 So today in our 20th lecture we will be discussing one of the important control circuits DC voltage regulators. DC voltage regulator how ahh this is an application of ahh negative feedback in fact all regulators whether they are speed regulators or position regulators or voltage regulators, current regulators, frequency regulators, speed regulators okay all of them ahh are ahh following the same basic principle of negative feedback with a reference. Now we had already discussed ahh an application of ahh ahh op amp in combination with ahh output transistors or in combination with bipolar or MOS transistors forming variety of signal processing functions in negative feedback. Today let us therefore consider the DC voltage power supply. We derive the DC voltage power supply using AC line AC AC to DC converter this is the line AC which is 230 volts 50 hertz and we are converting it to a DC voltage using AC to DC converter which is nothing but a rectifier in combination with the capacitive filter. Voltage regulator is supposed to make the output voltage independent of the line voltage the output voltage should remain constant independent of the load voltage line voltage temperature these are the factors that characterized voltage regulator here. So we will go into the details of how such a control circuit can be built. So AC to DC converter. Full wave rectifier with capacitive filter this has already been touched upon in applications of passive networks earlier. So this is just ahh revision of what we have already done VP sine omega t the line voltage gets applied here and there is a center tap transformer N is to 1 it gets converted so we have VP sine omega t by N here and again plus VP sine omega t by N minus VP sine omega t by N here around the center tap and this is rectifying the positive part this is rectifying the negative part and pumping it into the common capacitor. So we have the voltage waveform here in this case going like this that is suppose at this point. So this is going up to VP by N and this particular thing is diode is conducting for the positive half so we have that getting repeated here and this one is pumping the negative half in the same direction positive. So this particular output is because of the capacitor if the capacitor is not there it just the load is there this is the waveform and because of the capacitor we have the waveform dropping discharging. So that is almost linear and if the load current is II II by C is the rate at which it decays that into t so within a time period of t by 2 you have this dropping by this much that will be the peak to peak ripple that is occurring at the hurt. So based on the requirement of peak to peak ripple capacitor selection can be done because t is equal to 20 milliseconds corresponding to 50 hertz. So this is the complete design of the AC to DC converter and the DC voltage that we can approximate is VP divided by N that is the VDC. So N can be fixed based on what the unregulated DC requirement is for the input of the regulator. So this now goes into the input of the DC regulator. So we have this DC voltage which has been derived across the capacitor which is VP by yarn so APS here as DC as VP varies from its minimum to maximum this DC voltage will correspondingly vary VP minimum by yarn to VP maximum by yarn as the line voltage varies output has to be constant at a specified desirable value that is the voltage regulator function. We must have a device here that is active that is put here that is normally called the pass transistor. So the pass transistor comes between input and output of the voltage regulator in series okay and the drop across this is controlled in order to keep the output voltage constant it is equivalent to putting a potential divider and adjusting the output of the potential divider okay to remain constant okay comparing it with the reference okay and therefore varying the drop across the series resistance that is replaced by an active device that is the pass transistor okay and the control circuit will see to it that that voltage drop is continuously changed in order to maintain this constant. So this control circuit is what is necessary let us therefore characterize the power supply in terms of important parameters this is again a revision because this has been dealt with when we discussed Zener regulator earlier. So earlier Zener regulator was discussed in passive devices so all these definitions were dealt with earlier also. Now in this case input power of the voltage regulator is input voltage times input current that is the input power output power is obviously V naught into I naught in that two port network. So efficiency is output power divided by input power. So we would like to maintain design a voltage regulator in such a manner that efficiency is very close to 100% so that means the power that is spent in the voltage regulator itself should be minimal. Now power dissipated in the voltage regulator is input power minus the output power. So this particular power dissipation has to be kept to the minimum. In order to keep it minimum what is done is since input power is VI into II output power is V naught into I naught I naught is different from II only in terms of the