వాదిన్ణదిందిందాలెర్న్ అషిస్రంత్మండాప్నెదిందా. మికంత్సుపిలె, వాట్టిత్నండిందిందిందిందిందాంద్లె బిలాపిలెపిసికిక్లు. the concentration of unoccupied sides is S, these are capital is S and that occupied by various adsorbed species is S A, S B, S C, etc. Before that we have S naught and S, okay. Let me explain this, so I think you know happily would have written without even thinking you know what is the meaning but the meaning of that is given catalyst will have S naught number of active sides, right. So out of that S A, S B, S C are the active sides that are occupied by the species if you have A B C, if you have A B only two S A, S B like that then the remaining sides are S, okay. So now based on this how many sides have been occupied by the species, how many getting adsorbed, how many getting desorbed, all that will come in this and then we will assume that we have a reaction A gas, B gas going to C gas plus D gas. We have the catalyst, it is a reversible reaction, okay. This is the kind of reaction that is going on now on the catalyst. So now we have to develop a rate expression for this stoichiometric equation, okay. So now our imagination for catalytic reaction is that molecule A has to go get adsorbed, molecule B has to also get adsorbed. If they are side by side then molecule A will form some intermediate, molecule B will form some intermediate, both will react and then that is surface reaction step and then desorption, desorption of A and now there is no A, desorption of product. If there is only one product only one will come otherwise if I have C and D and C has to desorbed, D has to desorbed and then reach, come through the pores and through the film and reach the bulk that is what is the overall picture what we imagine for all catalytic reactions, okay. What is that? Once more the assumption is that molecules of A will get adsorbed on one side, molecules of B also get adsorbed on other side and both of them form intermediates and then these intermediate will react and they form the products C and D and C and D also they have to be desorbed off after the formation because they are the products where the concentration is high on the surface low in the bulk so that concentration difference will make it move through the pores, through the film and all that. So then out of these that means adsorption of A, adsorption of B, desorption of D, desorption of C and also surface reaction we have now five steps. Out of that any one may be rate controlling, okay and may be adsorption of A alone may be rate controlling or desorption of D alone may be rate controlling or five may be rate controlling. So how do we know this? We will know only when you first develop a model the general procedure is writing the main equation afterwards imagining the steps adsorption of A, adsorption of B and all that then developing a kinetic model, right. What you do is in general if it is a new process we do not know what is the rate controlling step. We write all the models that means for example here you will have lot of combinations simplest ones if you take adsorption of A, adsorption of B, desorption, desorption two steps and surface reaction so we will say that okay surface reaction is controlling one model, adsorption of A is controlling another model, adsorption of B is controlling another model. Then all these models before me now mathematically I have these models but how do you know which one is really rate controlling? I have to conduct an experiment, right and then I have to measure the concentrations of A, B if I know A, B, C, D I can calculate, okay or whatever is possible if I measure C, D then A, B I can calculate at any time. So once I have that information concentration versus time data like your normal kinetics then I have to fit this data to the overall kinetic models. So out of that five models one may fit if all of them are not fitting because each individual one which you have thought you know that is adsorption alone, desorption alone, surface reaction alone then you have to take the combinations so that is why it is hell to develop this LHHW kinetic models in catalytic reactions that is why we happily ask chemists to do that, okay but I think as chemical engineers also we should know how to do that and we should also develop because these are the macroscopic models still we are not worried about how the molecules are actually getting dissociated, what are the activation energies all those things we are not worried here, we need a macroscopic rate which is a function of concentration of A, concentration of B and if it is reversible reaction then you have concentration of C and concentration of D that is all what we require as an engineer but if you go deeper and deeper on the surface what is actually happening, what are the surface energies, where are these active sites, how do you make these active sites much more active, how do you generate more active sites in a catalyst all these things again is a big science, catalysis science and it is interface between chemical engineers and chemists where if both of us work together we can do much more because the idea is at the end with minimum amount of catalyst how do you produce maximum I mean as engineers we understand that, okay but at present what we are trying to do is that let me develop or let us develop a macroscopic model where it gives me a rate expression because this rate expression is necessary for me in my performance equation, in performance equation I have a term called kinetics and I have another term called input and another term called contacting, so contacting is given by you know the type of reactor