Electronic Devices for Analog Circuits
In the last class, we were exposed to one ideal
active device the ideal Op Amps is started with the ideal amplifier and then went over to
what an ideal Op Amps then we come out with the synthesis of ideal Amplifiers using ideal
Op Amps and went over to another device which is a comparator how the comparator is different
from the Op Amps ideal Op Amps has been made very clear to you. Today we will be covering the multiplier which
is the darling of communication signal processing, okay and we will see a variety
of communication applications about this multiplier. Further will be also covering the important
active devices which we have earlier sort of exposed to okay at the beginning itself
these things have taken a back ahh ground role now and are mainly used in ICís as basic
building blocks in IC designs are the MOSFETís.
We will also cover BJTís okay which is primarily
used today ahh in combination with MOSFET to improve the performance of integrated circuits. However, most present-day users are
concerning the MOSFET and also the power MOSFETS. So we will be covering these topics in today’s
lecture. Let us start with multipliers that provide
multiplication of two input voltages or currents either two variables as voltages or currents
can perform multiplication and if you perform multiplication what are the signal processing
activities you can do one such activity is if one voltage is kept as the control voltage
the other voltage gets the input voltages then the multiplication makes it a voltage
control amplifier and you can use this for face detection mixing modulation demodulating
etc.
Now the filtering and ahh other activities
are done by using normal RC components or LC components or active filters. Signal generation in terms of facilitating
frequency synthesis if you have a signal that is generated how to obtain ahh frequencies
other than this generated frequency that is called frequency synthesis. So all these activities can be performed with
the help of the multiplier. Let us see how this can be done are commercially
available okay as voltage control amplifiers which is why multiplication need not
tighten us it is nothing but a voltage control amplifier that can be used as multiplier
current control amplifiers digitally control amplifiers even ahh will say let us see that
DAC is acting as a multiplier where one variable is digital work the other is an analog signal
okay. So however the general analog multiplier can
be given as V naught equal to there are two inputs let us now consider there are going
to be two inputs VX and VY.
So if the output is a function of generally ahh
these two variables then what are the devices that this functions if it is nonlinear then
you can show that V naught is going to be a factor that is independent of VX and VY
that is called offset. If it is current output it is a current offset
so this is independent of the two inputs than one output due to only VX that is linearly
related to only VX independent of V by another linearly related to VY independent of VX these
are called Feed through components, okay and a multiplier these do not have any place to
appear the out wanted is this primarily it is K naught into VX into VY that is important
for us in multiplication other terms in this which are for example functions of VX squared
DY squared VX squared VY squared VX these are all called the non-linearityís in a multiplier.
The offset is the DC offset voltage that has
to be made equal to 0 and these fit-through components also have to be made equal to 0
after which K naught can be adjusted to a standard value in precision multipliers K
naught is a will see is adjusted to something like one over 10 volts okay where VX and VY
have the limitation of + – 10 volts which is called a 4 quadrant multiplier okay. So So this is the four-quadrant multiplier
I am talking about VX can take both polarities VY also take both polarities output changes
when anyone of these two okay chain polarity.
So that is why it is covering the entire four
quadrants of one of the variables VX where VY is the parameter that is varied okay. So let us say VY is kept constant than at
10 volts okay then output is equal to VX okay. So that is ahh it gives you a unity gain
okay slow okay so that means by varying VY to different values you get amplifiers with
different gains okay linear amplifiers with different gains you can even make it inverting
type of amplifier by just changing the polarity of his DC voltage.
So it becomes an inverting or non-inverting amplifier
and this slope can be varied by changing this voltage which is why it is voltage controlled
amplifier basically. Now what are the methods in hardware ahh
you can actually fabricate this multi-player basically I would consider these two are the
most important methods okay yeah to obtain electronic multipliers V naught is going to
be equal to mathematically we know that VX by VY whole squared ñ VX ñ VI whole square
divided by VR that is you add the two inputs square subtract it two inputs and square
and then subtract these two terms then you get this output as 4VX VY divided by
VY because the output of this voltage the dimensional of the constant K should be one overvoltage. So we get here 4VX by 4 VXVY by VR as the
output so this is one way to obtain a multiplier another way is using squaring devices this
is using squaring devices and added. This one is V naught is antilog of summation
of log VX + log VY ñ log VZ.
