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We were discussing the specifications of Op Amps.
The specification of op amps, the first specification about which we talked that was actually input
bias current
input bias current, and this is when we do not attach any external voltage at the inputs,
even then some output is observed in op amps. And this is the base current I V 1 and I V
2, these in spite of the fact that the both these inputs have been grounded, some currents
flow they go to the base region. You remember that first stage of the op amp is a differential
amplifier. So, these are the two bases, so that is why it is called the base current.
This one is inverting input, other one is non inverting input, so some currents flow
in these bases. Now ideally ideally I B 1 and also I B 2 both are supposed to be 0 but, normally some small currents
flow. These currents do exist and I B 1 and I B 2 are not 0 then, these currents are amplified
and they produce a output voltage, which is a error voltage. And smaller these currents
I B 1 and I 2 I B 2 better it is, so and the manufacturers define this current.
The input bias current by manufacturers is defined as the average current I B as I B
1 plus I B 2 by 2 and this is specified for various op amps. For example for 741 op amp
I B is given as 500 nano amperes. This is the maximum current this is the maximum current
at V c c equal to 15 volts same as also VEE when both the voltages are plus 15 and minus
15; then the maximum base input base current is 500 nano amperes.
And so, we will see that how corrective measures are taken regarding the errors which are created,
because of the finite base current in the absence of any input signal. There is another
specification input offset current input off set current, which is actually this is the
average true current. This input offset current is defined by the
magnitude of the difference of two currents, so I input and o for offset, this is given
by the magnitude I B 1 minus I B 2. And we have already talked, that what gives rise
to currents, this is because the two transistors, which form the difference amplifier of the
of the first stage. They are not exactly 100 percent identical,
they are not 100 percent perfectly matched, some differences in spite of the fact; that
they are assembled on a chip by the processes, which are used in integration integrated circuits
like the gas diffusion for making an N N p type and all that. In spite of that, some
mismatches do occur and which give rise to this. And this current is normally very small
and for 741, this input offset current this is 200 nano amperes and it is as small as
1 nano ampere in differential amplifiers, which are realized using MOSFETS.
So, often either this or this this is much smaller, then other currents so this is neglected
but, smaller the input offset current the better it is. Now, we talk about another specification
this is important and the remedy, which we will suggest for this, that single remedy
is is is sufficient and it takes care for these currents and for this voltage.
So this is input offset voltage, this is another important specification. Now, this input offset
voltage is the differential input here. This this input offset voltage is the differential
input here, V I o offset, V I o is the input offset voltage and again this arises, because
of the mismatches. Actually or ideally, there should not be any
input offset voltage, when we have not applied any signals, both these inputs are grounded
but, still some voltage will exist. So, ideally V I o should be 0 in practice, this is not
0 this is a finite value and this is amplified after all open loop gain of the transit, of
the op amp is very high, so this is amplified and then it gives a finite output voltage.
Now, so this is the error signal error signal and we have to take care of it, we have to
correct it, because the output will exist in the absence of any input signal; and when
input signal are applied they will be amplified and this will be in addition to the actual
signals which we expect, so this error signal error voltage this is to be taken care off.
Now to bring this output to 0 output voltage 0, we have to apply a signal voltage at the
appropriate place equal in magnitude but, opposite in phase of the existing differential
offset voltage. And this is done with the help of the offset
null pins, which were available with the operational amplifier. I remind you about the, this was
the pin diagram of the op amp, where this is pin number 2, this is pin number 6 this
is output, pin number 2 is inverting input minus in and pin number 3 is this is 3 and
this is the non inverting. Pin number 4 is minus voltage that means V
E E terminal and this is pin number 1, this we had mentioned that this is offset null
offset null the negative terminal and this is the offset null positive voltage. So, between
these two, 1 and this is terminal number 4, this is 5, this is 7, which is plus volts
that means for plus V c c. And this is the extra terminal, which remains normally closed,
N c, normally closed. So, a offset voltage equal in magnitude and opposite in phase of
what is existing here is applied between these two and how we do that let us look here.