I am choosing and kinetic models from this only I have to get and of course input you know how to get it, so that is why now let us write the steps, step 1 is A, A is the concentration and S is the active site and all the steps are reversible steps and we can also say this is K 1, K 1 dashed reverse yes giving me some complex A S, okay then step 2 B plus S giving me this is K 2, K 2 dashed this is B S then the reaction between these two step 3 A S plus B S this is K 3, K 3 dashed this will be C S plus D S those are the complexes then step 4 is desorption of C S K 4, K 4 dashed now this will be C plus S and step 5 I hope I will write here is D S this is K 5, K 5 dashed reverse D plus S, so if I call these numbers may be before that also I have to write one equation this is S naught equal to S plus S A plus S B plus S C plus that is equation 1 this is equation 2 and equation 3, 4, 5, 6, 7 definitely you know the meaning of equation 1 right in the notes which I have given you that we have S vacant sites S A occupied by A B C all together must be your S naught which we have taken in the beginning as a constant for a given catalyst, okay so out of this again equation 3 is adsorption step correct and next one also is adsorption step yes this is reaction step surface reaction and next one is desorption next one also is desorption good so this is what I have been telling any one of these steps may be rate controlling or all may be rate controlling okay two extremes okay good so now let us take that surface reaction is the rate controlling step this step surface reaction is the rate controlling step surface reaction is rate controlling so we will write a rate expression here or equal to this one we have to treat it as normal stoichiometric equation okay it is reversible reaction so the rate expression can be written as K 3 concentration of this concentration of this and minus K 3 dash concentration of this and concentration of this okay that is what we write there then we have K 3 S A S B S minus K 3 dashed C S D S so this is equation number 8 good so as usual I think you know I have been telling you this one for all heterogeneous systems this rate should be in terms of measurable quantities what are the measurable quantities here in this equations A because this is the concentration of A in the bulk which you have to we will see that and then B and C and D and all other things I cannot intermediate concentrations I cannot measure right so that is why we have to now write that equation in terms of measurable quantities the procedure is universal you know for all heterogeneous systems finally we should have then if I am able to express this rate in terms of all measurable quantities then that is called the overall rate observed rate measured rate global rate all these various names are there I am just repeating again good so now the general procedure here is that when you take reaction as the rate controlling step all other steps are so fast always you can see equilibrium of those steps in fact these what you have done even for homogenous systems let me recall your memory that you know you have non elementary reactions non elementary reactions if A plus B going to C is not actually A plus B going to C in between there are many many steps that means A may be first forming an intermediate B may be forming an intermediate then those may be reacting so all these again models you will imagine in non elementary reactions procedure is same there also you write all that imaginary steps okay how A is reacting forming the intermediates or B is forming the intermediates and then try to write for each and every equation what you write there as a elementary equation elementary means what is the definition of elementary reaction stoichiometry and then order will be the stoichiometry coefficients will be the same okay so similarly here when I write an equation this is what what you have written this is first order with respect to this first order with respect to this first order like this then overall second order whole second order because coefficient one here one here one here one here so this is the general procedure except that rate controlling step you have all other steps as I mean in equilibrium okay so that means thermodynamic equilibrium so how do you write those equations thermodynamic equilibrium okay I think you may forget later so I think better let me tell this also when step three and not step three here when step five is rate controlling okay step three is fine equation five or step three when step three is rate controlling all other steps are assumed to be under equilibrium then from step one yeah the thermodynamic equilibrium is A S A S equal to K 1 which is nothing but your K 1 by K 1 dash correct no right yeah so this is equation nine then from step two B S this is concentration of B separated concentration of A separately this is K 2 which is again K 2 by K 2 dashed 10 then we have step 4 step 4 C S by this is K 4 which is slightly change here that is K 4 dashed by K 4 that this constant I have just reversed for easy writing okay that you have to notice that okay I hope you notice it that normally it will be reactants by products by products by reactants but here I have reversed and then this is defined like that this is only for easy manipulation of algebra that is all nothing else okay then step five is B S D dot S this is K 5 which is equal to K 5 by K 5 dashed by yeah this is the one good. So now I can write A S B S C S D S here in terms of these equations correct no right so that means A dot S will come here B dot S come here and C dot S here D dot S there