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Text Books:
1
...
Roy Choudhury
2
...
Gayakwad
...
Digital Fundamentals – Floyd and Jain

Unit 2- Operational amplifies

Analysis of Ideal Op-Amp
 Internal Structure of Op-Amp
 Parameters and Characteristics of OpAmp


Operational Amplifier
An “Operational amplifier” is a direct coupled high-gain
amplifier usually consisting of one or more differential
amplifiers and usually followed by a level translator and
output stage
...


Op Amp
Positive power
supply (Positive
rail)
Noninverting
Input
terminal

Output
terminal

Inverting input
terminal
Negative power
supply
(Negative rail)

The Op-Amp Chip

741 Op Amp or LM351 Op Amp



Op-amp have 5 basic terminals(ie 2 i/p’s
1 o/p and 2 power supply terminals




The output goes positive when the noninverting input (+) goes more positive than
the inverting (-) input, and vice versa
...


Basic Information of an Op-amp
contd…
Power supply connection:
The power supply voltage may range from about + 5V to
+ 22V
...


Differential Amplifier
V0 =Ad (V1 – V2 )
Ad =20 log10 (Ad ) in dB
Vc =

(V1  V2 )
2

CMRR= ρ = |

Ad
|
Ac

Characteristics and performance parameters of
Op-amp


Input offset Voltage



Input offset current



Input bias current



Differential input resistance



Input capacitance



Open loop voltage gain



CMRR



Output voltage swing

Characteristics and performance parameters of Opamp


Output resistance



Offset adjustment range



Input Voltage range



Power supply rejection ratio



Power consumption



Slew rate



Gain – Bandwidth product



Equivalent input noise voltage and current

Characteristics and performance parameters of Opamp


Average temperature coefficient of offset parameters



Output offset voltage



Supply current

The Ideal Operational Amplifier


Open loop voltage gain

AOL



Input Impedance

Ri

=∞



Output Impedance

Ro

=0



Bandwidth

=∞



Zero offset (Vo = 0 when V1 = V2 = 0) Vios



CMRR

ρ

=∞



Slew rate

S

=∞



No effect of temperature



Power supply rejection ratio PSRR = 0

BW

=∞

=0

Ideal Op-amp
1
...
e
...
Thus its input impedance is
infinite
...


The gain of an ideal op-amp is infinite, hence the
differential input Vd = V1 – V2 is essentially zero for the
finite output voltage Vo

3
...
Thus its output
impedance is zero and hence output can drive an infinite
number of other circuits

Op-amp Characteristics


DC Characteristics
Input bias current
Input offset current
Input offset voltage
Thermal drift



AC Characteristics
Slew rate
Frequency response

1
...


It is denoted as Vios
For op-amp 741C the input offset voltage is 6mV

2
...
Input bias current
The average value of the two currents flowing
into the op-amp input terminals
It is expressed mathematically as

I b1  I b 2
2

For 741C the maximum value of Ib is 500nA

4
...
Input capacitance
It is the equivalent capacitance measured at either the
inverting or non- inverting input terminal with the other
input terminal grounded
...
Open loop Voltage gain
It is the ratio of output voltage to the differential input
voltage, when op-amp is in open loop configuration,
without any feedback
...
CMRR
It is the ratio of differential voltage gain Ad to common
mode voltage gain Ac
CMRR = Ad / Ac
Ad is open loop voltage gain AOL and Ac = VOC / Vc

For op-amp 741C CMRR is 90 dB

8
...
Practically voltages +Vsat and –Vsat are slightly
less than +Vcc and –VEE
...
Output Resistance

It is the equivalent resistance measured between the output
terminal of the op-amp and ground
It is denoted as Ro

For op-amp 741 it is 75Ω

10
...
Input Voltage range
It is the range of common mode voltages which can be
applied for which op-amp functions properly and given
offset specifications apply for the op-amp

For + 15V supply voltages, the input voltage range is + 13V

12
...
It is
also called as power supply sensitivity (PSV)
PSRR= (Δvios / ΔVcc)|constant VEE

PSRR= (Δvios / ΔVEE)|constant Vcc

The typical value of PSRR for op-amp 741C is 30µV/V

13
...
Slew rate
It is defined as the maximum rate of change of output
voltage with time
...

