 Welcome back. In this lecture, we will have this lecture for about an hour. This lecture will be about special devices and also diode circuits. Last week, Professor Shama talked about p-n junction in other details. There are a variety of diodes, which are used in all kinds of applications. We look at a few of them. Now, we know that when you reverse bias a p-n junction, you have a depletion capacitance and this depletion region, the width of the depletion region depends on the reverse bias. Now, because of this, the capacitance C j, which is the junction capacitance of a reverse bias p-n junction, can be related to the reverse bias voltage by this equation, where C j, which is the junction capacitance is C j 0 by 1 plus V r by V 0 to the power m, where C j 0 is the value of C j for 0 voltage and V r is the reverse voltage, V 0 is built-in voltage, m is a grading coefficient. Typically, for a p-n junction diode will be the order of 0.3 to 0.5. So, when V r is equal to 0, you would get the same value. Now, this property of a p-n junction is extremely useful. There are special diodes by the name varactors, where this particular property is made use of. Now, varactors you can think of as voltage variable capacitors, where they use this variation of the capacitance as a function of the reverse voltage. The only difference is they are optimized for this particular purpose. Therefore, the grading coefficient is made between 3 to 4, so that the capacitance variation is a strong function of the reverse voltage. Now, where do we use this? We are all familiar with the fine-tuned control in our radio and such devices, portable devices. Typically, if you take a radio, the main capacitance there, the variation is from 0 to 70 pf. When you change the station, you are actually going from somewhere between say about 10 to 70 pf. Now, we all have noticed why this fine-tuned and when this fine-tuned came into picture. May be about 20 years ago, if you had a radio, it was extremely difficult to tune to short ways stations, especially at night, because the variation, the way you could choose a station at night, it was extremely difficult to choose. That is why when companies came up with this fine-tuned. In a fine-tuned, what you are essentially doing is, you are putting a varactor in parallel to the main gangue capacitor and by fine-tuned, what you are doing is, you are actually changing the reverse voltage and that can be weighted very smoothly. So, you would get variation in sub picofarad, which is impossible in the gangue capacitor. Now, so, varactors find extremely common use. So, today, you would find this in almost, not only in radios, you would find also in several function generators and all and because of this variation of the capacitance through voltage, you could use this in lots of gadgets and the variation is typically in the sub picofarad range. So, varactors you would find extremely useful in many electronic applications, especially in RF kind of applications and being a reverse bias diode, you would find that the impedance, when you put them in parallel, there is not much change, I mean, it does not affect the other capacitance much. Now, let us look at another special type of p-n junction or a diode, which is a light emitting diode. Again, today, light emitting diode is something very, very common. We find it almost everywhere, you know, mobiles, all kinds of gadgets. Today, we are very familiar. Now, two things, I am sure we would have wondered, how do we get these different colors and also what is the principle of these light emitting diodes. Now, light emitting diodes, as the word diodes say, they are also a p-n junction, they are made of p-n junction, but these are special, they are made of special semiconductors. Now, semiconductors can be classified either as direct band cap semiconductors or indirect band cap semiconductors. Now, this is based on the shape of the band cap as a function of the momentum k. Now, in a direct band cap semiconductor, the conduction band minima and the valence band maxima, they occur at the same momentum. Now, generally, we draw the conduction band and valence band at kind of straight lines, but actually, you would find them. So, what we mean is, so in a direct band cap semiconductor, the minima of the conduction band and the maxima of the valence band, they occur at the same momentum, crystal momentum. Now, therefore, what happens is, when you in a indirect band cap semiconductor, the minima of the conduction band and the maxima of the valence band, they do not occur at the same values of momentum. Typically, to give you an illustration, it would in a indirect band cap semiconductor. So, the minima of the conduction band is here and the maxima of the valence band is somewhere else. Now, in direct band cap semiconductors, we know that when you forward bias a diode, the carriers are injected, holds injected from the p region to the n region. Now, what happens is, when these carriers, these minority carriers, they recombine with the majority carriers on the other side and when they recombine, they release energy. Now, in indirect band cap semiconductors, this release energy would be in the form of lattice vibration or this is also called non-radiative recombination. But in direct band cap semiconductors, a sizable number of these recombinations result in radiative recombination or they would generate photons. Now, so this is the basic principle of an LED. Now, what I have given here, some examples of direct band cap semiconductors with their band caps in electron volt in