analog circuits and systems prof. k. radhakrishna rao(rtd)...

Analog Circuits and SystemsProf. K. Radhakrishna Rao(Rtd)

Indian Institute of Science - Bangalore

Module No # 07 Lecture No # 31

Wavefrom Generation

Today in lecture 31 of our will starting this discussion with oscillators wave form generators both

sinusoidal and no sinusoidal.

(Refer Slide Time: 00:35)

Before we go to that let us review what we have done in thirtieth lecture first lock loop basically

what is called self-tuned filter. A filter a second order filter with ID where low pass output phase

is compared with that of the input and it should be 90 degree so that loop gets locked to 90

degree phase shift at all the time as the input frequency is changed phase remains constant at 90

degree that is what is called as phase locking and that facilitates automatic tuning of the filter to

the reference frequency which is incoming frequency.

So the negative feedback with loop gain high maintains this lock of phase to 90 degree very

accurately over a wide range of incoming frequencies.


Now the lock range for example is can sort of that is decided by the there are three blocks one is

phase detector and then there is this amplifier plus low pass filter and then what is considered as

the voltage controlled filter whose output goes here so that is the phase lock loop the sensitivity

is called KPD and sensitivity is called A naught divided by 1 + S by omega LP. The sensitivity of

this is K VCF converts voltage to a phase difference Phi which is dependent upon this VC.

So the loop gain is nothing but KPD A naught by 1 + S by omega LP into KVCF okay if it is an

integrator this one is neglected compared to S by omega LP that is all that happens with the

integrator okay. So that lock therefore lock range is governed by any one of the limiting the

range over which they function okay this may goes to saturation or here the loop gain can go to 0

I mean KPD it goes to 0 and here Op Amps can go to saturation VCF can reach the limit of

operations okay of it is omega naught.

So any one of them whatever is lower is that one that to miss the lock range capture range again

before the loop gets locked this is added current state hopefully and this filter is tuned to some

frequency and let us say this is the low pass filter output as we had taken okay so the low pass

filter output besides of the KPD of it because it depends upon the magnitude of the both these

inputs this is the multiplier type of a phase detector.

So the amplifier of these low pass filter output also governs the KPD of this so if there is no

amplifier there is no chance of this locking so one as to come very close to the VCF omega

naught Q let us say omega naught Q at which some output can be got so that this KPD can be

substantial in order to make the loop lock itself okay. As I capture range is always less than the

lock range capture must occur before long capture range is less than the lock range.

Lock range decided by the limits of any one of the PL in capture range occurs always close to the

croissant state where the loop can gain can be held that is the way the automatic locking occurs

of phase to 90 degrees summary of filter design was discussed second order filter blocks can be

cascaded together to form a complex higher order filter second order okay than okay first second

third second order so on then there may be a first order if it is hard.

So that is how you get the filter higher order filter design done poles of the second filter peak

around the band width okay this if one as to decide design let us say low pass or band pass okay

as a frequency like this then one knows that the basic second order is going to be like this at the

center frequency and this is the basic thing then other filters must be located okay with higher

and higher queues on either side of this okay.

So that this fall in gain can be compensated by peaking so we have these other filters which are

built around the pass band H okay so that it becomes maximally so these gains will be higher and

Q’s will be higher with the resultant effect one can get a maximally flat structured okay and if

you want to get rid of specific frequencies that must be zero’s located there and those zeros okay

bring about some variation in the pass band so that is a gain compensated for by more peaking by

these higher Q filters around the center frequency okay near the pass band edge.


So these are the intuitive feelings about the filter designs so one can actually really do the filter

design by a locating this second order suitably just by observation first locate zeros wherever

narrow band noise is present then locate the polls with peaking near the pass band edge if it is a

low pass filter okay R band pass filter higher Q poles with the higher frequencies get located

closer to the band width this is for the low pass okay.

Effect of gain band width product is to cause Q enhancement which can be compensated so all

these factors are important in this design okay the Q enhancement product how it can be

compensated without increase in the number of Op Amps and active devices.


Now wave form generation not drastically different from the filter design first let us know why

we should generate waveforms waveform generation is needed primarily for testing and testing

is important part of product manufacture or IC manufacture so testing and operation analog and

digital systems require very pure sine view to find out the distortion for a given particular stage if

it is linear system okay and also to obtain the frequency response of a given system the sine wave

is important.