This is done almost with every op amp, whenever you want to use the op amp, we have to make
corrective measures and this is invariably for all op amps it is very simple. This is
the two inputs, 2 and 3 this is non inverting, this is inverting, this is inverting, this
is non inverting and both are grounded and this is pin number 1 here, I will draw this
figure again.
This is 15 volts normally and this is minus 15 volts, this is V E E and here between pin
1 and 5 pin 1 and 5, which are meant for offset null connection. A potentiometer is connected
this is a pot potentiometer and this is the battery and this is the wiper; this is say
10 k pot pot is tens for potentiometer, it is a very tiny hardly few millimeters and
dia in few centimeter, long it is a cylinder and it is a that is a pot having 2 connections
and 3 connections. So, the extreme two are connected to the pins
1 and 5 and the movable one which can be moved through a screw driver that is connected to
the battery. So, here we make measurement of the output be 0, we measure across the
loop of few kilo ohms and these both inputs, the non inverting and inverting both are grounded.
So, what we do we take a 10 kilo ohm potentiometer a pot and that is connected to these null
offset pins and both inputs are grounded and the output is measured. And we change this
wiper, that means this the movable part a screw is provided, so by a screw a small screw
driver, we can rotate till we get a 0 voltage at the output, we stop there and we leave
the potentiometer in that position. So, that takes care the, this is called input
offset input offset voltage compensating network it compensates; so we rotate till we get the output 0 and that is it. So, at
that point this takes care it produces a voltage here a magnitude opposite in phase as the
input voltage; so, this is how we take the corrective measures. And as I said this is
required for accurate results almost invariably in all the operational amplifiers, now we
take very important characteristic.
For operational amplifiers two characteristics are quite important, one was the Common Mode
Rejection Ratio CMRR, this we have talked when we talked the differential amplifier
that, this is CMRR is defined as the differential mode and ratio of differential, gain in differential
mode and gain in common mode. Where A d is voltage gain of op amp in in differential
mode differential mode, we apply some difference voltage at the inputs and we apply and we
measure the output ratio of the two will give the differential gain we have talked about
all this. And A c n is the voltage gain of op amp in
common mode in common mode here, a common signal is applied to both inputs and output is measured ideally
this is supposed to be 0 giving this common mode rejection ratio is infinitely high but,
in practice that voltage will not be 0 and but, still it is very small.
And this common mode rejection ratio is measured in decibels and normally 70 to 80 even higher
CMRR CMRR common mode rejection ratio are there for there for op amps as I said several
types of op amps are available. So, if common mode rejection ratio is a very
important parameter for the performance then, we choose the op amp with very high values
of common mode rejection ratio, so this we have already talked; now we are going talk
about a another parameter which is which we mentioned earlier slew rate.
Slew rate slew rate is a frequency related parameter it is a frequency related parameter,
when input inputs change the outputs never change instantaneously. I repeat when inputs
change the change in the output of the op amp is never instantaneous, it takes some
finite time. And this finite time, why it is I will just talk but, let me say, that
this finite time how fast the output will rise that is given by slew rate; and why it
is not instantaneous? Because there are there are 1 or 2 small value capacitors, few capacitors
in the op amp internal circuitory. For example for example, in 741 there is one 30 pico farad
capacitor, which has been used for bringing stability to bring stability of the working
of the operational amplifier this 30 p f capacitor was not there in the earlier version; the
first version which was brought out in 1965 by fair child USA, it was not there; so, the
outputs will oscillate there will be less there was some problems and this capacitor
takes care for those problems, so this is there.
Now, there is a finite required for the charging this capacitor, now if charging current charging current is I, then the capacitor
c, will have a rate of change of voltage I which is is equal to c d v by d t; this is
from the basic theory of the capacitors that is if I is the charging current then the rate
of change of the voltage across the capacitor is given by this and there or d v by d t is
I by c I by c.