bracket. Now, most of these direct band cap semiconductors are kind of alloys or let us say compounds. Now, gallium arsenide is a very good example. It is a binary compound. It is a direct band cap with a band cap of 1.43 and so on. Another popular one is aluminum gallium arsenide. It has both direct and indirect band cap 1.42 to 2.46. It can be varied by changing the mole fraction of aluminum arsenide and gallium arsenide. So, this is a ternary compound. You have a material called indium phosphide. Then you have gallium nitride, indium gallium arsenide and so on. There are several such direct band cap semiconductors. Now, when the radiative recombination takes place, the emitted photon energy would be equal to the difference between the higher energy states E 2 and the lower energy state E 1. Now, that can be equated by an equation E is equal to E 2 minus E 1, which will be h f or h c by lambda, where lambda would be the light emission lambda. C is the velocity of a light. Now, the peak emission wavelength lambda, we can express in a more convenient way in terms of the band cap energy by the equation lambda is equal to 1.24 divided by E g in electron volt. So, we see that just by changing the band cap, we can get different light. So, this is how you get different colors. We know that the visible spectrum is from about 400 nanometers to about 700 nanometer. At 700, we have red, 600 to 700, you have red and you have blue somewhere around 300 to 400. Now, by changing E g, you can get different values. Now, let us take an example of a material like aluminum gallium arsenide. By changing the mold fraction of aluminum arsenide and gallium arsenide, you can get different band caps. We will not go into the details of the technology. Now, this is how you could choose different materials and you could get different colors. Now, let us talk about another very special device, again a diode called a laser diode. Now, there are days when laser diodes were very costly and they were not seen. Today, it is something very common. All of us are very familiar with the pointer, which we use for presentation and it costs hardly 50 rupees. Interestingly, it is made of a laser diode, which emits light of about around 500 micro, almost 1 milli watt, a huge amount of light. Now, what is the difference between a laser diode and a light emitting diode? Both are diodes. Both emit light. What is the difference? Now, in the light emission, in a light emitting diode is by what is called a spontaneous emission. The reason why they are called spontaneous emission is because the emissions are isotropic. We said that if you forward bias a p-n junction made of a direct band cap semiconductor because of recombination, we said there will be photon generation. Now, this can happen all over the device. Therefore, it is not at one point. It is not focused. It is not coherent and the phase also is quite random. That is why it is called a spontaneous emission. So, in a LED, as you would have noticed in a LED display, you would see that the light is actually emitting from a much larger area if you look closely. In most of the LEDs, we would use as a display device and there we want the light to be as dispersive as possible. All of us are familiar with the standard LED and you would see that the structure is made such a way that light is kind of diffuse. So, there the purpose itself is to diffuse the light. Now, there is another way to get a photon emission. This is what is called stimulated emission. Now, here what is done is the downward transition, which is basically releasing of energy can be stimulated, can be triggered through another photon. Now, if you do this, the emitted photon will also be in phase and this is what is called stimulated emission. Now, if stimulated emission has to happen, then you need to satisfy a condition called population inversion, whereby what essentially what we are saying is the number of excited states on the higher energy band has to be much higher than the ground state. Now, this can be the structure, device structure of an LED and a laser diode is very different from this point of view. In an LED, you just have a simple p n junction made of direct semiconductor of the right band gap to get the desired color. Whereas, in a laser diode, you need to do something extra to make sure that you have a huge amount of carriers and also they are kind of confined to a very narrow region, so that you can satisfy population inversion. So, this is done through what is called hetero structure. Now, if you have a simple p n junction, which we are familiar with, they are called homo junction, which means they are made of the same material p n n. You can also have what are called hetero junctions, where they are made of dissimilar materials with different band gaps. Now, we will not go in the details of it. So, in a laser diode, you would make a p n junction, it is not just a p n junction, it will be a p p plus n n plus kind of structure, where you would have different band gaps and the adjoining materials will be slightly different, but they will be matched. Now, because of this, you would have a huge amount of carriers kind of trapped in a very narrow region because of the band gap difference and also interestingly, they also would have different refractive index, because of which when you forward bias this particular junction, this huge amount of carriers are generated and after a threshold value of current, you have stimulated emission. So, if we look at the characteristic of an LED and also if you look at the characteristic of a laser, they