now let us write that substituting equations 9 to 12 in 8 substituting equations 9 to 12 in 8 first let us write that and then we can rearrange we will write here K 3 capital K 1 A dot S all this we can have a bracket like this then K 2 B dot S minus K 3 dashed K 4 C S K 5 D S yeah this equation also we can call as 13 yeah so this after rearranging a little bit then you will get R equal to K 3 K 1 K 2 now I have A B minus K 4 K 5 by K 2 K 1 K equilibrium or capital K also we can write C D bracket close I have now here S square this is okay where K equilibrium or K in general capital K I can write as K 3 by K 3 dashed good still can I use this equation immediately or do you have to do something else yeah we have to also eliminate the number of you know vacant sites okay that can be done because still this one these constants anyway I have to evaluate only from the experiments okay but this S square I can also eliminate by taking that equation this equation 1 yeah equation 1 gives me S naught equal to S plus S A S B S C here S D S D and I can also have here some units okay units also occupy some active sites okay good. So now I have I have to substitute for S A S A is nothing but this concentration A S okay B S C S like that that is the concentration on the active sites so that is why if I write this S plus A S B S C S D S and I can also have I S I is the inert component like for example nitrogen which is may not be participating in the reaction okay. So this equation now this is S naught this also of course these things I do not know but I have to write that in terms of again known measurable quantities what are the measurable quantities again these equations A S I know A S is nothing but K 1 A S right or K 2 B S is nothing but K 2 B dot S okay so you have to substitute again equation 9 to 11 here then you get S plus you have K 1 A S K 2 B S and K 4 C S K 5 D S K I K I okay I S this is the equation now you know I have S here S here S here S here S here S here S here all that S I can take out common like okay so this equation if I take as this is 15 this is 16 then equation 16 can be written as S equal to S naught divided by 1 plus K 1 A K 2 B K 4 C K 5 D plus K I I that is the equation this is equation 17 excellent good. So now equation 17 has to be substituted in 14 now you will see the format which normally you see for L H H W kinetics okay so what is that please take that substituting equation 17 in 14 what you get is R equal to K 3 capital K 1 capital K 2 S 0 square now I can write A B minus C D by I write capital K naught this is the bracket so now all this term 1 plus K 1 A K 2 B K 4 C K 5 D plus K I I whole square yeah so this is the equation actually this is equation number 18 that is equation number 18 and in the normal form when you write this I can write this as R equal to all this as some K and concentration of A concentration of B minus concentration of C concentration of D K naught whole thing divided by 1 plus K 1 C A K 2 C B K 4 C C K 5 C D plus K I C I whole square this is one format there is another format also which you will see of course this K is all that together okay let me also write that where small K equal to K 3 K 1 K 2 S 0 square good so I can also write this one this is another format normally we will see as P A P B minus P C P D by K naught I am retaining as the same constants but constants will be actually different so 1 plus K K 1 P A K 2 P B K 4 P C K 5 P D plus K I P I whole square this is equation 20 21 these are the two formats normally you will see in all the books okay many things can be understood from these equations right many things like this denominator whenever you have a rate expression you know this is the actual rate expression or this one C A minus C B minus this is normal rate equation you know when you have A plus B going to C plus D this is the kind of rate equation you will have right for reversible yeah but in catalytic reactions this is the denominator which comes and that is actually inhibiting the reaction that is why in biochemical reactions when inhibition is taken into account some terms are added in the denominator those terms are not just like that added but you know through mechanism 1 1 plus no but the constants here are not same from the previous that is what I mentioned yeah that is what I told you even though I am writing this in partial things I am retaining the same constants that is what I have told you okay yeah so you know you can the entire derivation you can also do in terms of partial pressures from the beginning you will have one only you will not have some other value here okay so that is why yeah these constants make a note I told that whenever I am writing that these constants even though I am maintaining the same they are not same because of partial pressures okay yeah good but what is that we can understand here is that you have the square here normally that square comes when two active sides involving the reaction two active sides if there are three like A plus B and also plus C going to the products then three active sides when they are involved then you will get here Q okay for surface reaction when you have surface that is why when someone gives you model if they give you in this format and also you see in the step 3 what you have that reaction step that will not be there in the denominator any constants K 3 will not be there in the denominator so in the denominator you will have only those steps which are not the rate controlling steps so here okay step 1 2 4 5 are not rate controlling steps they are the fastest steps right so that is the reason why you will have in the denominator