This is a log antilog multiplier it is called
the antilog of log off now VX into VY by VZ which is nothing but VXVY by V. Now so this results in an okay ahh multiplier
come divider. So this is really very interesting here we
have a multiplier come divider and so this is the log antilog device these users log antilog
device adders to obtain multiplication or division. So these are the two principles that are
eve now used for obtaining multiplies MPY 66 34 okay is a commercial multiplier made
by Texas Instruments, okay it is available as a log antilog multiplier with the same principle
that we had earlier given so this is the chip that is used it is a differential input that
it reacts can be a differential input VI can be a differential input okay and then we have
wizard terminal along with an Op Amps okay in the feedback it can give you what you consider
as VXVY / ahh VZ okay. VZ in this case V reference and that is equal
to 10 volts okay so that is something that we can adjust in this.
So its characteristic bandwidth is an
important aspect of this multiplier so only about 6 multipliers, however, most of the communication
activities take place at frequencies much beyond this, and however, you can understand
the signal processing activities by using this check very well okay? The slew rate of this
is about 20 volts per microsecond output offset voltage is + – 100 milli-volts output
short circuit current is about 30 millimeters these are the limitation of this multiplier. Let us see the application of this multiplier
if VX is VP1 sin omega 1T and VY is VP sin omega T2. We have here V naught = VX VY / VR, VR is
10 volts in this case so we have VP1 VP2 / 10 into sin omega 1T sin omega 2 you know this
trigonometric relationship can be therefore expanded as VP1 VP2 by 20 into cos of omega
1 ñ omega 2 into 20 the different components of frequency and ñ Cos of omega 1 + Omega
2 into T these are called sidebands okay? Actually therefore if you consider omega 1
as the carrier omega 2 has the modulating frequency around these 0 called carrier you
generate omega C ñ omega M omega C + omega M added two sidebands.
So this is what is called communication
double sideband okay modulation is called balanced modulation which means this is a balance
modulated circuit under this role when omega one is the carrier omega 2 is the modulating
frequency. So this is one way of ahh modulation which
is adopted in communication let us see what happens when we simulate this with this is
called as mixer odds it can be either called a modulator balanced modulator or mixed
okay.
So F1 is 10 kilos hertz F2 is 1-kilo hertz
omega 1 is okay 2 pie into 10 Omega 2 is 2 pie into 1 radius per the second VP1 is 2 volts
VP 2 is 1 volt this is taken as an example and this is the so called frequency we can
choose 10-kilo hertz and this is the modulating frequency 1-kilo hertz may be the audio frequency. So we know the output now which produces omega
1 ñ Omega 2 omega 1 + omega 2 which is the double sideband wave form we can see this
waveform here. So the signal comes like this here and like
that okay this is the signal modulating it so this is the output of the mixer. Now I just multiply by using along with F2
I added DC of voltage and then multiply F1 with DC + F2 ok. So then what happens is the carrier comes through
a feed-through component because when you multiply VX with VY having an AC and DC in
ahh added to it then we have a carrier coming through as a feed-through component. That particular thing is called amplitude
modulation okay? So this is what you get when have shifted the
modulating frequency by 1 volt you can see the DC of 1 volt added to it and then multiplied
by the carrier this carrier comes as such and then its amplitude is modulated okay by the
modulating frequency on either side you can see and this method of transmission is adopted
in AM transmission.
In order to facilitate this detection here
you can simply because you have transmitted the carrier also okay with a large amount
of power you can receive this and then detect ahh the modulating signal by simply using
an electric rectifier that is the easy detection method okay. That is why this particular multiplier application
is the one where we are having a feed-through component at the output. So we have discussed amplitude modulation, okay, and ahh double sideband in communication the other one application is linear delay
detection okay. Let us suppose that one input is a square
view another input is a square view with a certain amount of delay let us say tau okay
that is applied to the other both with the same frequency.