are different. Now, what we have here is the current versus light characteristic of an LED, which is almost linear. If you draw the similar characteristics for a laser diode, the difference would be in a laser diode, you would see that till a particular value of current, which is called the threshold current, the device works like a LED. So, which means it has only spontaneous emission. Once it exceeds a certain amount of threshold, which means number of carriers, it would go into stimulated emission and you get a huge amount of light. Now, the major advantage of a laser diode, which is generally written as L D is basically coherence. Now, when you talk about coherence, there are two types of coherence. One is called the spatial coherence, whereby what you mean is the light is now confined to a extremely narrow region as opposed to an LED, where we said the light is isotropic. So, it kind of emits from all over the place. Here, because of similar to emission, the light is extremely focused. Again, we are very familiar with the pointer, which we are talking about. But in a pointer, you also have a lens inside. You have another type of coherence, which is called the temporal coherence. Now, temporal coherence is the word used for the spectral purity of the light. In an LED, if you see, even though you see a light as red, if you look at the spectrum of the light, you would see that in an LED, if you plot lambda on the x axis. In an LED, you would see that the spectral width is quite large. Now, if you do the same thing in a laser diode, you would see that the laser diode spectrum is extremely sharp, meaning the light emits in an extremely narrow range of lambda. Now, this is what is called temporal coherence. Now, because of this, laser diodes are extensively used in several applications. LEDs are used in applications such as optical links, especially short range optical links. Today, we are familiar with LAN. Most of the LAN applications would use an LED, because LED is a very cheap device. The LED, which is used for LAN is not the one, which we are familiar with. They emit light in the infrared region, but the principle is very similar. Whereas, laser diodes are used in optical fiber communication. Today, in our country, optical fibers are used for communication throughout in all kind of telecommunication applications. So, that is the difference between LED and laser diode, which are very similar. Now, let us talk about another type of device, which is a photodetector. Again, photodetector is very similar to, let us say, a solar cell. The main difference in a photodetector, you would reverse bias. This is again a p-n junction, which is used in a reverse bias mode. Now, what happens in a reverse bias? When you reverse bias a p-n junction, any radiation temperature or any radiation would affect its reverse bias current. Now, that is the principle of a photodetector. In a photodetector, the junction, the reverse bias junction is exposed to light and the light energy, photon energy would be sufficient to break covalent bonds, which would result in what are called photocurrent. Now, in a photodiode, when you do not shine any light, you have a current, which is called dark current, which is essentially the reverse saturation current, as opposed to what is called a photocurrent, which is a light, which is the current, which falls due to light. Now, dark currents are typically extremely small, may be in nano amps kind of range and photocurrents can be, it depends very much on the amount of light you shine. Now, a photodetector can be thought of as a controlled current source. This is because of the reason that you have a reverse bias p-n junction, which has very high impedance. Now, because of this, you can model this more appropriately as a current source. Now, there is another very interesting device, which you can form out of an LED and a photodetector, which is called an optocoupler. Now, optocoupler is an extremely useful device, where this is nothing but a combination of LED and a photodetector. LED is essentially an electrical to optical converter, whereas a photodetector or a photodiode is an optical to electrical converter. There are situations, where you would like to pass signal from one system to another system. But unfortunately, you cannot connect a wire between these two systems, because the ground potential of these two systems may be very high and there can be damages. This is very true. If you are trying to take a signal from let us say a big vibrator or a vibrating equipment, let us say in a mechanical engineering lab, and you try to connect that signal to a PC. If you do that directly, your PC will burn immediately. In such a situation, what is done is, you would use an optocoupler where you want to connect, take the signal from the instrument without directly touching. Now, in LED, we know that would give you a light, which is proportional to the current flowing through it. So, if you apply a signal, it will give you a light, which is proportional to the signal. The photodetector, we again know, would give you a current, which is proportional to the light. So, at the output of the photodetector, you could take it may be amplified and you have a signal. It is an extremely useful device, which is used for achieving electrical isolation between two systems. There are many practical applications, where you cannot take signal from one system to another system through a wire. In such systems, you can use optocouplers. It is very easy to make an optocoupler in a lab. You need to just paste, maybe just