why I am telling all this is when you read a when you see a book or when you see an equation even in the even now people are publishing papers on this when you look at that you can easily find out what could be the rate controlling step from that what could be the rate controlling step with experience even just without just by seeing you will know what is the mechanism of the you know based on which that particular equation is derived okay good so this is one thing and then what we have to do is now evaluate K 1 K 1 K 2 K 4 K 5 K i that means you have to now conduct experiment and experiment you conduct to find out what is the partial pressure of A partial pressure of B or concentration of A concentration of B then concentration of C and D you can definitely get from stoichiometric equation 1 mole 1 mole 1 mole that is no problem then with time this rate is nothing but minus depending on your base right most of the time for catalytic reactions we base our rate based on weight of the catalyst okay so how do I write that it is minus 1 by W D N A by D T so the number of moles of A changing with respect to time I should know right when you know the concentrations you can find out how many moles are changing various times you are finding out the concentrations then you know what is the change in moles of A right so you can calculate easily rate once you measure the change in concentration or the change in moles of a particular component good so that means rate I will know and then corresponding concentrations normally it is time and concentrations then you can convert that into rate and concentrations and once you have that information then you have to go to this particular model and then try to find out k1 k2 k3 there are many many methods available for finding out very accurately k1 k2 k3 k4 k5 and also other other constants right the many methods that is why again you know here it becomes purely experimental I mean mathematical techniques and whole type engineers where the complicated mathematics when they have not used what they did was that they conduct the reaction forward reaction and then avoid as far as possible this term that is why you know there is a method called initial rates for finding out kinetics I do not know whether you still remember that or not initial rates and these initial rates mainly came from for forward reaction first and then you take the products because you are trying to find out the kinetics okay so then you have to take C and D and then have the backward reaction and those initial rates so that means separately without this term you should have all this and without this term you should have all this and then conduct one experiment for the entire normal A plus B going to C plus D and then check that data with the initial rate data that is given that you have checked with so that is the overall procedure and my God to actually find out K1 K2 K3 it takes lots of time but there is a pleasure in doing that there is a real pleasure in doing that you know evaluating these constants and accurately measuring the rate of reaction because all your design now depends on this rate I can tell you very quickly here if you want to find out weight of the catalyst in a packed bed what is that you know the equation what you use the equation what you use this F A not equal to D X A by minus R A and this is minus R A for me this is the equation which you have to substitute here and many times it may not be possible to have an analytical expression you cannot integrate just like that so that is why you go for either graphical integration or numerical integration or some other technique finally to get what is W by F A not and what is this equation for which reactor P of R which is packed bed plug flow reactor all packed beds are treated as plug flow reactors so that is why this rate expression finding out is the first step and then I have been telling you in homogeneous in heterogeneous reactions most difficult steps are only finding out the rates okay finding out the rates so this is one thing I think very quickly I can also tell you another rate controlling step that is let us take adsorption of A rate controlling procedure is same again exactly same that means first writing an equation for this alone minus R A equal to this one K 1 into A S minus K 2 into sorry K 1 dashed into A S so now you have to try to eliminate this A S using all other steps that is all the procedure is same so let us do that very quickly I think we have time or no time I think because already we have some steps there okay so let us take another very simple one okay this is adsorption control I am not taking the earlier one because it takes time so we have a reaction A going to R A going to B also one can write because I wrote there A plus B do not want confuse there so now here this is the reaction that is going on the catalyst what is step one the way we imagine here I have catalyst step one is A plus S giving me A S that is adsorption of A step two is A S giving me R S that is the surface reaction step okay then step three is R S giving us R plus S you see this active site again is ready regenerated after this step so now this one as usual I will write K 1 K 1 dashed K 2 K 2 dashed K 3 K 3 dashed now we take this one is the rate controlling step so if I take this one as one two three so when this is rate controlling step so we have the equation R equal to K 1 A S minus K 1 dashed A S okay good that is the actual rate expiration for now we have to find out from the other two steps because they are under equilibrium the other two steps so I can write from step okay from step