So whether it is testing of DAC ADC or anything these test wave form as to be precisely

generated with the stable frequency and stable amplitude okay. Cock this is a important thing it is

like a heartbeat of an electronic system. So the clock generation is a very important part of

today’s system design it is necessary in digital systems also it comes necessary in switched mode

analog systems.

Square view there is one of the wave form there are necessary as clock for example even

rectangular wave with pulse width modulation okay generation these are now becoming more an

more useful okay in terms of efficiency because the active devices is mainly used as a switch in

these. Saw tooth waveform generation it is mainly for this displaying wave forms in

oscilloscopes also in category or television receivers triangular wave form this is again an

important version of symmetric wave form or sine wave okay which as a rich harmonic content

in it.

Arbitrary wave form for some applications arbitrary wav form are required so that one form one

can generate get gathered multiple information about the characteristic of the system. In all these

things constant amplitude as frequency varies is a must. Amplitude must be independent of

frequency variation precise adjustments of amplitude is necessary frequency stability is another

important aspect in oscillator design. So all these we will touch upon in terms of detailed

discussion as how to achieve these.


So these are the typical waveforms this is a sine wave this is the clock view this is the triangular

view is this the saw tooth this is square view this is the arbitrary waveform. So in all these things

again the amplitude and the frequency become very important or design stability of this.


Coming to the fundamental aspect of sine view oscillator this is something that you have studied

in your plus two because everybody knows that this is what is called harmonic oscillator

equation del squared X by delta squared T square okay this is here is this a + K = 0 so solution of

that is X = A amplitude sin root K is K forms the root K forms the radiant frequency of the wave

form plus this is the phase A and phi depend upon the different conditions that we know.

In the case of electrical oscillation X is replaced by the voltage or current that solved the

differences so in our network or current exists at any point is governing this kind of equation if it

is an oscillator.


So what is it actually what is the network this we have already seen earlier when introduced you

to the inductor and the capacitor this is the storage element this is also a statement this source

energy in the form of the electro-magnetic form in this the energy stored in the electrostatic form.

So it keeps on changing from one form to the other right switching from one to the other that is

how the harmonic oscillation works.


Now that is by equation is indicated as V = - L DI / DT = 1 over V integral IDT. So this now

forms the second order differential equation with the DI by DT term being absent that is why it is

called as harmonic oscillator this quad by DT squared + I by LC = 0 the solution of this I = some

magnitude IP existing the initial conditions IP is determined by the initial condition IP sine T by

root LC it is root K1 over root LC is the coefficient K squared governing this.

So this is the frequency omega = 1 over root LC + phi IP sin omega LC + phi IP and Phi depend

upon the initial conditions omega N is the frequency which is 1 over root LC.


If the capacitor is initially taught to 1 volt let us say at T = 0 an inductor current at T = 0 is then I

= IP sin omega and T phi = 0 because at T = 0 N = 0. So phi is automatically 0 it is a sin wave

starting with 0 reaching IP after quarter of a second DI / DT therefore the slope at T = 0 however

is IP by omega N Cos omega NT is cosine and L DI by DT is multiplying this by L okay you get

the voltage that is present okay across the inductor okay L DI / DT okay.

So omega N = 1 over root LC which is also the voltage across the capacitor natural frequency of

the system okay if will be DI by DT = 1 volt okay IP = omega N amperes okay that is how the IP

gets fixed by the initial conditions.


So this is what is simulating it L = 1 milli henry C = 0.1 micro farad gives you a time period for

the wave form off okay 63.61 micro sec. So voltage across C = 0 is 1 volt and current through

the inductor at T = 0 is 0. So we have this current through the inductor in the voltage across the

capacitor and this is the sorry current through the inductor and voltage across the capacitor starts

with 1 volt goes on like this so that is sustained throughout and this frequency is exactly what we

have calculated 63.65.


So now if there is a resistance across this the equation turns out to be V by RP total current plus

this is actually now being called as harpy plus 1 over L integral VDT that is the current in

inductor CDV by DT is the current through the capacitor. So summation of all these current

should be 0 that gives a second order equation it is D squared B by DT squared + 1 over PC DB

by T V + LC = 0 which gives us normalized representation of this as omega N squared so this is

called Q if the tank circuit is called a circuit.

Because it can store energy okay if the Q is infinity very clearly stores energy in one form or

another or it is an oscillator. So Q = omega NRPC RP into root of C by L omega N being 1 over

root LC if you replace this is the Q of this tank circuit parallel resonant circuit omega N is the

natural frequency Q is known as quality factor of the resonant system.