tie together an LED and a photodetector, and you could do very interesting experiments. Now, when we talk about diode circuits, so we talked about three types of diode, special diodes. We talked about varactor diodes. We talked about LED's. We talked about laser diodes. We also talked about photodetectors. Then, we talked about an application, where you would use both photodetector and an LED, and we said it is an optocoupler. Now, diodes, we are all familiar with. The most popular and the most common use of a diode is it is used as a rectifying device. We are familiar with both half a rectifier and full wave rectifying applications. We will spend a little bit time on wave shaping circuits, which is another very major application of diodes. Now, very often, you can think of a scenario that you have a sine wave signal, and you want to get a square wave out of it. How do I do it? Now, one way is to use a comparator, maybe an op-amp and so on. You see that the moment you talk about an op-amp, you are talking about more complication, power supply and so on. This is something you can achieve easily using diodes or senor diodes. So, wave shaping circuits, I have a kind of family of circuits, where you would use the property of a diode and you would combine them with kind of your applications. Now, before we look at some simple wave shaping circuits, let us look at diode models. Now, there are different diode models exist. All of them assume diode to be an open circuit for rewards bias. Now, they all differ in the way the forward bias region is modeled. Now, we have one model, which is called the exponential model, which is a very accurate model, which essentially uses the diode equation. Now, there are two applications, where you might like to determine the diode current very accurately. For example, one such circuit is shown here. Now, if you connect a power supply and a resistor, a series resistance, connect a diode. Now, how do I find out I D and V D? Unfortunately, we can write only one equation here and there are two unknowns. I D and V D are both unknowns, but you can write only one equation here. Now, this is a scenario, where we can solve this in two ways. Either we can solve it graphically or we can solve this iteratively. Now, the exponential model would solve this either in graphical way or iteratively. Now, it is very easy to solve it iteratively and we would get very accurate results. For example, in the previous circuit, we can write an equation. We can write the equation for the current through the diode as I D is equal to I S times e to the power V D by V T, where V D is the voltage across it, the photobias voltage across it. V T is the thermal voltage and from the same circuit also, applying K V L, Kirchhoff's voltage law, we can write current V D as V B, which is the input voltage, minus diode voltage by resistance. Now, we could solve this iteratively. Let us just take an example and see how quickly we get the result. Now, initially, let us assume that the battery, which is given to you, power supply given to us has 5 volts, resistance is 1 K and I S is 10 power minus 12 amps and V T is 25 millivolt. Now, we wrote the first equation, where we wrote the equation for the diode current. From there, we can write the equation for V D, the diode voltage as V T L N I D by I S. Now, initially, you could assume V D to be 0. That would give the maximum current to the circuit. So, that current I D can be V B by R 1, which is 5 milliamps. Now, we could substitute that back into the equation for V D. So, V D will be then V T L N 5 milliamps by I S. This will give you 558.3. Now, let us see how quickly the equations converge and that shows the beauty of this method. In the second iteration, you could use this particular voltage as the diode voltage, recalculate, find I D again as V B minus V D. In this V D, substitute 0.5583 and if you do that, you get the current to be 4.44. Earlier, the current was 5 milliamps. Now, it has become 4.44. Now, you recalculate and find V D. You would get V D to be 555.4. You see how close it is to the previous result. Now, do the third iteration. Interestingly, the third iteration gives the same value, which means in just two iterations, you got the exact value. This method is quite accurate, but unfortunately, it is not very useful in a diode circuit. Because most of the time, you do not want to get this accuracy. You are interested in a reasonably accurate model, but one which makes the analysis faster. Now, this is where we have about three models. The commonly used diode models are piecewise linear model, which has fairly good accuracy and that is the model, which is used most commonly. Now, in the experiment, which we will be doing today afternoon, you would be using this. The handouts, which are given to you, gives you very detailed analysis of the circuit. Now, in the piecewise linear model, what you assume is, you assume a linear I B characteristics. We know that the I B characteristics is exponential, but here you would make an approximation. You assume it to be linear. You would see that if you choose a proper value for the resistance, the approximation, you would see that it is fairly accurate. So, you can think of here, the exponential curve is approximated by two straight lines, one which is before the threshold point with a slope 0 and the second line with a slope of 1 by r d, where r d would be the diode forward resistance. So, the piecewise linear model equations would be when I d is equal to 0, v d. So, that is the situation where v d is less than v d 0, which