Now, when the charging current reaches a maximum when charging current reaches a maximum value,
the rate of change of voltage gets constant
gets constant. And taking the voltage across the capacitor as output voltage, the voltage
across capacitor may be taken as output voltage, then the maximum rate at which reaches. And this by the maximum
current this maximum current will come from the input signal, so this is called the charging
current puts this rate a maximum and this is known as slew rate; and this is written
as SR. Now, this slew rate is expressed SR slew rate it is expressed in the units of
volts per micro second. So, if the slew rate is for example, 0.5 let
SR be 0.5 volt per micro second and if the output goes as high as say 10 volts, then
slew rate puts the restriction and it says that it will take 20 micro seconds, when the
output will rise to 10 volts. And so this is the meaning of the slew rate, it cannot
be faster than this; and again there op amps with different slew rates, in some applications
will require very fast slew rates and those op amps will are manufactured differently.
Now, manufacturers they define the data sheet the data sheet of the op amp by the manufacturer,
they give slew rate for unit gain for unity gain; by unity gain is v 0 is gain in to V
I and if gain is unity, then V 0 is V I; for this the data sheets give slew rates. So,
let us take a sinusoidal signal v I at the input value and the peak value of v m sin
omega t and same as output V m sin omega t then d v 0 d t will be V m omega cos omega
t. We said slew rate we define, when d V 0 by
d t the rate of change of output voltage is maximum; so this is maximum when cos omega
t is 1, so d V 0 by d t maximum and this is V m in to omega and omega is 2 pi f and this
is 2 pi f into V. And from here we get a relationship between the peak voltage and the maximum frequency,
so f max comes out to be slew rate, this is the slew rate defined, slew rate by 2 pi V
m S R is the slew rate. So, for example, if we have the highest frequency
at a certain value, when peak value is say a 10 volts and this maximum frequency depending
on of course, slew rate suppose this comes out to be 5 kilo hertz or 20 kilo; hertz 20
kilo hertz when V m is 5, when V m is high magnitude a higher magnitude signal is used
frequency will fall. Frequency the maximum usable frequency that
means, maximum frequency, which will give undistorted output is fixed, so it is related
to two things all these parameters are related; depending on the slew rate the maximum frequency
for the peak value is fixed. And if peak value increases the frequency will go down; if this
falls, then this maximum frequency will increase. If we exceed that frequency, then for example,
a sinusoidal signal will appear as triangular at the output a distorted signal will appear.
So, this is the slew rate which is measured in volts per meter second and already expressed
that finite time output takes to rise to come to the maximum level and that is given by
slew rate. So, that cover the basic of the specifications
of characteristics of operational amplifiers; in fact we have finished this module and this
course as such is over. I will first summarize what we have done in this module, then I will
write the references which are good enough for the whole course and then if time permits,
which I hope will permit quickly I will take some problems from this module. To summarize
what we have done, we started with a differential amplifier, the differential amplifier has
two inputs it is very different from conventional amplifiers and one input is called inverting;
inverting in the sense that the input signal will appear with a inversed phase at the output.
And the other terminal is non inverting, where it will appear as such will appear in the
same phase at output, if the and these signals for operational amplifiers they can be d c
as well as a c, because direct coupled direct coupled amplifier it is and hence this is
signals can also be used. Now the differential amplifier can be used in four different modes
which we said, normally the outputs we take from the two collectors and when there is
a perfect symmetry of the two transistors, their characteristics are 100 percent identical
then output will be 0 for the same or no inputs. But, there are departures as we have seen
because of lack of perfection, lack of 100 percent symmetry of the two transistors and
that give rise to certain currents and voltages; which with a pot we can correct. So, anyway,
so the differential amplifier it can be normally we take from the two collectors the output,
and then, this is called dual input and balanced output balance, balanced output this is one
configuration, which is most widely used for differential amplifier.
There are the next usable which is the which is quite widely used is a dual input and unbalanced
output that means, the output is taken from the collector of q 2 with respect to ground.
