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In the last class we discussed about wide band amplifiers which used pairs without any
feedback. And we came out with a very important configuration called cascode configuration
for the wide band. We had other configurations like common collector cascaded to common base,
common collector cascaded to common emitter and things like that. So, in this series of
lectures we will discuss about negative feedback and its use in wide band. Therefore ultimately
we will go to negative feedback wide band integrated circuit amplifiers.
Let us now just revise our knowledge about negative feedback. We had seen earlier that
negative feedback has to be given cautiously. In case negative feedback is likely to turn
itself into a positive feedback and result in oscillation it is a dangerous thing because
we have to cut down the oscillation by introducing dominant pole and that will cut down the bandwidth
further. If at all we in use negative feedback the negative feedback amplifier should not
need any frequency compensation. That is the condition of negative feedback that we must
utilize in wide banding.
We have seen that any negative feedback system which has three or more dominant time constants
will invariably result in serious problem of oscillation. Only systems which are less
than third order that means only first order and second order systems will not oscillate
when used under negative feedback. So the best system therefore is the one that is simplest
first order system. But we know that a single stage amplifier for example, a common emitter
amplifier has two time constants namely the input time constant and output time constant.
So the minimum order of a single stage itself is going to be 2. So, if we cascade more number
of stages we are landing ourselves in more problems because the order of the system will
increase above 2 it will become 3 or more.
Further the loop gain is also going to increase. The consequent need for frequency compensation
becomes more serious. Therefore the best negative feedback configuration for wide banding is
a single stage. Now, how do we have the negative feedback arrangement for a single stage, let
us consider. If it is a single stage transistor we know that only two types of negative feedback
will be valid. What are those? Out of h y z g type of feedback what are those which
are possible in a single stage which will result in negative feedback?
It is y and z type of feedback. So we know that only y feedback and z feedback are the
allowed types of feedback if it is to become negative. What is the purpose of this type
of feedback, the y feedback? What happens to the input admittance and output admittance?
Input admittance is increased. That means input admittance is made to go towards a higher
value as possible. The output admittance is going to be increased. That means it is leading
you towards idealization of current control voltage source, this type of amplifier. So
this is going to lead you towards current control voltage source.
The dual of that is voltage control current source. That is nothing but z feedback. Voltage
control current source is the dual of that. That means if I put z feedback input impedance
is going to increase and the output impedance is also going to increase and therefore it
is going towards an idealization towards voltage control current source. Now this is important.
What is idealization? The forward transfer parameter corresponding to that type of source
is going to become desensitized with respect to active parameter. If it is y feedback the
type of feedback structure is going to be this. This is y feedback. About z feedback
you have the same configuration like this but it will come in series at the input and
series at the output. Therefore what we have here is nothing but the feedback element,
the z feedback. You will call this RF.
Now what will be the transfer parameter that is going to be desensitized in this particular
case? It is the relationship between current and voltage so it is the forward transfer
resistance because Ii is the input current let us see and this Ii is going to flow through
RF totally and result in a voltage which is Ii times RF with ground terminal being positive
and output terminal being negative that means there is an inversion.
Therefore V0 is going to be Ii minus Ii times RF. This Ii will be going through this totally,
a very small current is going to flow through the transistor amplifier and most of it will
flow through RF due to Miller effect where RF is going to appear as RF by 1 plus AV where
AV is the voltage gain of the stage that means it is going to act like a short circuit. If
AV is very high most of the current will be pumped into rs. So this current will flow
through this and develop a voltage which is minus Ii into RF and therefore forward transfer
resistance is nothing but minus RF.
So it is an input current control voltage source developing a voltage which is equal
to minus Ii times RF. So we have desensitized the forward transfer parameter by this kind
of feedback which is nothing but trans-resistance in this case by using y type of feedback.
That is known to you. What must be emphasized here is, if you now take the y parameters
of the transistor and the feedback network everything put together and evaluate its bandwidth,
the bandwidth of forward transfer impedance in this case and then that will also get modified
by loop gain. That means this bandwidth also is going to improve by a factor of looping.
Everything improves by a factor of loop gain. In a feedback network always we can take for
granted that improvement is always by loop gain so the bandwidth also improves by a factor
of loop gain.
Therefore this particular amplifier should be used only for obtaining trans-resistance
type of amplifier, this type of negative feedback and it will improve the bandwidth of transimpedance.
The dual of that is nothing but the trans-admittance that is nothing but the z type of feedback.