bias current requirement of the voltage regulator. So that bias current is in addition to II I naught that gets supplied in II. So if I naught is made close to II for if improving the efficiency then VI minus V naught into I naught is the power dissipated and that power is primarily dissipated in the past transistor in such a situation and the way to maintain good efficiency is to maintain this difference voltage VI minus V naught to the minimum as far as the circuit itself is concerned should be kept to the minimum. This is known as this voltage is known as dropout voltage. It is one of the important criteria in design in order to improve efficiency. Let us consider other parameters associated with voltage regulator line regulation. The line regulation is percentage change in V naught as the input voltage VI changes from its maximum to minimum that is delta V naught by V naught into 100. Load regulation is percentage change in V naught as the output current I naught is changed from its no load value to its full load value minimum to maximum again. It is delta V naught by V naught into 100. Temperature coefficient of output voltage this is an important criteria. Change in output for a small change in input voltage at a specified output voltage okay. So change in output that is actually called this temperature coefficient of output voltage is change in output voltage for a small change in temperature at a specified output voltage expect in terms of parts per million delta V naught by delta T okay around a specific output voltage okay parts per million. Output impedance change in output voltage for a small change in output current okay for a given load current ripple rejection factor. Percentage change in output voltage for a small change in input voltage around the nominal value of input voltage delta V naught by delta VI into VI by V naught is the power supply rejection ratio expressed normally in terms of 20 log that ratio is in decibels this should be very very small. Now other things are also of interest load and line transient regulation. Voltage at the output terminal is likely to have undesirable transient at the time of switching on the input power or when step load change changes occur. The output impedance of the voltage regulator is a complex is normally complex impedance okay. It is not necessary that it is purely resistive all the time and the impedance is evaluated at the frequency at which power is delivered to the load. The load may be working for a certain frequency of operation it may be an RF circuit or an IF circuit okay. So it is at that frequency that the DC voltage is to be maintained constant therefore that the regulator is supposed to maintain voltage constant at that particular point even at that frequency. So output impedance is of great importance depending upon the use of the voltage regulator output in applications. The presence of feedback loop with large loop gain and the multiple poles associated with this loop makes the output impedance pretty complex. Compensation has to be provided to make the output impedance somewhat resistive and low. VCVS as a voltage regulator. Now let us consider the actual design of this voltage regulator. So we have a reference later on we will see that this particular thing also is available as an ICJ because this voltage reference need not be necessarily a Zener it is equivalent to a Zener so but it can be a circuit so that the voltage or the reference voltage the Zener voltage here as zero temperature coefficient simulated okay. So and if it is biased by means of resistance for example it is taking the unregulated voltage and converted into a bias current here which is V unregulated minus VZ by RZ that is the Zener regulator that we had earlier seen. So that itself can be the input to this voltage control voltage source this has already been discussed earlier in application. So R1 and R2 form the attenuation network R1 by R1 plus R2 from the output of the op amp to do input. So this is nothing but the feedback circuit which is called by us as a voltage controlled voltage source with gain equal to 1 plus R2 over R1 attenuation is R1 by R1 plus R2 inverse of that is the gain of this. This is nothing but G parameter that is important for voltage controlled voltage sources this also has been discussed that is it is H feedback. So including the load and the source impedance everything load impedance source impedance and finite gain frequency dependence of the gain one can evaluate the G parameter of this H feedback circuit this was the topic of earlier lectures. So by putting finite load and assuming finite output impedance for the op amp and input impedance also finite right source impedance being finite gain frequency dependence also being taken care of one can evaluate the total effect of all these parameters on the performance of the voltage voltage source and how the macro model of such a device can be evaluated in terms of G parameter also has been told okay. So the voltage regulated output is going to be 1 plus R2 over R1 into VZ. So VZ being constant assuming that it is not changing with respect to temperature it is not going to change with respect to the current through it okay. Then the