Then when you multiply you can see this is
+ 10 volts and this is ñ 10 volts. So + 10 volts into ñ 10 volts is / 10 volts
is ñ 10 volts so when both are plus then again + 10 volts again when it is changing
this one is changing ñ 10 and okay this is at + 10 it is ñ okay. So within one had a period you have one full
cycle of this output okay then again this whole thing gets repeated and that way we
have produced once again okay the ahh double the frequency because it is omega here the
omega here double the frequency with a DC what is the Dc average you just take this
area DC is corresponding to the area okay total area over this time period T. So this
is ñ 10 into tau okay ñ 10 into tau this is that area + 10 into T minus tau divided
by the ahh half the time period T by 2. So this is the average voltage of this output
okay? So you can therefore see that this becomes
DC which is proportional to the average which is proportional to tau by T. So that is how
we can detect the delay okay in terms of a DC. Now I am also going to show you ahh this
simulation you can see that average is what we have just now computed is 10 into that
is Dc voltage 1 ñ 4 tau by T.
So for example, if the phase shift is the delay is by T by
4 okay this becomes 0 so that is what I have done I have applied here and this is VX
which is delayed by ahh T by 4 okay and then the output here is just this that we have
already shown in the earlier diagram. And if you take the average of this that is
0 okay because the area is the same as the negative area and it has produced the frequency. So this is wasted the delay detector which
is used in phase lock loops okay and in any place where you want phase detection or delayed
detection know that we are going to repeat it for ahh sin waves you can see I am applying
to sin waves instead of two square waves of the same frequency.
The frequency is 10 kilohertz and the phase
shift is 90 degrees one is the sin wave the other is the Cosine wave okay? So VP1 = VP2 = 10 volts so then we get 10
into 10 divided by 20 which is 5 volts okay and double the frequency with the cost 5 because
now the omega 1 ñ omega 2, because D2 frequency is these, are the same with the phase shift. The first term is cost five the next term
is 2 omega T Cos 2 omega T + 5. So this is the cost to omega T + Phi okay
5 being Pie by 2 again become a sin wave, okay and the average is 0. We will do this for the ahh phase shift this
phase shift of 90 degrees is called quadrature okay? So if you have a sine and a Cosine applied
to the multiplier you get double the frequency as the output with 0 DC. So now it is the same frequency the phase
shift is adjusted to be 60 degrees okay.
So Cos 60 is half so we have VP1 = VP = 10
volts so it will be 10 into 10 divided by 20 Cos 5 which is half okay which is therefore
going to result in an ahh voltage of 2.5 volts as the ahh DC average is okay. So this is the ahh twice the frequency component
emerging with a DC shift okay of 2.5 volts. So these are the applications of this particularly
here I can show that this is also used in electrical engineering as an analog ahh watt
meter for example if VX is proportional to line voltage using the voltage transformer
and VY is proportional to the line current using a current transformer you can actually
get the output average as nothing but proportional to the real power okay which is going to be
ahh, the ahh voltages multiplied, and Cos ahh 5 okay.
So I can also measure the power factor okay
and that is why it is almost equivalent to a watt meter okay. Now the fourth example we are taking for the
application of the multiplier is nothing but sin wave generation from a triangular wave. So the triangular wave okay can be generated
in terms of for example Sin wave Sin X is nothing but a polynomial in X okay let u series
expansion of it is X ñ X Cubed by factorial 3 + X2 power 5 by factorial 5. So on and hence so forth that means any period
waveform can be generated from the what is that ahh triangular waveform using this polynomial
series for expansion.
So X is nothing but the original triangular
input then you have to cube this and divided it by factorial 3. Let us approximate it to this sin wave if
X is the triangular waveform it is possible to create a sin wave by using X- S cubed by
6 So this is what is done. You can see this is the input triangle this
is ahh cubed by using ahh first squaring by feeding the same input to this triangle to
one multiplier you get squaring after squaring this squared output is again multiplied with
the original triangle and you get the cube and the cube is then subtracted okay.
From the original triangle as X which is omega
T, so we just have this it is omega T ñ omega
T cubed divided by 6 so that is what is done okay then we will therefore see that okay
this is what is done omega T ñ omega T cube by 6. If you want more accurate this thing you can
actually remove the higher order harmonics by using a low pass filter. Now we come to this important point which is
the transistors. Let us get introduced to this in a very continuous
manner from what we discussed in the earlier input-output relationship of an ideal device amplifier
okay active device is the output matrix related to the input matrix by means of this in a
two-port okay that we had already seen immittance matrix PF is the important parameter from
input to output the transfer parameter forward parameter transfer parameter.