is the threshold voltage or the voltage which you consider beyond which you consider it to be conducting. And I d will be v d minus v d 0 by r d provided your v d is greater than v d 0. So, you have these two equations for these two lines. Now, for signal diodes, which you typically use in the lab, the v d 0 is typically 0.7 volts and r d would be somewhere between 10 to 20 ohms. Now, remember these values would change drastically depending on what type of diode you use. If you use a diode like IN 4001, which is a rectifier diode, you would see that this resistance value would be much smaller. The reason is IN 4001 has a rating of 1 amp and 1000 volts PIV. So, therefore, it is meant for that kind of an application. Therefore, you would see that the resistance is very small. Whereas signal diodes, which you are meant for applications up to several higher frequency, you can up to use it up to almost up to about 1 megahertz. Whereas, these IN 4001, you cannot use beyond let us say about 1 kilohertz. They have very large capacitance. So, the forward voltage, which you would get for an IN 4001 would be very different from the parameters you would get for a signal diode. Now, what we have here is a quick simulation or a quick graphical way of showing how accurate the piecewise linear model is. You see that the wide curve here gives you the diode equation assuming i s to be 10 power minus 15 amps. The other one, you have 0.7 volts as the forward drop and beyond up to 0.4, 0.7 volts, you have a line with slope 0, no current. And beyond that, you have a line with a slope 1 by r d, where your r d is 10 ohms. And you see that this particular model is fairly accurate. So, it all depends on the point you choose and also the value of the resistance you use. Now, in a lab, once you are able to get this i v characteristics, you could choose two currents. So, you could choose two currents on the y axis and find, if you expand your CRO and make a proper reading, you could get the difference in the diode voltage there. And from that, you can get a fairly good estimate of r d. That is how you would measure, if you want to model it properly, that is how you would do in the lab. Now, you have another model, which is called the constant voltage drop model. Here, you would assume that the diode is essentially an ideal diode. So, you would assume that in the forward region, once it, once it conducts, you would assume that it has a constant voltage drop of 0.7 volts and there is no series resistance. Now, this is a popular model from the point of view of analysis, because this makes analysis much simpler. If you have the previous model, which is a piecewise linear model, then it might require a few computations, whereas this is much simpler. Let us have a look at how accurate or how this particular model would compare with the actual scenario. So, if you compare the constant voltage drop model with the actual scenario, you would get something like this. So, here you see that this is a very, let us say crude approximation and still in spite of that, it is still used for the sake of convenience. You also have another model, which is called the ideal diode model, where you would assume that when the diode is forward biased, you will assume that the forward drop is 0 and the diode is also assumed to have 0 resistance. Now, this is used in circuits especially, let us say, when you talk about a rectifier circuit, you would generally ignore the diode drop. The reason, the argument there is that in a rectifier kind of application, the input voltage is much higher than this 0.6 or 0.7. So, there it is well justified. So, all these four models are used depending on the kind of application we have in mind. Let us look at, let us try to apply this particular, some of these models here. Now, what we have here is basically, we are using a ideal diode model here. We have a clipping circuit. So, essentially we are applying a 12 sin omega t as the input here. We have a 1 k series and you have a diode here, where we want to assume this diode to be ideal and you have a power supply connected in series with the diode here with 3 volt and you have the positive terminal here, negative terminal here. You have a 3 k resistance of the load. Now, how do we go about this? Now, in such a circuit, what we generally do is to see the scenario, where the diode, split that into at least two scenarios, one scenario where the diode conducts or the scenario where the diode does not conduct and then arrive at it. So, we know that the way the diode is conducted, we know that for v s positive, we know that diode cannot conduct. Now, so therefore, the output would be in this particular case would be 0.75 v s. Now, once you make v s negative, because of that we can see, we can apply k v l and we can write the currents there as i, we can apply k v l here. So, the current moving towards the node is i and i 1 and we have i 2 leaving the node here. So, we can write i as i 2 minus i 1 and you could, for when the diode is connected conducting, i would be greater than 0. From that, you could simplify and you would see that the only when diode voltage rather the input signal is less than minus 4 volts, the diode conduct. So, in summary, we would have in this particular case using the ideal voltage ideal diode model, v out will be minus 3 volt provided v s is less than minus 4 volts that is the situation when d is on and it will be 0.75 v s when v s is I am sorry here, this should be greater greater than minus 4 volts. Now, the scenario here is simulated here. So, the white waveform