regulated output voltage is 1 plus R2 over R1 into VZ. So we can design this regulator for any voltage that we desire. So this can be for example 10 volts or 15 volts and then we can find out for a given reference what the ratio of R1 by R1 plus R2 is that completes the design. Now as the unregulated voltage keeps varying from its minimum to maximum what actually happens is the current in this keeps varying and VZ varies to a certain extent that variation in VZ also comes into picture at the output as the direct variation that is equivalent to line regulation factor change in this voltage correspondingly change in VZ okay how that gets reflected is by this gain right. So you have to minimize the variation in current here so one way to do that is to use this output which is going to be regulated okay and it will remain constant for biasing the Zener itself. Then what happens is at the initial point this Zener might have broken down and therefore the voltage across the Zener is going to be 0 it is off okay and this entire circuit will remain off. So it needs a starting circuit which is again a resistance okay with a Zener there okay and then that circuit biases this so that output goes to roughly this value and then that biases the second Zener right when that is biased this is taken off that is called a starting circuit. So in normal regulators in order to improve line regulation this Zener is biased using the regulated output voltage itself in which case it needs a starting circuit for initializing the output voltage to roughly close to this value and thereafter the regulator okay takes over. Now the application of voltage regulator as feedback system we have already discussed this its dynamic performance characteristic as a feedback network G1 is the gain of the open up gain of the op amp in our control system sort of terminology this was the G1 block and this was the G2 block. So G1 is equal to G10 the DC gain divided by 1 plus S by omega 1 the first pole okay and 1 plus S by omega 2 the second pole. So this kind of 2 pole characteristics also has been discussed at the system level discussion on feedback systems okay and how the distance between the first pole and the second pole should be very nearly equal to the DC loop gain okay is what was discussed as the Q factor being made equal to 1. In such situation over the useful range of this particular device this factor is more dominant than this one. So this is the dominant pole then it is called and it is called dominant pole compensation. So in such situation G10 into omega 1 by S is the approximation to this that into 1 plus S by omega 2 okay that way in internally compensated op amps have omega 1 that also has been discussed very nearly equal to omega 2 by G10 this is done in order to make the Q of the system of the second order system become equal to 1. So that for the transient response of the feedback system with unity gain this is for the unity gain topology of this Q is equal to 1 okay if you select the what is that first pole as equal to second pole divided by the DC loop gain. So this is the DC loop gain so hence G1 is equal to GB divided by S this is called the gain bandwidth product that also has been discussed for a system level discussion G10 is the DC gain omega 1 is the first corner frequency and G10 into omega 1 is called the gain bandwidth product of the system. So G1 is equal to GB by S so almost the op amp behaves like an integrator itself that with the second pole effect taken into account is the loop gain of this unity gain system designed using the op amp. Now in the feedback path if you introduce this attenuator then the DC loop gain is going to be getting multiplied by R1 by R1 plus R2 it is going to be less that is Q in such a situation of modification okay Q becomes less than 1 when R1 by R1 plus R2 factor gets introduced okay Q becomes less than 1. So the system slows down so this is the depiction of the loop forming the negative feedback in voltage control voltage source GB by 1 plus S by omega 2 that divided by yes so this is the transfer function of the op amp and this is G2 this is the error detector. So V naught by VI for such a system is ideally equal to 1 plus R2 over R1 however in reality it is 1 plus R2 over R1 divided by 1 plus 1 over loop gain always and the loop gain has already been depicted as GB by S okay into R1 by R1 plus R2. So GB by S into R1 by R1 plus R2 that is the factor that we have read GB by 1 into R1 by R1 plus R2 so this goes up there as 1 plus R2 over R1. So the whole thing is now 1 plus R2 over R1 divided by 1 plus S into 1 plus R2 over R1 divided by GB S squared into 1 plus R1 okay divided by omega 2 into GB. Now the transfer function of the overall system now becomes 1 plus R2 over R1 frequency dependent and the Q is root of GB divided by 1 plus R2 over R1 into omega 2. So if it has been designed for unity gain with Q equal to 1 that is this is 0 so we have root of GB by omega 2 as Q and GB is equal to omega 2 is what is going to happen okay and in the design that is how omega 1 is going to be chosen in order to facilitate Q equal to 1. All the internally compensated op-amps have this GB nearly becoming equal to omega 2 so that they have Q equal to 