So but most of these devices have limited
dynamic range which means they get saturated in the value which means this value okay really
is not constant at all operating points okay it keeps decreasing on either side of the
maximum okay. So generally all these systems will be having
PF tending towards okay ah lower and lower values on either side of the maximum value
that is the non-linearity. So ultimately it may go to 0 in what is called
saturation DC okay it is really a small variation of the output caused by a variation
in the input it is not perfectly linear.
So this nonlinearity will consider only the
first order nonlinearity okay itself can be such that PF is a function of one of the
two variables input or output. So we are having only two variables here one
is the dependent variable and the other is the independent variable so PF is nothing but
the incremental change in output caused by incremental change in the input. So this itself is not constant when it is
non-linear so this can be a function of the input variable or linear function of the input
variable or a linear function of the output variable that is the kind of nonñlinearity
that we are first considering. If that is so what happens to this ahh nature
of the nonlinearity? This is very interesting let us, therefore,
consider such an example wherein in electrical engineering we have only the variable as current
and voltages. We are therefore considering the ideal transconductance
amplifier that we have already discussed as the voltage control current source.
So the output variable is the currents, okay
and the input variables are voltages and this is the trans-conductance GM we all call it
as it is normally called input to output the transfer of input voltage to output current
is occurring by the trans conductance here it is normally termed as GM okay. This GM is a relationship between an output change
in current for an input change in voltage it can be therefore a function of VI and I naught
these are the only two variables of significance here. So this is equal to either K times VI when
it is proportional directly to the input variable VI or the output variable as linear K times
I naught interestingly the first relationship gives us this is delta I naught = K VI into
delta VI. We integrate this we get I naught as K into
VI ñ some constant VT whole squared so this VT according to you can easily recognize
this as a square log relationship of the famous field effect transistor.
So VT is known as the threshold voltage so
we are not bothered too much about any particular device we have started with what is possible
as a first approximation to the non-linearity either it is directly proportional to the
input voltage or directly proportional to the output current and we have got a device which
should have the non-linearity and that is there with what we called as field effect
transistors. Next, let us see interestingly the other relationship
leads us to nothing but the other that is important. We will see delta I naught in this case divided
by I naught because it is proportional K times I Naught GF okay this I naught is brought
to this side this is equal to K into delta VI. So we get here a log of I naught = K into VI
obtain decorating and I naught = IS into exponent K VI ñ 1. So if you include the constant also this
IS, therefore, is known as a reverse saturation current in the case of a Bipolar junction
device.
So this results in bipolar junction transistor
relationship so you can see how beautifully this two relationships where the trans-conductance
is proportional to the input voltage or trans conductance is proportional to the output current
result in respectively field-effect transistors with square lock and bipolar transistors in
with exponential now. So ahh these are the and even in ahh field
effect transistor this if you are operating in what is called above threshold region it
is going to follow square lock and below threshold region, it jumps into the other ahh device
characteristic that is exponential one that is the beauty of these ahh bipolar and mass
devices.
They are forming a complete set by themselves
most probably if you therefore ahh looking to completion of a set you would have naturally
got this relationship first and actually invented the devices later okay. So semiconductor devices that exhibit this
relationship are respectively effort ease and mutators F it exhibits a square law
relationship in the region above threshold voltage and the exponential relationship between
input and output in this up whole region BJT exhibit exponential relationship okay. Now something of history sees basically the
field effect device was ahh predicted okay much earlier than the bipolar junction device
okay that is the important only thing is it was very difficult to fabricate this field effect
device okay and it took a lot of time because it is a surface phenomenon, okay and it took
a lot of time for people to ahh have technology that facilitated fabrication of MOSFET okay. The effect however was ahh got the moment
one could really fabricate a BJT right so one could fabricate the junction okay.