It is ability to stock energy it indicates Q = infinity means it is very nearly storing energy so the

circuit is popularly known as the tank circuit because of its ability to store electrical energy okay.

Now writing down the whole thing in applause transform and solving for the roots of this you get

S = - omega by 2Q okay plus or minus omega N by 2 Q square root of 1 – 4 square for Q less

than half there are two poles on the negative real axis okay.

This is omega N by 2Q – this is sigma this is G omega axis of your S plane so this is – omega N

by 2Q + omega N by 2Q square root of 1 – Q squared this is – omega N by 2Q square root of 1 –

4Q square. So these are the complex conjugate and these are the poles on the negative real axis

they become complex conjugate pair for Q greater than half then the poles are going to be

located like this.

Let us see so this is – omega naught by 2Q okay or higher Q is going to be closer to the G omega

axis this distance is decreasing and the this is the complex conjugate pair of poles. So varying Q

you get it in a if you put it in a normalize fashion where you put a sigma by omega N + J omega

by omega N and then it becomes a unit circle otherwise it is going to located around this point.


Now typically for this circuit for the same value of L and C R is put as 1 kilo Ohm so that Q is

10 now what is the physical significance of this. There are therefore it starts with 1 volt nearly 1

volt and then you go on up to 110 and then you can count 1 to 10 such peaks before with it

becomes after which it becomes less than 0.1 volt. So there are 10 such peaks appearing okay as

far as this time circuit is concerned this way you can quickly estimate the Q of this system.


Now what can we do to enhance this Q so that it can oscillate so this loss which may be due to

combination of capacitor loss and inductive loss combine to single resistance in parallel can be

compensated by a negative resistance which is going to be simulated by a de active device so it is

negative resistance which is the active simulated one in any oscillator.

So you can use any LC oscillator whatever may be the type okay as basically having some loss

component compensating compensated by the negative resistance. So whether it is hardly

oscillator cockpit oscillator or any crystal oscillator any of these belong to this category of this

LC oscillators and we will see later how it can be a part of as bringing about a negative

resistance. So this is the basic principles.


So how to simulate this negative resistance this negative resistance of course can be simulated

using active device in our present we are taking an Op Amps it could be a FET or a bipolar

transistor or a MOSFET or a junction any of these can act as active device to simulate this

negative resistance.

So we have LC and the R so this circuit is the one that simulates negative resistance we had

already discussed in our filter case right please recollect this entire with a gain of 2 for example

simulates between its input okay and ground and negative resistance of – RP dash how does it

happen ? RP dash is connected between input and output of a gain of two stage because it is

having R and R here the system is nothing but a non-inverting amplifier with a gain of 2 this is 1

– G okay this means this is –RP dash.

So whatever resistance is connected here in the gain of 2 situation that gets reflected as negative

resistance. So that is how we simulate and the effective resistance therefore is the original

parallel positive resistance the loss component shunted by – RP.


That is a shunt combination of RP and RP dash which is the effective resistance actually it is 1

over effective resistance please remember that 1 over effective resistance therefore = 1 by – RP

dash + 1 over RP that is the admittance that should be negative so that means RP dash should be

less than RP in order to make it negative if RP dash is greater than RP it is positive effective

resistance.

So then the oscillation amplitude will progressively increase instead of decreasing in our earlier

situation we have seen by putting 1K resistance across the LC a finite Q makes it decaying sine

wave whereas if it is having effective negative resistance it will be a exponentially growing sin

wave as it is shown here. So in order to be self-starting an oscillator has to be self-starting or as a

requirement.

First of all this condition should be valid that means the initially that should be a negative

resistance effectively across the L and C which facilitates growth of sin wave oscillation from a

initial energy that is just some little bit of noise has to be there okay and then it has to be having

effective negative resistance then it will be self-starting and it will keep on growing. Then as it is

keeping on growing you must make sure that the required amplitude of oscillation the effective

resistance should be infinity so that Q of the system is infinity.

So at that amplitude the oscillation get sustained once again let us understand initially it has to be

negative so that there is a growth of oscillation at the required amplitude of oscillation this

effective resistance okay should become infinity so that the Q becomes infinity so that amplitude

it gets sustained.