1. Q equal to 1 means again we have discussed this in the transient response when we give a step okay is going to be if you give a unity step as input there is going to be one peak okay and it is quickly coming to statistic this rate of rise is going to be the fastest. So voltage regulator feedback high rate of rise and least amount of ringing occurs at Q equal to 1 G2 equal to VZ by V0 is equal to R1 by R1 plus R2 is determined by the required output voltage. So whatever is going to be designed is based on what we need as we not for a given VZ so R1 by R1 plus R2 is what we are designing then what happens as omega 2 and G1 0 are fixed for a given op-amp omega 1 is chosen to make Q equal to 1. So this is how omega 1 should be chosen and for this it is better to have a externally compensated op-amp instead of internally compensated op-amps like 741 and TL081 okay so that the Q can be made equal to 1 for any chosen value of R2 by R1. So again internally compensated op-amps have Q equal to 1 for V0 equal to VZ or G2 equal to 1 omega 1 has been already fixed as omega 2 by G1 0. So for any other G2 less than 1 so that gain is greater than 1 Q will always be correspondingly less than 1 resulting in unsatisfactory transient response. So the transient response will not be satisfactory like the unity gain case right. So it will be having Q which is much less than 1 that means it will be sluggish in rising to the required voltage every time switching occurs. It is therefore necessary to use uncompensated op-amps like LM748 to design voltage regulators with good transient response for the desired value of V0. A design problem design a voltage regulator with a reference of 1.2 volts for a regulated output of 10 volts for a maximum load current of 15 milliamps using op-amp. So we select the op-amp let us say 741 or TL081 we know that these op-amps have roughly the short circuit current or the maximum current possible as above 20 to 25 milliamp years. So this requirement is already met with. So they have a short circuit protection in the IC itself. So they can only act as voltage control voltage source up to the maximum current beyond that they act as constant current sources giving the maximum short circuit current whatever with the load. So that kind of short circuit protection is also necessary for a voltage regulator. Now since 10 volts is the output voltage that we desire and 1.2 is the reference this 1.2 volts reference is known as band gap reference which is also available as an IC with 0 temperature confusion very few parts per million per degree centigrade rise in temperature over the military range of temperature. So 10 by 1.2 is what we should select as 1 plus R2 over R1. So if you select R2 as let us say this R1 as 1.2 this as 8.8 K then the design is over okay. This RL is equal to let us say we have designing it for 10 volts okay and current is maximum load current so RL minimum will be 15 10 by 15 K. So this is the choice that we have done. We also put a capacitor across the voltage reference so as to reduce the ripple appearing at the output okay power supply rejection ratio can be improved by putting such capacitors across the reference. Now simulation we change this voltage from 9 to 9.1 let us say then this is considered as small signal okay step so that the transfer function that we have assumed for the 741 can be valid. So it is showing that there is just one peak that means in fact 741 has already been designed for working at unity gain with Q of 1 because there is one peak. Now if you design our regulator using this as R1 and this as R2 obviously we get the output voltage as 10 volts okay and the Q is going to be very poor okay much less than 1 okay and therefore you can see that the rise time has increased considerably there is no ringing but it is exponential okay because the Q has correspondingly got reduced okay. Now coming to the current boosting of past transistors. So as far as the devices are concerned like transistors are concerned op amp okay is able to deliver only let us say 20 milli amperes for example in our case the general purpose op amp and we want to boost that current to higher level. So we can use a trans conductor like bipolar transistor or MOS transistor like this. So these are the current boosters that can be used in order to boost up the output current level and this particular device for example you just replace the transistor okay with transistor okay driven by an op amp then this is called a super transistor this kind of technique is adopted in IC design also right. So this power boosting of the device can be done this way. So here this is a new MOSFET for example with the same source and drain but gate is nothing but the input of the op amp. So the GM of this combined device now becomes GM into A naught that is why it is called a super transistor. So at the output therefore it can come in series and form a better transistor for delivering the required amount of power. So all these are power transistors okay we can handle large amount of current in the load. So in the unity gain this is the voltage follower mode okay and our regulator simply becomes just this. So we have the Zener set so the output voltage is connected to a