So that is going to realize an idealized version of voltage controlled current source. In this
case you must remember that it is the trans-admittance which is going to have wide banding. Therefore
you must know to give the correct feedback to improve the bandwidth of transfer parameter.
If you are interested in transfer parameter as admittance then the type of feedback to
be given is in turn the z type of feedback and not the y type of feedback. In the case
of y type of feedback it is only trans-resistance that will have wide banding effect. In the
case of any feedback you are going towards idealization.
What is idealization? If it is y feedback it is going to become current controlled voltage
source. That means the modified thing is the z parameter. If it is y feedback the modified
thing is z parameter. In z parameter all the other parameters will go towards zero and
only the forward transfer parameter will go towards a smaller value than originally by
the extent of loop gain. Going towards the zero of the other parameter is also by the
extent of loop gain. In terms of parameters if you remember you will never commit mistakes
as to what gets modified and how by what extent. All these depend upon your proper identification
of the feedback and what is it that gets modified?
When you give y feedback it is the z matrix that gets modified automatically. All the
y parameters will simply add and it is the z parameter that will get modified. Those
y parameters will be divided by ly which will involve the loop gain. Therefore the z parameters
will get modified and all the z parameters like z11, z12 and z22 will go towards 0 and
z21 will go towards the stabilized value desensitized value and how will this get desensitized?
It is because of the loop gain coming into picture and the desensitized value is primarily
going to depend upon the feedback component. It is not going to depend upon active device.
These are y parameters y11, y12, y21 and y22 and this is the composite y of the amplifier.
Therefore the z parameter is going to be y22 by ?y, y11 by ?y and minus y12 by ?y and minus
y21 by ?y. This is the inversion of the matrix, the plain mathematics.
Let us take this: y22 by ?y? What is ?y? It is y11 y22 minus y12 y21. If you take this
out then it is 1 by y11 y22 [1 minus y12 y21 by y11 y22]. Therefore y22 will get cancelled
with y22. And 1 by y11 is the original z parameter. It is the short circuit impedance. That is
getting modified by a factor of 1 minus y12 y21 by y11 y22 which is by definition nothing
but the loop gain.
If you consider this as a voltage amplifier it will be nothing but a by 1 plus a beta
factor. This a and beta factor business is all applicable only for voltage whereas in
this case it is a general parameter. In terms of any parameter you can say that the parameter
that is getting modified is by a factor of 1 minus p12 p21 by p11 into p22 where p is
called immittance matrix immaterial of what the parameter is. The 1 minus loop gain is
defined in terms of immittance matrix immaterial of what the parameter is. It is this loop
gain which is going to modify all the factors. If the gain is getting reduced it will also
get reduced by the same factor. Similarly this is nothing but z11, now let us do that
for z21. Similar things can be done for other parameters.
What is z21? z21 is equal to minus y21 by y11 y22 into 1 minus the loop gain. If the
loop gain is very high that 1 can be neglected. So, if the loop gain is very high this 1 can
be neglected and it is nothing but minus gl and what is it? It is nothing but into minus
y12 y21 by y11 y22 so you will get this as plus 1 by y12 which is nothing but the total
feedback factor and no frequency component comes here because y12 is nothing but y12
of the amplifier which is negligibly small plus y12 of the feedback structure which is
nothing but 1 by RF. Since y12 of the amplifier has gone very close to 0 or it is very small
even with very high frequency the improvement factor comes simply because of that because
of desensitization itself.
And if you do this similar thing here, if the loop gain is very high you will note that
it is the loop gain which makes this go towards 0 because here also these things will get
cancelled with that and it is y12 y21 product which will make it go towards 0 which is not
getting cancelled there, y21 is still a large factor assuming that you are using a good
amplifier with good forward transfer parameter. In all the other factors this forward transfer
parameter will be the one responsible for making it go towards 0. In order to understand
more clearly you have to work out a specific problem and see how these parameters will
have the wide banding effect, what will have the wide banding effect? The forward transfer
parameter will have the wide banding effect. In this particular case of our example it
is the z parameter the z21 which is going to have wide banding effect.
Now the basic things in negative feedback that we should be aware of is, if that is
the case the reason we have used a single stage is because it is only in the single
stage we do not have more than two time constants and single stage feedback amplifier never
becomes unstable. It does not need any frequency compensation. Whatever be the negative feedback
it is never going to become unstable because it is at most a second order system. A system
is likely to become unstable when it is of the third order or higher, when the loop gain
is higher. So in wide band amplifiers we always select a single stage and not multiple stages.
Multiple stages will result in serious problems.