two what we have is K 2 equal to R S by A S from step three it is K 3 equal to R S by R dot S so this is equation number five equation number six now we have to substitute this in this okay equation four so if we do that we will have R equal to K 1 A S minus K 2 sorry K 1 dashed R S by from this R S by this also I have bracket that is very important step two R S by K 2 this is equation seven right but still this is unknown to me R S right so now we have to substitute equation six in seven because R S R dot S right confusing okay good so R equal to K 1 A S minus K 1 dashed for this R S I have to substitute K 3 capital K 3 capital K 3 R dot S by K 2 this is equation eight so now I have to write this equation as K 1 S into A minus K 3 by capital K 1 K 2 capital K 1 K 2 into R okay where I will write here where capital K 1 equal to K 1 by K 1 dashed so this is yeah and S is there already so this is nine this is ten what is the other equation now I have to eliminate S procedure is same I have to eliminate S okay so when I eliminate S to eliminate S I have S 0 equal to S plus S A S R yeah plus S I in it so this is equation eleven good so now I have to substitute S plus for S A it is A S plus R S plus in it also if I want to have that there it is I S so the equation twelve now I have to substitute for A S R S I S okay we have the equations here first one if I want to substitute for A S this will be R S by yeah R S by K 2 right A S what is the K 1 K 1 capital K 1 A S can we use that capital K 1 how can you use that okay capital K 1 cannot come there no capital K 1 is only for this reaction thermodynamic equilibrium capital K 1 okay so here when I substitute this I will have here S plus R S K 2 yeah plus R S I am writing that slowly now I S this is equation thirteen now these two together S plus for R S I have to use this equation K 3 R S right so this one is what K 2 yeah okay so for R S I have to use K 3 actually I can take common also there so this will be 1 by K 2 plus 1 multiplied by K 3 R S R dot S in fact okay plus I S correct no K I S okay so now S I can take common so this is S not equal to 1 plus K 3 by K 2 plus K 3 R plus K I okay whole thing multiplied by S yeah that is why I am also running fast yeah right here also here also I am is there no okay dot S yeah S not by 1 plus K 3 K 2 plus K 3 into R plus K I so that is the one yeah good so now I have to substitute there and then you will get the substitute in which equation yeah equation nine substituting in equation nine may be I think I have to write here I will give only one expression substituting here also I have to write thirteen fourteen this is fifteen yeah substituting equation fifteen in nine what you get is R equal to K 1 S not A minus K 3 K 1 K 2 R whole thing divided by 1 plus K 3 by K 2 plus so this is the expression so this is of course one can write also this one as some constant K C A minus another constant for example R by C R by K not whole thing divided by 1 plus K 3 K 2 K 3 C R plus K I of course you can also write this one in terms of partial pressures okay where K not equal to all this K 1 yeah you can go okay tomorrow we will discuss


At the suggestion of Alexander Hamilton, Congress charged him to assist the federal government in its financial operations. Thomas Jefferson and his followers protested violently. The Constitution, Jefferson pointed out, conveyed upon Congress a number of carefully enumerated powers. The power to charter a corporation such as a bank was not among them. The federal bank, therefore, was unconstitutional. To this, Hamilton replied, Congress under the Constitution may enact all such laws as are, quote, necessary and proper to carry into execution its enumerated powers. The bank is a necessary and proper means to collect taxes, to further the nation's welfare, to conduct war, and so on. The federal bank, therefore, is constitutional. Hamilton's view had been accepted by the President and by Congress. The bank's charter had been allowed to lapse just before the War of 1812. It was renewed four years later. But in 1818, the bank's existence was once more in serious danger. The case for and against the bank was argued before the Supreme Court of the United States within the framework of a case known as McCulloch v. Maryland. It can be said that the whole nation, by taking sides, participated in it. At stake, after all, was more than the existence of the bank. At stake was the reality and the vitality of a federal government. The fight against the bank was a fight to contain and limit the power of the federal government. The fight for the bank, on the other hand, was a fight to create a strong central government for the Union, capable of dealing with the problems of an ever-growing, ever-changing nation. McCulloch v. Maryland entailed of necessity the question, who is supreme? The federal government or the government of the several states? Chief Justice John Marshall delivered the court's answer in March of 1819. It was not at the time of popular decision, that's a fact worth remembering, yet it provided a cornerstone of the American system of government as we know it today. The origins of McCulloch v. Maryland go back to the last days of April 1818, when a Maryland official by the name of John James paid a visit to the Baltimore branch of the Bank of the United States. Subject of James' visit was the failure of the bank to comply with state law. Only Maryland bank was entitled to freely print notes which could be circulated and used as money. The bank of the United States was not. The federal bank said Maryland law must buy stamped paper from the state on which