So, these two configurations are out of the foue are most widely used then, we talked
about the importance of the differential amplifier, that differential amplifier is the first stage
of the multi stage direct coupled very high gain amplifier, which we call operational
amplifier op amp op amp. So, we gave the block diagram of various stages
of the op amp and what was the purpose of each stage that was briefly explained. And
then we gave the why it is called the operational amplifier, because it can be used for mathematical
operations, we have taken several applications like sign changer, summing amplifier and subtraction
can also be done by a differential amplifier for with gain unity; then it will just be
the difference of two input signals at the output.
And integrator and differentiator that also we took and these were the mathematical applications,
which we have taken and some other amplifiers were discussed like log amplifier, where output
will be log of the input; and so these were mathematical applications applications for
mathematical operations, which are used in analog computation and these circuits are
there. And then we have covered basic three amplifier modes in which op amps are used;
one is the inverting amplifier, in inverting amplifier the one basic thing was that the
input inverting input is virtual ground that is at ground potential and it is called virtual,
because actual ground can absorb infinite current but, these are small power devices.
So, hardly maximum few 100 mille ampere current they can tolerate, that is why it is called
the virtual ground but, the concept of virtual ground is very important and it simplifies
all the analysis, which we have done. Whether it is a integrator, differentiator or is summing
amplifier or whatever it is, it simplifies the analysis significantly; and so that is
why we used a inverting mode for these applications though it can be used realized using non inverting
configuration also. So and then, the amplifier how simple it is
to construct a amplifier using op amp, just to choose two resistors, one the feedback
resistance R F and one the input resistance R 1 and in the inverting amplifier the gain
will be the ratio of two resistances R F by R 1. Very simple nothing could be simpler
than this, where R I will give you the input impedance of the amplifier feedback amplifier
also; and then we took the non inverting amplifier and we have shown that, non inverting amplifier
comes closest to an ideal voltage amplifier. Ideal voltage amplifier in which we can use
the feedback concepts and the term 1 plus A B, A is the open loop gain and this is the
gain of the feedback network. So, this term is used to get the modified parameter for
the non inverting amplifier.
For example the the input impedance it will be changed it will be enhanced it will be
enhanced, by how much amount this much; the input impedance without feedback into this
term that will be the input impedance for the feedback non inverting amplifier. Similarly
for the changing bandwidth, that has to the bandwidth also increases and that change is
given by this. So, there are several parameters and the gain is also very simple to remember
1 plus R F by R 1 this is the voltage gain for the non inverting amplifier; so that we
have taken and then we covered applications of op amps in designing filter circuits.
Filter circuits are very widely used in electronic systems to select or to reject frequencies,
from a wide spectrum we select certain frequencies for our purpose, then a band select filter
is to be used; if we just want up to this you can see, they should be available, they
should pass through our network and remaining work should be rejected and rejected one is
the stop band and this is the pass band. So, this is a low pass filter and similarly, high
pass filter and so on; this we have covered in a almost quite reasonable well, the circuit
design and the analysis. In analysis just the important thing was,
how to choose the components for the cut off frequency and for pass band gain, gain of
the pass band frequencies, so these were done. So, what is a ideal op amp, we also discussed
and a practical op amp is a direct coupled very high gain and very high input impedance
amplifier, it is very useful. Hardly now actually the design of the systems using discrete components
has gone drastically, it it has been cut down. Most designers take the help of various kinds
of op amps, because op amp is available on a chip and because they are produced in bulk
in millions and billions, so the cost per unit is very low. And hence all operations
can be obtained by using a operational amplifiers, in the system last one or two stages may be
high power they may be taken from high power transistors so they are discrete components
and this is how the op amps are used.