So the resistance RP dash must be made non-linear such that it increases in magnitude as voltage

across it increases to a given amplitude so R should be dependent upon the voltage or current

right. In a such a manner that R at a given amplitude it only becomes equal to RP that is this is

RP dash I should say magnitude of RP dash should be voltage dependent it should be less than

RP initially at the required amplitude it should be exactly = RP it is SS at that amplitude of VP.

This effectively means okay that admittance of the entire network this is inductor this is

capacitor. so we have omega N = 1 over root LC what odes it mean omega NL = 1 / omega NC

that means the effective suseptance of the whole system is 0 and effective real part is also 0. So

the total admittance net admittance of this at omega = omega N = 0 this is what makes a sin

wave oscillator.

So please again remember in terms of a network design its total admittance should be going to 0

at omega = omega N precisely that means both the real path and the imaginary part should go to

0 at the same frequency = omega = omega that is then a candidate for sin wave oscillator

negative resistance can be obtained by using tunnel diode for the example it is negative

resistance which is called N type of negative resistance okay this is voltage that than this current

say this we have discussed earlier and the discussed devices BJT’s and FET’s or Op Amps.

We have seen how it can be done with the help of an Op Amps now diode BJT’s and FET’s are

used in a micro wave ranges okay Op amps are used at lower frequencies.


Non-linear negative resistance how to bring about this a grounded negative resistance can be

simulated by using an non inverting amplifier of gain greater than 1. So if you have let us say

non-inverting amplifier let us say non- inverting amplifier. So any gain greater than one so this

gain is 1 + R2 over R1 so it always greater than 1 as long as some value of R2 some value of R1.

So it can always simulate therefore a negative resistance it is not necessary that R2 should be =

R1 so that it is = 2 in that case this resistance self gets reflected as negative otherwise the

resistance will be different okay by the extent. So what is the negative resistance that gets

simulated that is going to be just this R divided by 1 – G which is – R2 by R1. So this is known

as the negative impedance invertor or convertor because depending upon which resistance is

being used as a terminating resistance it can be called an inverter or convertor.

So this is an important block so frequency of oscillation is 1 over root LC now the amplitude of

oscillation if it is not limited by anything all the way can go up to this saturation limit of the

device in this case if you consider that these are the supply voltages VDS and – VS after it

reaching saturation + VS or – VS there is no such negative resistance that gets simulated here. So

the gain is 0 the loop gain goes to 0 and therefore it does not work as a negative resistance an

longer.

So what happens if this is the limit + CS – VS is the limit up to which it works as a negative

resistance then that divided by 2 is the limit up to which resistance at the input can work at the

negative resistance. So that is the main contention of this what happens to this negative

resistance it will just let see the negative resistance okay as far as this input is concerned right if

this is V and that is I so then ultimately it gets limited to VS by 2 and V2 by 2 on either side okay

with slope which is determined by -1 over RS here it is 1 over RS here this is I okay.

So this is positive resistance of 1 over RS in fact okay that is the slope and this is the negative

resistance which is -1 over RS. So delta I by delta V is the slope so it is going to useful only in

this range okay.


That is what is plotted here because this is output is limited to + VS and – VS because of its

saturation limits this negative resistance effects is seen only until this voltage reaches +VS – VS

between this voltages half of this. So up to that value of V it is negative there after only the

positive resistance occurs because this is constant and this voltage – this constant voltage by RP

dash is the resistance it sees which is giving you the slope of 1 by RP.

So this is the point that we have to see here it is V okay – VS and by RP RP dash these are all

dash okay. so that is the limit here it is going to be equation is V + VS by RP dash so only here it

is negative resistance okay where it is V – 2V by RP dash.


So let us see what happens due to this the RP dash used to 600 Ohms RP is 1 kilo ohms so it is

much less than this effective resistance of this parallel combination is same C and L are used C is

made 1 micro farad R = 10 kilo ohm Op amps used to LM 741 to simulate this so one can see

that there is a growth of oscillation taking place and then it gets limited to this supply voltage

which is nearly plus minus 15 volt for this.

So it gets limited to that you can see it almost okay gets chopped of here and here so we do not

want this to be dependent upon the supply voltage and all that. So would like to limit it to voltage

lower than this okay so that can be done one way is by using a nonlinear resistance okay what is

one is same negative resistance effect is brought about RP L and C gain of 2 stage RP dash – RP

dash comes across this except that there is a positive resistance which is brought only when the

voltage across RP reaches the Zener voltages.