The slew rate is caused due to limited charging rate of the
compensation capacitor and current limiting and saturation of the
internal stages of op-amp, when a high frequency large amplitude
signal is applied
...

S = Imax / C

For 741 IC the charging current is 15 µA and
the internal capacitor is 30 pF
...
5V/ µsec

Slew rate equation
Vs = Vm sinωt
Vo = Vm sinωt

dVo
dt

= Vm ω cosωt

S =slew rate =

S = Vm ω = 2 π f Vm
S = 2 π f Vm V / sec
This is also called full
power bandwidth of the
op-amp

dVo
dt

max

For distortion free output, the
maximum allowable input
frequency fm can be obtained as

fm

S

2V

m

15
...

It is denoted as GB
...
Equivalent Input Noise Voltage and Current
The noise is expressed as a power density
Thus equivalent noise voltage is expressed as V2 /Hz
while the equivalent noise current is expressed as
A2 /Hz

17
...
For 741 C it is 0
...
For 741 C it is 12 pA/oC

18
...

It is denoted as Voos

19
...
8mA

Op amp equivalent circuit

Block diagram of op amp

The Inverting Amplifier

Vout 

Rf
Rin

Vin

A 

Rf
Rin

Analyzing the Inverting
Amplifier

1)

inverting input (-):

non-inverting input (+):

Inverting Amplifier Analysis
1)

:
:

V Vin  VB VB  Vout
2)  : i  

R
Rin
Rf
 : VA 0
Vin  Vout
3) VA VB 0

Rin
Rf
Rf
Vout

Vin
Rin

The Non-Inverting Amplifier
 Rf
Vout  1 

R
g

Rf
A 1 
Rg


 Vin



Analysis of Non-Inverting
Amplifier
Note that step 2 uses a voltage
divider to find the voltage at VB
relative to the output voltage
...
Voltage gain=-Rf/R1

1
...
The output is inverted with

2
...
The voltage gain can be

3
...
The input impedance is R1

4
...


Temperature

2
...


Time

Thermal Voltage Drift
It is defined as the average rate of change of input offset voltage
per unit change in temperature
...
The drift is not constant and it is
not uniform over specified operating temperature range
...
These parameters vary randomly with
temperature
...
e
...

in oC

20
-55

-25

0

25

50

75

Input Offset current drift
It is defined as the average rate of change of input offset
current per unit change in temperature

Thermal drift in input offset current =

I ios
T

It is measured in nA/oC or pA/oc
...
i
...
they may be positive in one temperature range and negative in
another

Input Offset current Drift

Slope can be of
either polarities

2
Iios in
nA

1
0
-1
-2
-55

TA , ambient
temp in oc
-25

0

25

50

75

AC Characteristics
Frequency Response
Ideally, an op-amp should have an infinite bandwidth but practically opamp gain decreases at higher frequencies
...


The plot showing the variations in magnitude and phase
angle of the gain due to the change in frequency is called
frequency response of the op-amp

When the gain in decibels, phase angle in degrees are
plotted against logarithmic scale of frequency, the plot is
called Bode Plot

The manner in which the gain of the op-amp changes with
variation in frequency is known as the magnitude plot
...


Obtaining the frequency response
To obtain the frequency response , consider the high frequency model
of the op-amp with capacitor C at the output, taking into account the
capacitive effect present
Where

AOL
AOL ( f ) 
1  j 2fRo C

AOL

AOL ( f ) 
f
1  j( )
fo

AOL(f) = open loop voltage gain as a
function of frequency
AOL = Gain of the op-amp at 0Hz
F = operating frequency
Fo = Break frequency or cutoff
frequency of op-amp

For a given op-amp and selected value of C, the frequency fo is constant
...


ii)At f=fo , the gain is 3dB down from its value at 0Hz
...
It is also know as corner frequency
iii) After f=fo , the gain AOL (f) decreases at a rate of 20 dB/decade or
6dB/octave
...

iv) At a certain frequency, the gain reduces to 0dB
...
e
...
Such a frequency is called gain cross-over frequency or
unity gain bandwidth (UGB)
...

UGB is the gain bandwidth product only if an op-amp has a single breakover
frequency, before AOL (f) dB is zero
...