load here. So this VZ is the Zener voltage at the output V naught equal to VZ and the current is going to be almost the entire load current is going to be carried by the pass transistor this is called the pass transistor. So this is the simple voltage regulator with unity gain configuration but with current boosting. Now same thing can be done with this not necessarily being connected to this. So this is independent now I can bring about R1 and R2 as G2 in order to form the output voltage of any value that I desire. So this is what is going to be connected now to the Zener so that is the voltage regulator this is the load. So this is using N channel MOSFET but please notice that the drop okay that difference voltage between input okay and output keeps on increasing as you add further boosters okay like this using only N channel MOSFET. So this gate to source voltage which is going to be VT plus something is going to keep on increase the difference between VI and V naught minimum whereas if you use instead of N channel a P channel MOSFET like this it is this that is the gate to source voltage and the VI minus V naught is nothing but VDS minimum which can be going as low as 0. So this is the advantage of using P channel over N channel as pass transistor that is why in what is called low dropout regulators it is the P channel MOSFET that replaces the N channel in the current booster topology okay. So in the case of NPN it is going to be replaced by PNP transistor at this point but however one cannot go with bipolar transistor to the level of minimum voltage VI minus V naught that can be achieved by P channel MOSFET as pass transistor. So presently it is the P channel pass transistor which has dominated the scene of LDO design in most of the applications. So these are the arrangements you can see here whatever we have drawn earlier okay it is drawn neatly and this is the voltage regulator with current boosting caused by N channel MOSFET and this is the input voltage unregulated this is the regulated output voltage which is going to be again equal to VZ into 1 plus R2 over R1 that does not change okay only the current handling is going to be now solely done by this pass transistor instead of by the op amp okay. Here on the other hand this voltage can be made as low as few under 70 volts for a large current okay without any problem and therefore this is one of the most efficient ahh linear regulators. However once you know that there is going to be assigned change from here to here there is going to be inversion and therefore the negative feedback is achieved by connecting it to the positive of the driver op amp okay. So this is the negative feedback structure then again we have this equal to this all the time so V regulated is equal to VZ into 1 plus R2 over R1 in this case also. So the design equations remain the same okay except that VI – V naught minimum is much reduced in this case than in this. The compensation here in the DC loop gain remains the same as before the method of compensation here remains the same as what we have just now discussed that if you put a capacitor across this Q becomes equal to 1 okay if you do not put the capacitor then ahh the Q is very low and it is luggage. Now here you are having ahh DC gain change by GM of this device into RL roughly if R1 plus R2 loading is negligible that is how we are going to select R1 and R2 then GM into RL is the gain of the stage with ahh negative sign that is how it becomes negative feedback and therefore the loop gain DC gain is going to be the G10 of this okay and G10 into GM into RL approximately and that into R1 by R1 plus R2 is the DC loop gain. So the DC loop gain gets altered from this value which is G10 okay into unity gain almost nearly so it does not change into R1 by R1 plus R2 as before whereas here it is low dependent that is the main difference the loop gain here is independent of load because this is a unity gain stage nearly independent of load as it is dependent upon the load here okay. So if you for maintaining ahh the voltage constant here okay at high frequencies right if a capacitance is put here electrolytic or dentalum capacitor then it is going to be having a time constant which is pretty ahh large so it will change the loop gain considerably that means it this is second order system with the capacitor here it becomes a third order system and it may become unstable such a thing is highly unlikely with this unless the GM is pretty low if the GM is large for this device this is nearly unity gain throughout okay even with the capacitor coming into picture the time constant may be not that large that it will not make any impact on the loop gain. So whereas here it might start compromising the loop gain and the phase shift increases considerably and the system may become unstable. So the stability ahh criteria of this okay is ahh very critical and the compensation here is similar to what we have discussed that means we can introduce okay ahh capacitor with series resistance this is already that this is what is called equivalent series resistance of this capacitor or ESR okay. So if this resistance is ahh large then this introduces a zero in the transfer function so that the Q can still