That is in this case chosen to be one volt Zener that means it can limit the or it comes into picture

or it switches on shunt resistance across RP and lowering the positive resistance or making that

becomes dominant only when the amplitude of voltage is reaching plus minus 1 volt. This is a

very crude mechanism of limiting the amplitude to whatever value you want independent of the

power supply with this kind of limitation one can see that this output the non-linearity of this

Zener brings about this linear resistance in series with it okay and whole effect is coming to

picture and limit the amplitude to something like 3.6 volt in this case okay.

So very close to let us say a lower value than the supply voltage so and it looks almost like the

sin wave however please remember this amount of current flowing in this which is bringing

about the effect of this resistance in shunt with the RP is the one that bringing about non linearity

in the wave form. So brining about amplitude stabilization using this kind of non-linearity or the

non – linearity due to the Op Amps is causing distortion in this sin wave okay.

So it is at the expense of this distortion that the amplitude is getting limited okay however the

frequency is okay almost independent of the amplitude if these are not frequency dependent if

these are frequency dependent okay this non linearity is frequency dependent then that frequency

dependent will shift the frequency of the system. This will later on see in the next class however

you can see that I can get a fairly good amount of sort of distortion reduced due to clipping etc

by introducing a smooth non linearity okay with the device okay.


Now precision amplitude precision amplitude stabilization this precision amplitude stabilization

is brought about by again in the same circuit by using an amplitude stabilization technique using

a control system this is what is called automatic gain control. The gain of this loop should be

controlled in such a manner that in this case for example okay this whole system is bringing

about this RZ effect in shunt with RP by means of a control here.

So I am sensing the output amplitude I am sensing it using a multiplier so if you have this output

let us say it is fixed at certain amplitude VC sine omega T so what is the amplitude it is VP

squared sin squared omega T by tan so sin squared omega T is 1- Cos 2 mega T by 2 so it is VP

squared by 20 which is the DC voltage which gives a measure of the amplitude of this sine wave

so if a low pass filter or an integrator is put that gets rid of this component okay.

So the DC component corresponds to the VP squared by 20 that is compared with positive

voltage square and it is compared with the negative voltage okay which is V reference right. So

that is when the integrator stops integrating and keeps a fixed value of voltage such that an

amplitude stabilizes at that point. So this is he comparator same control system that we have used

earlier in PLL and all that so this voltage is the reference that voltage is 0 that means this current

is same this current.

So that is under this condition that means C peak gets fixed as square root of 20 times V

reference. So precisely we can adjust the amplitude to remain at this constant value of 20 times V

reference. So irrespective of the frequency of oscillation decided by this so this is the gain

determining loop here okay such that this compensation occurs precisely okay when this control

voltage which is remaining unaltered is applied to this and that control voltage gets amplified

when this condition gets satisfied in this controller.

So this voltages should be equal to this that is 0 so that these two currents are one and the same

in the steady state DC currents so you can see now this control system working that is there is

growth on oscillation working place initially okay and that is necessary that means this voltage is

such that effective resistance is kept negative so that it starts building up then as the buildup this

voltage keeps increasing and therefore it is applied to inverse.

So this voltage keeps decreasing until it reaches a point and it remains constant that is when this

voltage is 0. So output amplitude remains constant at this for this actually V reference has been

chosen to be say 0.2 volts so that 0.2 into 20 is 4 square root of 4 is 2 so this doubles at a

amplitude of nearly = 2 volts or here it is this is taken as 0.45 a V reference in which case it is 9

here and it is square root 9 which is 3 so that is exactly what it is getting stabilized at T.

So I will use two values when it is 0.2 and 0.25 so that it is precisely a 2 or 3 so this is the

stabilization V reference in this case is 0.45.


So this is the technique of and we can see that VP = precisely = 3 volts 3.04 okay this I have

sampled small portion of this in this steady state so that is indicating exactly 3.04 as simulated

amplitude for V reference = 0.45 so this is precise amplitude stabilization.


So what is the called automatic gain control system or AGC or ABC which is one of the most

popular blocks analog system block used in communication receivers cell phones or television

receivers or radio receivers from time immemorial. So this is part and parcel of communication

system as the front end RF or IF okay all these amplifier are controlled such that output of these

stages are remained fairly constant irrespective of D received put at the antenna which keeps

fading often okay.