here is the input here and the red graph here is the output. Now, the you see here that the the the the the output will be greater than minus 4 voltage here, you can see it is a clipped and you have a flat line. If you perform this experiment in the lab, you would see that you never get such a flat line, you might get it depending on the value of resistance is used, but for most of the values you would use, you would see that you this would be a kind of you would see the small variation of the sign here. This you can get if you if you use the piecewise linear model which is given in your handout. So, if you do that you you you would be able to get a fairly accurate estimation of what you are actually going to see. Now, again synodites we have been already discussed here we will look for look at synodites on the point of view of their use in clipping circuits. Now, as we know synodites are reference voltage regulators. Now, you could use them especially there are if you want to get now if you use a synodite kind of a back to back like this and if your input is sign assume that let us have a 10 sin omega t here and we assume these to be 6 volt senors. And if you assume the diode drop the forward diode drop to be about let us say 0.6 volts then what you would get at the output would be a kind of a clipped sin wave with a a plus 6.6 and a minus 6.6. Now, in most applications this kind of a square wave would be sufficient in case we want only positive side we could just use one of them. Now, coming to another the other applications another popular application of a diode is what is called a clamping circuit. Here you would use a diode in series a diode and a capacitor in series. Now, the circuit which is shown here we have input as V m sin omega t we have a capacitor here and a diode here. Now, the way the diode is connected we know that it will permit only current to flow only in the direction from the top to bottom. Now, what will happen is as the current flows through the diode the diode that will charge the capacitor with the results that the capacitor would get charged to the maximum voltage of the input. So, in this case the input is V m sin omega t therefore, the capacitor will get charged to V m. Now, what happens is at the output side now since we have V m here with positive here negative here and the polarity of the capacitor voltage is positive this side and minus here you see that the output here would be nothing but V m sin omega t minus V m. Therefore, we would see that the output would be shifted to the maximum voltage and the output would be shifted to the negative side and another way of arguing is this way you see that the way the diode is connected here we know that this output cannot be positive. So, in one sense we can think of this circuit adjusting itself such a way that the diode charges this capacitor and the output never becoming positive. Now, clamping if you connect the diode the other way we would have a scenario where the capacitor gets charged the other in the other polarity and the waveform getting shifted up. Now, these are very useful circuits these kind of circuits are very commonly used in what are called DC restoration circuits where you could restore the DC level. There are other applications such as voltage doublers where you can use a clamping circuit and a rectifier circuit together. Now, in this case what we have here is the same circuit where we have the diode connected in this fashion. So, with the result of this circuit that the capacitor gets charged in this fashion and we said that the voltage here would be negative will be negative and what we have here is basically a rectifier half a rectifier and this will conduct only in this direction. So, the output the polarity shown here is wrong here. So, you will have minus 2 V m here. So, this circuits are very very useful especially voltage doublers circuits are used in oscilloscopes and also in television sets where you need to have very large voltages. Especially the plate voltage in a C R O or in a television requires voltage is the order of 10000. So, there voltage doublers are very useful in this circuit the moment you put a resistor you would see that the voltages slightly change and in most of the voltage doublers applications the current drawn would be very very small. Now, we could spend little time on simple rectifier circuits especially the use of a capacitor in a rectifier. Now, rectifiers circuit if you consider a half a rectifier and if you have a load here and if the input is V m sin omega t. Now, if we did not have the resistor there then the capacitor would have if the input was this. Now, if we did not have the resistor there then the capacitor would have got charged to the full V m here. The moment we put a capacitor capacitor here the and the resistor here both charging and discharging takes place. Now, one of this is this is one of the common circuits used to get a DC voltage and one of the common misconception is the method to reduce the ripple voltage. Now, in this in this case what happens is the capacitor would charge and because of the resistor it would discharge and during the next positive half cycle it will charge and so on. Now, very often it is thought that we know that the ripple the peak to peak ripple here can be decreased by increasing the value for a given R L if we for a given R L we can decrease the ripple by increasing the capacitor. So, that is very commonly thought as a way of reducing the ripple, but one very important thing to remember thing to remember is the not only the voltage