be made equal to 1 in by the introduction of the zero here. So this is an important fact that we should consider in the design of these LDBOS ahh so voltage regulator with current boosting requires all these things to be considered one is most important thing is that the VI-V0 minimum okay is achieved very easily with P channel MOSFET. However P channel MOSFET brings it out okay ahh because of its ahh gain okay ahh the Q increases increased loop gain causes increased Q that means it will start with a ripple when the transient ringing in the transient okay so which is indicating the Q enhancement that occurs because of the ahh additional pole that comes due to the load. So if the load is having a capacitor connected across it in order to maintain ahh at high frequencies low output impedance okay and hold down to the voltage due to sudden fluctuations okay. So this enhances the Q because of the additional pole however the ESR associated with the capacitor safety situation right by bringing in a zero that means the ahh loop gain is going to be GL0 into 1 plus S by Omega Z divided by 1 plus S by Omega 1 to 1 plus S by Omega 2 okay. So ahh the this Omega 2 that is brought about due to the capacitor is ahh offset by the zero okay that is introduced and therefore we can exploit the presence of the zero in order to make the Q equal to 1. This design also has been thoroughly dealt with in terms of system level ahh pole zero compensation earlier. So please look at these things and the LDOs are available today with ahh this kind of characteristic with internal compensation everything carried out so that they were satisfactorily for a range of capacitors and they unload. LM2940 is one such load dropout regulator manufactured by ahh TI input voltage range is 6 volts to 26 volts output current in excess of 1 ampere dropout voltage typically 0.5 volts at 1 ampere current output voltage trimmed before assembly that means you can ask for ahh output voltage of 5 volts 8 volts 9 volts then 12 or 15 volts okay. All the adjustments regarding ahh the compensation etc will be accordingly set. Load regulation 80 to 130 millivolts from I naught equal to 50 milliamperes to 1 ampere change no load to full load current. Land regulation is about 50 to 80 millivolts change okay for corresponding output voltage in input voltage is changed from 2 volts to 26 volts. Output impedance is only about 35 to 55 milli ohms at I naught equal to 100 milliamperes and V naught equal to 5 to 8 volts. So out of this actually it is the output impedance and ripple rejection ahh which are the small signal parameters others are all large signal parameters that means the models are ahh linear models are of no use okay in the case of line regulation and row regulation. This is something that has to be ahh kept in mind. Ripple rejection is about 72 to 66 decibels for I naught equal to 100 milliampere. Temperature coefficient of the output voltage is only 33 parts per million for V naught equal to 5 volts. This is the schematic. Please note that the current limit and thermal shutdown okay and ahh the over voltage ahh protection okay etc are there okay in this ahh setup it is a band gap reference okay. And the pass transistor here is PNP and this is what is set okay ahh at your request okay by the manufacturer. This is the output capacitor okay which is 22 micro pilots here and you know to maintain stability okay ahh this should be the value okay. So we have considered in this structure voltage control voltage source okay as ahh unit with ahh reference input forming the voltage regulator and ahh it is the G parameter of the whole system that becomes important in order to do the exact analysis. So I would like you to therefore use the G parameter technique okay. We have already derived ahh these ahh G parameters of this block in the earlier lectures to show the effect of load source input impedance output impedance and the transfer function of the ahh op amp okay on the performance of this system. And that can be utilized in coming to conclusion about the stability issues and how to fix the Q okay in terms of the 0 location okay for any ahh load and ahh the feedback factor R1 by R1 plus R in the next class will be actually dealing with ahh other applications okay of the negative feedback like filtering. Please remember that there is continuity in this whole ahh set of lectures filters has already been dealt with in terms of parasitic effect in feedback amplifier. So we have discussed the second order system thoroughly which is ahh low pass filter with certain amount of peaking at times okay and the peaking can be contained by suitably adjusting the location of these poles. So the filter design has already been dealt with as a parasitic effect in amplifier design. And now we are going to assume ideal blocks okay as building blocks to design filters. So there is continuity throughout in terms of lectures you will see that analog design involves mostly theory of filter design okay negative feedback and theory of filter design throughout whether amplifier design is concerned or control system design is concerned or filter is on oscillator design is concerned. So in all aspects the filter design comes into picture.