A single transistor cascade, cascode is not a single stage, cascode is a pair, a single
stage cascaded to another stage, a single stage meaning an active device which may even
be a Darlington pair but it is a composite device with three terminals. So that kind
of stage is only this for y feedback and therefore the other two do not exist, h and g using
a single stage cannot result in negative feedback, it will result always in positive feedback.
So h and g feedback do not exist. Then how do I obtain other sources, which are the other
sources? The other sources are the voltage controlled voltage source and current controlled
current source, how do I obtain? I obtain them by simply cascading because if I cascade
a current controlled voltage source with a voltage controlled current source there is
ideal mismatch because this is a voltage source and this is voltage control. There is ideal
impedance mismatch, a gross mismatch.
Voltage control means it is an open circuit and voltage source means it is a source impedance
of zero magnitude. Therefore there is gross mismatch of impedances. Therefore it is retaining
the wide band nature. Now I can cascade these two together and result in current controlled
current source, how do I do it? I put y feedback first then I cascade z feedback. This is the near
ideal what current controlled current source of gain equal to, here gain also is retaining
its property.
How does it happen? If I apply a current here the voltage will be input current times RF
and this is going to be directly coming here as Ii into RF by RE which is the current,
the output current. Therefore the current gain is, if this is the input current Ii this
current will go into this Ii into RF and that will be divided by this which means current
will be going into this stage and it is going to be I0 is equal to RF by RE into Ii.
The current is going to be in the other direction or this is going to be minus and the actual
voltage is this. So this is a wide band current amplifier of gain equal to minus RF by RE.
Now what is the dual of this? In order to get a voltage controlled voltage
source I cascade with, so what happens when I apply Vi here? The current in this is Vi
by RE and that current will go directly into RF so output voltage will be Vi by RE into
RF.
Again it is a wide band structure. And this is what is utilized in one of the most popular
wide band structures called [ ] this wide band amplifier which is called muA733. If
I have to convert this into a differential configuration path bias purpose what should
I do? If I have to convert this into IC so that biasing is taken care of automatically
without the need for bypass capacitors and coupling capacitors then what should I do
to this?
The standard technique for converting this single stage structure into differential structure
is to convert it into differential structure from single stage to differential then it
can become an IC. Let us see how this can be converted into a differential structure
for application in integrated circuit. Now see how we can convert this structure, this
is a configuration which has been now chosen based on our basics about negative feedback.
Now we want to convert it into an integrated circuit. This is a good exercise for us to
convert this particular structure into an integrated circuit.
Any single stage structure can be converted into an IC by simply making it differential.
This is a single stage. As already pointed out this is the output and there is a load
or RC whatever it is so that load exists, this may be the next stage. Then I will make
another structure here which is exactly identical to this. Now I have to convert it into differential.
Whenever I convert it into differential I make this into a current source. And again
there is grounding of these two and that will also become a current source.
Therefore you have the differential integrated circuit version of the so called voltage controlled
voltage source. The only thing is, if you want the gain as RF by RE you have to take
the differential output. So it is a differential output to differential input whose voltage
gain is now RF by RE. Other than that you can now independently fixed the biasing current
as, let us consider this as I01 and this as I02. These are going to fix up the biasing
currents here. And if you want to still use a wide band configuration you can still cascade
a common collector output stage. Now we are very liberal with transistors. So, instead
of taking the output here I will just put a common collector stage here and then take
the output here. Then this has to be biased so I will put a current source here. I am
very liberal with current sources now because of designing the IC. Therefore I put I03.
Similarly I do it here, if you look at it this it is nothing but the structure as it
is without any modification.
Let us identify the current sources and the respective transistors. The transistors are
T1 and T2 and the current source that is I02 is this. That is obtained by a reference that
is getting generated. This is a transistor connected as a diode so VEE minus V gamma
by R12 plus R8 and you can accordingly fix the voltage here so that you obtain the desired
current by adjusting R7. So this is I02.
Next we have the second stage which is nothing but this structure. Here we have I01 which
isĂ–..and finally I03 is through the common collector stages and in the final output stages
we have I03. Try to do the analysis of the circuit not neglecting anything but considering
all the non idealities into account that means beta is not infinity or alpha is not equal
to 1 and then consider all the effects of other transistors in evaluating the gain or
the loop gain etc.