And you see that this is the history it was
shortly with the help of Bardeen and Brattain who really got us the first theory and then
actually fabricated the device and when they were really trying to look for the device
action in terms of field effect they stumble upon this okay ahh effect first and that is
why BJT predominated the scene thereafter okay until ahh MOSFET become a reality ahh
once the IC fabrication set is fort okay. So now what are the situations regarding the
present status of these devices it is seen that bipolar junction device was very popular
okay before mass VLSI ah try to replace most of the ahh front end components with
bipolar device and VLSI circuits. So ahh bipolar has disadvantages primarily
it is a minority carry device and the leakage current is important as we saw in exponential
itself it figures in predominantly the reverse saturation current which doubles for every
10-degree rise in temperature. And therefore is highly sensitive to temperature
that means actually power device particularly as a gets heated its device current keeps
on increasing drastically and then it might go into what is called thermal runaway.
So it might destroy itself unless we take
care with each whereas in the MOSFET there is a very interesting thing if you put a
BJT in a calculator and put a soldering line on top of it right you will see the characterizes
simply rises up okay. On the other hand, replace it with MOSFET and
the design soldering line to its entire characteristic comes down that has temperature increases
the current decreases in the same condition okay that means actually there is a safety
the mechanism in MOSFET and it is MOSFET devices that have also become powerful units of power
electronics today. So BJTís always have almost vanished okay
in as even discrete devices altogether okay. However, people are trying out because of getting
the advantage of a large value for the GM for the same geometry an order of magnitude higher
GM is possible with BJTís as compared with MOSFETís it is ahh nearer to the ideal than
the corresponding MOSFET and therefore people are trying out okay BJT in combination with
ahh CMOS is called BICMOS technology for some of the analog functions.
Now ahh this is the sum and the substance
of electronics today. And therefore ahh ahh particularly today
the ahh devices using discrete small signal ahh low power bipolar devices have vanished
altogether in industrial usage. So ahh because of the fact that mass as a
device has this weakness that the gate oxide which is coming right at the input between
the gate and this source is very sensitive to ahh the voltage right? So because of this very high input possible
with high input impedance possible with MOS, it cannot be directly used for that high input
impedance because one might destroy the gate oxide by just touching it. So even though the inside integrated circuit is
well protected as a device by itself it is not a bipolar device unless you put the protection
circuit typically indicate and the source which again brings down the high impedance
it has okay. So ahh these are for IC applications right
for them to be rugged for input devices it better be a bipolar device okay at the output
you can use ahh most devices and therefore that is why CMOS technology sometimes is adopted
for small-scale integrated circuits.
Now let us consider the field effect transistor
which is a 4-terminal device source-drain gate and sustain it has. So the substrate voltage control source the
the current between the source and the drain. The source and drain are separated by the
channel this channel can connect the source and drain if there is an ahh channel existing earlier
or it can be created by a applying suitable voltage to the gate. This kind of thing where the channel already
exist is called depletion type of MOSFET where the channel is created by applying the voltage
it is called enhancing type of MOSFET and again we can have an N channel and a P channel
okay type of MOSFETS so we have a variety of MOSFETS available to us ahh apart from the
MOSFET we have the J effect okay which were in the gate and the channel is separated
by a reverse bias junction, okay and that also can be an N type or P type. In a MOSFET there is an insulating oxide layer
and therefore the incident at the output can be pretty high. So now we come to the preferred devices in
VLSI enhancement mode of FETís is predominantly used why because the source and drain are not
connected in they connected only if a suitable voltage about their sole voltage
is applied to the gate with respect to the substrate and therefore this is normally of
a device that if you do not apply any voltage it is off-right if you apply zero voltage
it is all right.
So these normal of devices are suitable for
ahh digital design and therefore it is going to be made only if an applied voltage is
crossing the threshold voltage. So because in today’s world 99% of the signal
processing is carried out digitally and digital technology is what governs what we
used to enhance the type of MOSFETís have been universally used in VLSI. On the other hand, if there is a choice or analog
processing depletion mode MOSFET is suitable mainly because with 0 voltage has a bias voltage
you can directly apply a signal and it is working in the active region which means the gate
voltage can be made to go positive or negative it still works as an active device. As the enhancement mode of technology is
used mainly by digital even analog circuitry has to go along with that okay and therefore
ahh in today ahh activity of ICís it is primarily an enhanced type of MOSFET which is
CMOS which is primarily reused.