to print its notes. It must, in other words, pay a state tax on its operations. The Baltimore branch, so far, had failed to do so. Mr. James, John James, treasurer for the western shore of Maryland. I'm James McCulloch. You're the cashier. Yes, sir. At your service, Mr. James. Do you recognize that bank note, Mr. McCulloch? Yes, sir. It is a note issued by this institution, isn't it? Issued by the Bank of the United States in Baltimore, Maryland. That is correct. It bears your signature. Right again. Mr. McCulloch, you are no doubt aware that all notes issued by this institution must be printed on stamped paper, stamped paper bought from the state. Now I ask you, is that note printed on stamped paper? No, sir. No, sir, indeed. The paper you're required to buy, Mr. McCulloch, lies in my vault, untouched. I've offered you delivery, Mr. McCulloch, how many times, four or five times? I wouldn't know, Mr. James. I wouldn't know.  The law provides for a fine $500 for each and every offense. We'll see that you are made to pay it, unless you will assure us that you will comply and comply at once with the state regulations. Are you threatening to take the bank of the United States into court? Yes, sir. Yes, sir, indeed. It's a very interesting prospect. Put yourself, Mr. James. Big pardon? We have no intention of paying the state tax, not now, not at any time in the future. If under the circumstances you want to take us to court, please do. I'll see you in court, Mr. McCulloch. John James, as he said he would, brought suit against James McCulloch and the bank of the United States. What James demanded was that the federal bank pay the state tax as well as a fine of $2,500 for having issued unauthorized notes. The case was heard on May 8, 1818 in the County Court of Baltimore County. Mr. Martins? Yes, your honor? Mr. Martins, Mr. Pinckney's just informed me that his client is willing to admit to the facts in this case. That's reasonable. The bank's been doing business without paying the Maryland tax. It's common knowledge. I take it your client is aware of the provisions of the law. He is, your honor? Well then, is there any reason why this court should not find him guilty as charged? Yes, your honor, there is. We suggest that the Maryland law is unconstitutional. Unconstitutional? No state under the Constitution may lay a tax on a federal agency.  The right to raise revenues by laying taxes is founded in her sovereignty and guaranteed by the Constitution. Mr. Pinckney, I'm sure, will recall that under the Constitution only exports, imports, and tonnage are exempt from state taxation. Does he know of any reason why this exemption should be seen as including a bank? The right to tax without limit or control is essentially a power to destroy, but power to destroy a federal agency clearly isn't granted by the Constitution to any state. The argument works both ways, your honor. If the right to tax, in fact, implies the power to destroy, why do we allow the federal government to tax state banks? And we do allow it, don't we? Surely, if the federal government may tax state banks, the states may tax the federal bank. The Baltimore County Court sustained John James, McCulloch appealed, and the case went to the Maryland Court of Appeals. Here the crucial question arose, had Congress the power to create a bank in the first place? Mr. Martins, your honors, Mr. Pinckney claims that the right to tax implies the right to destroy. If this be the case, your honors, we should resist federal taxation of our state banks with as much determination as the federal government now resists taxation of its banks by the states. As a matter of fact, we've accepted federal taxation of our banks. Now, either both parties have the right to latest tax or none. Not so, your honors. Federal government and state governments under the Constitution are not equals. The federal government is supreme. Federal law, your honors, supersedes state law. Federal six of the Constitution, Mr. Martin, I'm sure will recall it. He does indeed. Federal law is the supreme law of the land, yes. Provided, your honors, provided it has been enacted in pursuance of the powers vested in Congress by the Constitution. Now, as it so happens, the Constitution of the United States is silent. It is silent on the matter of chartering banks. Mr. Martin, am I to understand that you consider the federal bank unconstitutional? Your honors, Congress twice chartered a federal bank each time the question of its constitutionality was gone over in great detail. Granted, however, the question as to whether or not the bank's constitutional is not for Congress to decide. It's reserved for the Supreme Court of the United States. Throughout 1818, states' rights man across the country rallied to attack the federal bank. Prominent among them were Virginians, men like Spencer Rohn, judge on Virginia's Court of Appeals, Thomas Richie, publisher of the influential Richmond Inquirer, John Taylor, planter and political philosopher, John Brockenbrough, president of the Bank of Virginia, whose mansion in time would become the White House of the Confederacy. Taylor and Rohn were disciples of Thomas Jefferson. Like Jefferson, they were profoundly suspicious of federal power. When they spoke of their country, they spoke of Virginia, not the United States. Banks are necessary and proper means to carry into execution the great objectives of our federal government. If a bank's a necessary and proper means of government, what is not? It was not too long ago that we defeated in Congress a bill which would have given the federal government the right to operate their