The break frequency is nothing but a corner frequency f o
...
The op-amp for
which there is only once change in the slope of the magnitude plot,
is called single break frequency op-amp
...
The maximum possible phase shift is -900 , i
...
output
voltage lags input voltage by 900 when phase shift is maximum
vi) At a corner frequency f=fo , the phase shift is -450
...




Closed Loop: ( The utility of an op-amp can be greatly
increased by providing negative feed back
...


Open loop configuration of op-amp



The voltage transfer curve indicates the inability of opamp to work as a linear small signal amplifier in the open
loop mode



Such an open loop behaviour of the op-amp finds some
rare applications like voltage comparator, zero crossing
detector etc
...




No feed back from output to input is used in such configuration
...


Differential amplifier

2
...


Non inverting amplifier

Differential Amplifier
The amplifier which amplifies the difference between the two input
voltages is called differential amplifier
...


Inverting Amplifier
The amplifier in which the output is inverted i
...
having 180 o
phase shift with respect to the input is called an inverting
amplifier

Vo = -AOL Vin2

Keypoint: The negative sign indicates that there is phase shift of 180o between
input and output i
...
output is inverted with respect to input
...


Why op-amp is generally not used in open loop
mode?
As open loop gain of op-amp is very large, very small input
voltage drives the op-amp voltage to the saturation level
...
For a
...
input voltages, output may switch between
positive and negative saturation voltages

This indicates the inability of op-amp to work as a linear small signal
amplifier in the open loop mode
...
It is
available in 8pin, 10pin or 14pin configuration
...

Features:
i)No frequency compensation required
ii)Short circuit protection provided
iii)Offset Voltage null capability
iv)Large common mode and differential voltage range
v)No latch up

Internal schematic of 741 op-amp

The 8pin DIP package of IC 741

Realistic simplifying assumptions


Zero input current: The current drawn by either of the
input terminals (inverting and non-inverting) is zero



Virtual ground :This means the differential input voltage
Vd between the non-inverting and inverting terminals is
essentially zero
...
The closed loop
operation is possible with the help of feedback
...
In the linear applications, the opamp is always used with negative feedback
...


The output is inverted with respect to input, which is indicated by minus sign
...


The voltage gain is independent of open loop gain of the op-amp, which is
assumed to be large
...


The voltage gain depends on the ratio of the two resistances
...


4
...


If the ratio of Rf and R1 is K which is other than one, the circuit is called
scale changer while for Rf/R1 =1 it is called phase inverter
...


The closed loop gain is denoted as AVF or ACL i
...
gain with feedback

Ideal Non-inverting Amplifier
1
...


The voltage gain is positive indicating that for a
...
input, the output
and input are in phase while for d
...
input, the output polarity is
same as that of input

3
...


The desired voltage gain can be obtained by selecting proper
values of Rf and R1

Comparison of the ideal inverting and noninverting op-amp
Ideal Inverting amplifier

Ideal non-inverting amplifier

1
...
Voltage gain=1+Rf/R1

2
...
No phase shift between input

respect to input

and output

3
...
The voltage gain is always

adjusted as greater than, equal to

greater than one

or less than one
4
...
The input impedance is very
large

Parameter consideration for various
applications
For A
...
applications

For D
...
applications

Input resistance

Input resistance

Output resistance

Output resistance

Open loop voltage gain

Open loop voltage gain

Slew rate

Input offset voltage

Output voltage swing

Input offset current

Gain- bandwidth product

Input offset voltage and current
drifts

Input noise voltage and current
Input offset voltage and current
drifts

Factors affecting parameters of Op-amp

Supply
Voltage
1
...


Voltage gain
Output Voltage
swing

Frequency

Temperature

1
...


Input offset current

2
...


Input offset voltage

3
...


Input bias current

3
...


CMRR

4
...


Power consumption

5
...


5
...


Input noise current

Gain-Bandwidth
product

6
...


Input resistance

Practical Inverting Amplifier

Closed Loop Voltage gain =

ACL 

AOL R f
R1  R f  R1 AOL

Practical Non-Inverting Amplifier

Closed Loop Voltage gain =

ACL 

AOL ( R1  R f )
R1  R f  R1 AOL

The End



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