So, this is about this unit and now I give the text books for this course, there are
two text books, which will be sufficient for almost everything, what we have covered, one
is electronics ELECTRONICS circuits and analysis, I have authored this book, this is by Dinesh
c Dube for India and neighboring countries the publisher is NAROSA narosa India they
have branches in Delhi, Chennai, Calcutta and Mumbai all the cosmopolitan have their
branch. And for Europe, United States and Canada this has been published by Alfa international
U K this is you can see on the internet by giving these details electronics circuits
and analysis by Dinesh c Dube. The other book electronic principles electronic
principles this is by Albert Paul Melvino and this is published by Tata McGraw hill,
new Delhi. These two books should be sufficient for op amps, those who want to go in greater
detail about op amps, there is a book by Rama Kanth Gaikwad.
Op amps and linear integrated circuits this is the title op amps and linear integrated
circuits, this is by Ramakanth A. Gayakwad and this is published by Prentice Hall of
India private limited very good book whole book is on op amps and integrated circuits;
besides in this in general you can have a reference book and that is integrated electronics
by j Millman and c halkias this McGraw hill publication McGraw hill international. So, as a reference
book for any details you want to consult this can be a nice book; now there is time for
few examples, which I can take.
For example there is a, this is a problem that for this circuit, which I am drawing
I will write briefly what is required, this is a differential amplifier this is plus V c c which is 12 volts plus
12 volts and this is minus V E E which is minus 12 volts and this is R E which is a
24 kilo ohms and these resistances are 12 k, 12 kilo ohms and here we take V 0 and this
is V i 1 and V i 2. So, in this question how much is V out, this is between two collectors
c 1 and c 2, how much is the current I E, this this is I E this is also I E, I E how
much is I E in each transistor Q 1 and Q 2. So and this voltage, we can find how much
is the voltage V out between with collector from one collector to ground; now for this
solution is simple first, we have to find out the tail current, this is tail current
I T, in I T is if you simply this is a potential V E, V B E is this voltage but, and and this
is at V E E. So, the potential difference across this resistance
is this divided by R E this is tail current, this voltage this voltage is very small in
comparison to this, so this approximately equal to V E E by R E and this is 12 volts
and 24 k. So, I T becomes 0.5 mille ampere if we take resistance in kilo the current
will be in mille amperes, this is will go 10 to power minus 3 here, it will come, so
this is the tail current. And the answer I E is equal to half of I T, so 0.25 mille ampere
is the current in each transistor; and this much current.
Now, to find out the potential difference between the two collectors, we apply, we find
V c 1 the collector of first one is at what voltage, we apply the summation of voltages
for this circuit and that gives I c R c plus V c 1 equal to V c c. I c in all B j t's
I c is equal to I E, so I c equal to I E, which is equal to 0.25 mille ampere. So, this
current we substitute here 0.25 into 10 to the power minus 3 in to R c, R c is 12 k,
so 12 k and plus V c 1 equal to 12. And from here we get V c 1, this is at 9 volts
V c 2 will also come to be at 9 volts, so this is the potential with respect to ground
and between the two V out is V c 1 minus V c 2 and this is 9 volts, 9 volts both are
0. So, we expect that for no signal or same signal the out put will be 0, so we can find
out the input impedance Z i is 2 beta r e prime; and this is beta if we take 100 R E
prime we calculate, once we know I E; so we can find out the value of this impedance.
There is time for one more problem and that is construct, suppose this is the problem
construct a inverting amplifier.
Inverting amplifier such that input impedance with feedback is 5 kilo ohms and gain is 80
it is simple, this is we have to choose these 2 values rightly, this is V out, this is R
L this is V c c, this is V E E this, we choose 5 k and this we choose as 400 k and apply
the signal here. Then gain is R F by R 1 which is 400 by 5,
which is 80 as desired and input impedance Z i F B is equal to R 1, which is 5 k so that
is it. So, this is very simple and similarly, the non inverting amplifiers are simple and
construction of the filter circuits is very simple only one or two expressions are to
be used. The gain is R F by R 1 and cut off frequency is 1 by 2 pi R c, R and c values
connected with the filter circuit; so I hope we have done justice to this course and you
all have enjoyed, thanks.