So that is simulated using this AGC system which is part and parcel of all sin wave oscillators if

they have to precise stabilization of amplitude and part of all communication receivers so VP sin

omega T is fed to that let us consider this to that voltage control amplifier which is nothing but a

multiplier VXVY by 10 so VY is VC so this amplifier gain is VC by 10 that into VP sin omega T

is the output.

So this is the output that is easier depending upon VC and then it is squared just like we did in

the amplitude stabilization loop for sensing the output amplitude in terms of DC so you get here

VP squared by 20 right that is VPO let us call it is = VPO. So this VP is different this VPO it is

multiplied by VP by 10 okay. So this is VPO square by 20 is the DC that is produced that okay

has to be = the negative reference that is put there so what happens here that if the input is 0 for

example and V reference is still there it is 0.

So this negative voltage will make this go to positive saturation so it is starts with positive

saturation right that means it starts with highest gain possible for VC which is let us say 10 volts

so the maximum gain of this is 1 okay. So this output is going to be input is going to be just

reflected at the output if it is 0 nothing comes there so whatever it is applied comes with gain of

1 as long as this is in saturation as the amplitude is increased as a certain when this voltage is

rich okay then this starts increasing above this then this is positive.

So this goes towards negative saturation or it becomes less positive as it becomes less positive

the gain of this reduces a value less than 1. So output is going to be sort of decreasing such that

this voltage ultimately gets adjusted to be = square root of 20 times V reference that is the

negative feedback that is working for you as AGC okay.


So for input voltage of 3 volts and V reference of 0.2 we have simulated the same circuit here

using multiplier okay and you can see the control voltage from maximum saturation it is coming

down to the steady state value of 6.9 volts required to maintain an output voltage of 2 volts

because expected output voltage is 2 volts so it is coming out as 2.054 volts right. So that is with

the reference of 0,2 into 20 is 4 square root of 4 is 2.

So now let us say we change this input voltage now 3 volts to some other value let us say 10 volt.


So again this control voltage is adjusting automatically such that it comes to 2 volts from the

original 6.9 volts so as to maintain the output as nearly 20 volts 1.946 volts. So this is precise

AGC control system so if the input is greater than 2 volts the AGC takes over if it is less than 2

volts since our multiplier only work up to 10 volts let us say.

So then it is going to be struck at saturation value of Op Amps or that of the multiplier input

which corresponds to 10 volts that will maximum gain it can give is 1. That means up to input

voltage of 2 volts it is AGC does not work it is going to have a gain of 1 throughout maximum

gain possible. So the AGC dynamic range V naught VP naught is going to be in the case of 2

volts remains up to a input voltage VP of 2 volts it follows the input voltage with the slope of 1

and then it remains constant at 2 volts.

So this is how the AGC function then beyond 10 volts the multiplier against stops functioning so

we have that sort of remaining constant the gain remaining constant okay at that value

corresponding to that. So there is no point in using this so this is the AGC range lock range.


Lock range is determines by the range of operation of the multiplier output can be limited input

can be limited to 10 volts let us say saturation range of Op Amps whichever is lower so we have

here the various blocks this is one block as far as the loop gain is concerned it is delta VPO delta

VPO change in output variation for a delta VC that is that of the VCA this being constant. So it is

now going to be = to VP by 10 because this is directly proportional to VC.

So it is this is the K VC of this block VP/ 10 it depends upon the VP so if VP is more it is going

to be more and as far as this is concerned this is going to produce an average delta V average

divided by delta VP that is the transfer parameter of this or sensitivity of this. So that is going to

be nothing but 2 VPO by 20 that is that of the amplitude conversion AC to DC convertor. So that

is K AC DC this is K VCA and then the integrator transfer function is 1 by S here okay.

So minus so the loop gain is nothing but KVCA KACDC into – 1 by SCR so the change in what

is that amplitude for a change in reference this change with respect to this change is what is 1 by

1 + 1 over loop gain which is going to be K let us say VCA K ACDC into 1 over SCR. So that is

the transfer function the band width of that is controlled by this is the transfer function for delta

ACDC convertor to delta V reference.

So let us say unity gain is minus this is the transfer function of this loop so in conclusion we have

discussed here a very interesting loop which is called AGC AVC and we also discussed the

aspect of sin wave oscillator LC oscillator the harmonic oscillator the fundamental oscillator

circuit in electronics and how the amplitude stabilization can occur approximate amplitude of the

amplitude using nonlinear devices then precise control of the amplitude using gain control loops

thank you very much.

analog circuits and systems prof. k. radhakrishna rao(rtd)...

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