So let us now consider
the ahh FET characteristic IDS drain to source voltage drain to source current IDS = K / 2
we use K earlier but that will put as K / 2 into VGS ñ VT whole square this is the saturation
current in what is called the active region is called the current saturation region
as long as VDS is greater than VGS ñ VT this is valid for the young channel enhancement
device. For VDS less than ah let us just see the
status VGS ñ VT right it is ahh IDS this is IDS = k into VGS ñ VT into VDS ñ VDS
square / 2 right.
So VDS less than VDS ñ VT IDS = okay this
is VL that is called triode region that before reaches the current saturation this
is the region where it is normally used as a resistor voltage control resistor this is
the region where it is held as an active device as an amplifier and this is the physical
the appearance of an integrated circuit MOSFET where we have a young as source N + Source
and drain and by applying voltage here okay which is positive. You can make this surface good into inverted
mode compared to the sub-state which is P so that links the source with the drain with the
channel of these minority carrier electrons come towards this and make this young. So it can be very unpleasant by applying a higher
voltage so that is why it is called an enhancement mode of MOSFET where this conductance here
is enhanced by applying a voltage here. So this is the micro model of a MOSFET ahh
for the last signals, we have a VGS supplied okay and the current IDS = K / 2 VGS ñ VT squared
this is the last signal model.
It is a trans conducting amplifier voltage
that is converted to current in a nonlinear fashion. The micro model of a higher level is
the model for the small signal C where delta VGS is the change in input voltage, okay and
it is called GM into delta VGS what is this value of GM you can simply consider it has
a change in output current for a change in input voltage delta IDS/delta VGS. That is equal to differentiate that relationship
square lock you get it as it was earlier K / 2 VGS ñ VT whole square = IDS.
So delta IDS/delta VGS is K this by 2 get
cancel with 2 of these coming here into VGS ñ VT means directly proportional to
the input voltage VGS is what we started with right? So if the GM is directly proportional to the
gate to source voltage through this relationship or it is also = root of you can replace this
with ñ VGS ñ VT by ahh say we have IDS we have therefore IDS = K / 2 VGS ñ VT whole
square so you differentiate this you get this two here it becomes K into VGS ñ VT.
So VGS ñ VT itself is the root of 2 IDS / K if
you substitute it here okay you get it as the root of 2 IDS into K in the region where VDS
is much greater than VGS ñ VT this we have already mentioned earlier okay. Now higher level model for this is just
that the current is not constant at the saturation value throughout it is IDSS into 1 by lambda
times VDS again. This Lambda is known as channel length modulation
it is increased slightly so that it does not remains constant at saturation value with
VDS variation it is dependent upon VDS the second order is okay it keeps on increasing
instead of remaining constant at IDS it keeps on increasing. So this is an important fact that you should
remember instead of remaining constant with the respective VDS increases that are
the effect of channel length modulation. So GDS which is the variation in IDS with
respect to VDS okay IDS variation with respect to VDS at the output it is called the output conductance
of the device okay it is not 0 it is delta IDS/delta VDS which is lambda times directly
proportional to IDS roughly okay.
So this is the second-order effect that there
is a finite non-finite output resistance. In the high-frequency equivalent circuit we have
these between every electrode okay two electrodes we have a capacitor so between the gate and source
between these are all overlapping capacitors they are called the gate and drain and then drain
and substrate okay. So we have these capacitors in addition to
the earlier circuit okay?
A bipolar junction transistor is a three-terminal
device emitter-based and collector now you see the number of process states increase
here that is why it is not a preferred device okay ahh integrated VHI schemes mainly because
the more the number of steps less will the yield in any technology right. So the ahh mass device requires the least
number of steps compared to the bipolar device is why the bipolar device as in totally rejected
okay as a device for VLSI structures.
So BJT is a three-terminal devices emitter
based and collector okay this is the based and collector and emitter this should be normally
N + region. So made very rich okay in electrons here so
that the total current is IE is made up of only these electrons in N + region. So that is ahh the transistor action here
simply means by suitably forward biasing emittance-based junction okay and reverse biasing collector-based junction the entire current IE is made to appear as collector current that is IC
is very nearly = IE okay.