What is the differential input impedance of this structure? It is 2RE into 1 plus hfe
straight away. It is the voltage control because it is of high input impedance here plus input
impedance is 2RE into 1 plus hfe, what is the output impedance? The input impedance
is RE into 1 plus beta and the output impedance of this is, if this is a current source then
you apply voltage here V by RF plus hie which is going to flow into the transistor resulting in hfe times that
current through this. So the current is V by RF plus hie plus V by RF plus hie into
hfe and this is the total current when I apply a voltage of V. This is the total current.
That means V divided by this current is going to be nothing but the output resistance or
impedance. Therefore it is nothing but 1 by 1 by RF plus hie into 1 plus hfe or it is
nothing but RF plus hie by 1 plus hfe. So you can see that output impedance is going
to be very low if the hfe of the transistor is high and that is why it is a voltage source.
Similarly, for the differential structure the output impedance depends upon RF and the
hfe of the transistor. Now we know the input impedance, we know the output impedance and
we know the voltage gain. Therefore we know all the small signal parameters of this wide
band amplifier. You must also analyze the voltage swing etc because this wide band amplifier
may be ultimately amplifying large signals. So I would like you to evaluate the DC voltage
at this particular point. It is very easy.
Please remember this is the wide band amplifier. That means it is a negative feedback amplifier
even for DC. Therefore there is DC negative feedback here. So you can evaluate the operating
point only by finding out the DC voltage first. It can be straight away found out and from
that value you have to go back. You do not know the voltages of these two points as there
is going to be current here drawn. Now what will be the current? It is simply I02 by 2
so the current drawn here is known. This voltage is Vcc. But please remember, there is a considerable
amount of current pumped into RF. It is not pumped into the transistor but since because
there is y feedback as the next stage even there is going to be considerable amount of
DC current flowing in RL so you cannot neglect the current flowing in RL, that is, this RF
and this RF. So you have to evaluate this current in order to find out these voltages.
Here I01 is the current so what will be the current in these two? It will be I01 by 2
and I01 by 2 so what will be the voltage at this point? It is Vcc minus I0 so you know
that voltage that is fixed already. So these two voltages will be Vcc minus I02 by 2 into
Rc2 and that minus V gamma minus V gamma will be the voltages at these two points. Therefore
the output voltages are already known. Now you know these two DC voltages, you know these
two currents and you know this voltage so now you write down the KirchoffĂs load equation
at that particular node and evaluate the voltages at these two points. Therefore it is one equation
and one unknown.
After working out this problem you will know how much these amplifiers can handle as output
signal. And depending upon the bias voltage here their capability for handling signal
is going to be determined. So I would like you to come out with the voltage swing capability
of the stage. That means how much input swing it can handle, how much output swing it can
handle as for as this wide band amplifier is concerned. Please determine that after
determining the operating point of all the transistors. After giving this structure for
some test I wanted to know the cohesent power dissipated in the IC. It is Vcc plus VEE into
current drawn.
Now there have been cases where people have evaluated the power dissipated in each one
of these devices and then added. But you can evaluate the cohescent power dissipated simply by finding out the current drawn from
the supplies. Unless there is a load resistance that is connected to ground you can easily
determine by simply finding out the current drawn from Vcc and VEE.
Now we have seen one such IC wherein we have cascaded a voltage controlled current source
with current controlled voltage source. If you are desirous of obtaining current controlled
current source of the same gain you have to just simply change the gain and cascade it
or convert it into an IC in a similar fashion. So now you are aware of how an IC design is
conceived of starting from a single stage structure up to the final IC without bothering
about biasing. Biasing is becoming a trivial thing because we can use any number of current
mirrors and convert the single stage into a differential stage. In the next class we
will see why not go for two stages.
You just said single stage is the most preferred stage because the order of the system is going
to be 2. If I go for two stages the order is definitely going to be 3 and it is likely
to cause serious problems of oscillation when used. This is what happens. Even in IC amplifiers
you have two stage amplifiers but they will require external frequency compensation in
order to maintain them stable. Frequency stability is what we are talking of and we will see
such structures in next class. When we use two stages you will automatically see that
y and z will be positive feedback structures and h and g will be negative feedback structures.
When we use three stages again y and z will become negative feedback stages and h and
g will become positive.
Actually speaking people have gone only up to three stages as negative feedback wide
band amplifiers but those amplifiers are not at all popular. The once which are most popular
are these single stage structures and sometimes if we can afford to understand the working
of a negative feedback amplifier you are advised to use the two stage structure otherwise you
can simply languish in the luxury of using this low loop gain. These are all having low
loop gain. If you use two stages loop gain is going to be boosted up and it is going
to remote desensitized. But the price you are paying is in terms of trouble due to quick
oscillations. Thank you.