1
1)1(V
RAR
RV
vf
f
i
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1.6 Op-Amp Basics - constant-gain multiplier
Usually and
Then1
1
VRA
RV
v
f
i
1vA fv RRA 1
11
1
1
RR
VV
VRA
RAVAV
fo
v
fvivo
The ratio Vo/V1 is dependent onthe external components RfandR1 only.
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1.6 Op-Amp Basics
Basic Op-amp unity gain
If Rf= R1;
Shown that the output voltage equal to input voltagewith 180 phase inversion.
1
1
V
Vo
11 R
R
V
V fo
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1.6 Op-Amp Basics
Basic Op-amp constant magnitude gain
If Rf= 10R1;
Shown that the output voltage is equal to 10X theinput voltage with 180 phase inversion.
10
1
V
Vo
11 R
R
V
V fo
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