And that is a factor called alpha is very
nearly = 1 in a good bipolar junction transistor. So then since it is forward by the junction at
between the emitter and base IE = IE naught reverse saturation current exponent VBE divided by
VT this we had already seen so array diode okay the emitter current is very nearly transported
to the collector current if it is suitably forward by biased between base and emitter
and reverse bias between ahh collector and base. The emitter current is very nearly transported
to collector current this results in IC = alpha ñ 1 by alpha times IB or this is called beta
factor and beta is going to be very high typically o the order of 200 or so in the case of bipolar
junction transistors times based current if you express this in terms of base current
as the input.
Then VB = VT log IE by IE naught this is the
input relationship from which you can find out delta VB by delta IE and that will be
the ahh input resistance is okay. Common emittance configuration of the transistor
IC = alpha IE naught exponent VB by VT GM which is delta IC delta VB, therefore, = alpha
IE naught exponent VBE by VT okay divided by V if you ahh differentiate this you get
this. So that is equal to alpha IE okay it divided
by VT so this is the GM VT is typically KT over Q okay about 26 millivolts at T = 300
degree room temperature is what you should always remember and this is the equivalent
circuit of BJT in common emitter you called as the impedance 1 over GM appears as beta
+ 1 that is the difference between the ahh emitter current and the base current okay
beta + 1 into 1 over GM.
And this is what is called RC this is the
second-order effect okay this is coming as an impedance across the current source. So again it is a trans-conducting device. So this is what I have already mentioned to
you that and a relationship between the alpha and beta is this. Typically for bipolar junction transistor
working at one milli-ampere current okay this will come out as GM will come out as, please
remember this 40 milli-Siemens at 1 milli-ampere at room temperature. Now we come to ahh model of three terminal
trans conducting devices if GM tends to infinitely what happens it again becomes an operational
amplifier type of device therefore you can just see that this is a three-terminal device
now where the transfer parameter goes to infinity if originally all the other parameters or 0
then only GM exists if GM is med to go to infinity for finite output again the other parameter
that you have assumed to be finite also goes to 0 it becomes the insulator at the input
port and orator at the output port.
So we have now developed the insulator narrator
model for the bipolar transistor as well as moss both moss and bipolar transistors have
the same equivalent as the insulator narrator in the following fashion. So when GM goes to infinity between the base
and the emitter that is the input voltage okay that goes to 0 and the base current goes
to 0 okay anyway gate current was originally itself 0. So we have this becoming an insulator both for
mass as well as bipolar base and the emitter region is replaced by an insulator. Gate and source are replaced by an insulator and
since this source current now cannot flow here it will flow through the train or the emitter
current will flow through the collector. So the narrator comes in series at the output
insulator comes in series at the input that is the model if the emitter is common between
input and output or the source is common between input and output.
So both these transistors lead to the same model
insulator narrator model in three-terminal okay. Now we have synthesized several such structures
using the emulator narrator voltage amplifier with game one this is the earlier synthesized
model and that can be replaced by a transistor-like junction being the emitter or source
this being collector or drain end of the collector this being the end of insulator base or gate
if you replace this you get a common collector this ahh particular structure, okay there
is a mistake again to this that is the emitter. This is the collector so the same thing source
follower this is the emitter follower, okay so the next one is current gain with gain = – 1. So the emulator comes in shunt narrator comes
in series here so input current is same as output current flowing in opposite direction
to I naught, the okay gain is ñ 1. So that is again replaced by a bipolar transistor
here and a MOSS transistor their resulting in this is nothing but a common base or common
gate which is known to have gain = – 1.
Then this is the transconductance amplifier
that we have synthesized again replacing the transistor with either MOSFET or bipolar result
in this kind of trans-conductor amplifier design and you can see these realizations
okay or nothing but this is called emitted degeneration topology this is this is the
source regeneration topology this is the emitter degeneration topology this is the last one
trans-resistance amplifier here. So we have this RF coming in shunt here insulator
in shunt, narrator is shunt resulting in a current getting transferred to the output as a voltage
II into RF with a mega design this is the topology. In summary today we have discussed a multiplier
discussion is primarily a communication application and then introduced you to two devices which
complement one another in terms of nonlinear relationship okay square law and exponential
law devices and how they are used for ahh designing ideal amplifiers also have been indicated.