at the output, but also the diode current. Now, the diode in this particular case in the circuit shown here the diode can conduct only for a extremely short period. Now, the entire charge or the entire voltage at the entire the discharge the charge which are discharged through the resistance has to be picked up through the small interval through which it is charged charging period. Now, if you increase the value of the capacitor this time period will keep reducing the ripple will definitely decrease it will become much smaller, but the same way the the peak current would keep increasing very often there are situations where a diode may be an IN 4000 1 which is used for an application like say 100 milliamps. You all of a sudden find that the diode has packed up diode has burnt and one really wonders why it burnt and the answer is if we look at if you put a small series resistance and try to monitor the diode current we would see that the peak diode current is most of the time about at least 10 times the current that is flowing through the average the average current flowing. So, this is something which is to be kept in mind very often. So, in a power supply therefore, the solution is to reduce ripple the solution is not to put a large capacitor rather to put a some reasonable value like 1000 mF or so the solution is to use voltage regulators. Now, to give a small recap of what we did in this particular lecture let me just spend another 5 minutes quickly to recap what we did. We talked about special devices we talked about varactors we talked about them being used as kind of voltage controlled kind of capacitors. We said that they are very useful in not only appliances in a radio especially in fine tune and today we would find this very often and the principle there is that of a p-n junction a reverse bias p-n junction which the capacitance changes with the reverse bias voltage. Then we talked about light emitting diodes we said that they are again p-n junctions but these p-n junctions are made of special semiconductors which are called direct band gap semiconductors and the crystalline silicon which we are familiar with silicon is not a direct semiconductor band gap semiconductor and there are materials like gallium arsenide aluminum gallium arsenide and many such materials. If you make a p-n junction out of these materials then when you pass when you forward bias this particular diode you would see that they emit light and this kind of phenomena is what is called radiative recombination and we said that in some of these semiconductors you can change the band gap by changing the mold fraction because most of them belong to like especially the ternary like aluminum gallium arsenide or even quaternary. There by changing the mold fraction you can change the band gap thereby you can change the lambda of the light emission. We also talked about laser diodes where we said the process is what is called stimulated emission where the light which is emitted is coherent both spatially and temporarily and they to achieve population inversion they use special structures which are called heterostructures which are made of different materials with slightly different band gap but matched and we said that LEDs are very commonly used even in communication especially in small LAN applications but laser diodes are the devices of choice especially in optical fiber communication and today in our country all over the country optical fibers are used as the backbone for all communication and then we talked about photo detectors which we said are nothing but p-n junctions which are reverse bias and also the junction is exposed to light and you would generally find photo detectors with kind of a quartz window and they have what are called dark current which is nothing but the reverse saturation current and also have what is called a photo current which is the current caused by light and the photo current we said is directly proportional to the light falling on it and we talked about another interesting device which we could even make it in a lab easily which is what is called an optocoupler which is made out of LED and photo detector which we said can be used to couple light sorry couple a signal from one system to another system when you talk about system we are talking about maybe major equipment maybe taking a signal from a very big equipment to a PC in some kind of scenario we cannot directly take because the grounds may be a different potential and this optocoupler is one such is a device which helps us in such a situation to achieve electrical isolation. We also talked about different diode models we talked about the exponential model which we said is a very accurate model and is very useful if you have a simple circuit and you want to find out the exact voltage and diode voltage and diode current but we said unfortunately it is not very easy to use and we talked about three more models we said the piecewise linear model where we assume a linear I V characteristics and we said this particular model is an extremely accurate model and we when we fitted this with an actual characteristics we found that the fitting was very good and we also said occasionally we would use a volt constant voltage drop model to make or hand calculation simpler and occasionally we might also use ideal diode model especially in rectifier circuits and then we talked about clipping circuits. We also talked about both synodiode also being used in clipping circuits we finally talked about clamping circuits and voltage doublers. So, I would stop my lecture here.