copper mines. That rules about New Jersey. How do they try to justify that? By the doctrine of implied powers. Just as they're trying to justify the bank. As they said, it is authorized by the Constitution to provide for our common defense. Well, ships are necessary for our defense, a copper is necessary to build ships, a mine is necessary to provide the copper, a company is necessary to operate the mine. Therefore, Congress is authorized by the Constitution to operate the Roosevelt copper mines. Yes, sir. It was reasoning to remain unchecked. It won't be long before we'll have more to contend with than a federal bank. There'll be federally operated newspapers, federally operated mines, federally operated manufacturers, federally operated stage lines, name it, and the federal government will have its hand in it. State rights will be at an end. And state rights in this country are the bulwark of our individual freedoms. Gentlemen, the federal bank must be destroyed. Now let the doctrine or the implied powers remain unchecked and we'll never again be able to place limits on our federal government. In September of 1818, McCulloch v. Maryland was docketed in the Supreme Court of the United States. It then consisted of seven men, Chief Justice Marshall and Associate Justices Washington, Johnson, Todd, Livingston, Story, and Duvall. Power, Mr. Marshall, to a public official. Whether he holds his office by the will of the people or the grace of God, power is what monies to a banker. Not a means but an end, something of which he can never possess enough. That's the difficulty we're facing. The fact that our government is an elected one in and of itself is no guarantee, no guarantee at all against an abuse of power. In your opinion, Mr. Duvall, what is the Constitution strictly interpreted? A grant to the federal government of powers not expressly vested in it by the Constitution, in my opinion, is dangerous in the extreme. The Constitution, Mr. Duvall, allows the federal government to enact all such laws as are necessary to carry into execution all powers that are expressly granted. What does that mean? Strictly interpreted? Strictly interpreted, it's virtually meaningless. The term necessary, in my opinion, means indispensable, not just convenient, not just useful, but indispensable. Congress under the Constitution may enact laws without which the expressly granted powers could not be carried into execution. If federal bank is useful, it is convenient, but is it indispensable? It's not. Mr. Duvall, the need for a federal bank was proven twice, not once, but twice, during our war for independence and again during the war which we've now just barely brought to a successful end. Twice we almost perished, for lack of a government having sufficient authority to ensure our survival. The salient fact, Mr. Bartol, is that twice we survived without a federal bank. Mr. Duvall, the word and the purse, all external relations, and an inconsiderable portion of the industry of the nation are entrusted to Congress. Now it seems to me that a government entrusted with such vast powers can also be entrusted with ample means to discharge its tasks. Why claim to an interpretation of the Constitution which makes government operations difficult, even hazardous, and expensive? Expensive not only in terms of money, but also lives. Chief Justice Hazard, when the American people decided to form a union and to establish a federal government, they meant for it to ensure their welfare. You don't think, do you, that the framers of the Constitution, after granting vast powers for the public good, intended to impede their exercise by withholding a choice of means? You say ample means, Mr. Marshall. How ample? That is the question. Let's answer by saying that as long as the end is legitimate and within the scope of the Constitution, then the means, if they too conform to the spirit and letter of the Constitution, are legitimate as well. That's rather too generous to suit me, frankly. To be anything but generous, Mr. DeVal, is to rob the federal government of its ability to deal effectively with the nation's needs as they arise today and a hundred years from now, when the world may not look quite as we see it. Feeling against the federal bank ran high. Maryland by now was not the only state with a stake in the case. Half of the states in the union had, like Maryland, laid a heavy tax on the federal bank. Tennessee, Georgia, North Carolina, Kentucky, Ohio. Illinois and Indiana had gone even further, prohibiting the establishment of branches of the federal bank altogether. From Marshall's fellow Virginians, Roan, Richie, Broken Bro, and the men who represented Virginia in Congress, Tyler, Burwell, Johnson, came a move to destroy the bank before the Supreme Court had an opportunity to hear the case. Virginia would ask Congress that the bank's federal charter be repealed. Yes, Congressman, a motion to repeal. I don't know if it will carry. Congressman, the country is in one of the worst economic depressions since our war for independence. And whom are they blaming for it? Right or wrong, the federal bank. Feeding against the bank has never run higher. Will the motion carry? The people demand that the Congress set aside the Aidean and Sedition Acts. The people will demand that Congress repeal the federal bank. Well, your paper supports us, Mr. Richie. The National Press has been hammering at the bank for a year now. The motion will carry. I assure you. I believe it, but do you say farewell? There are two things to be considered. One, New England, the North and the East. They're fond of banking up there than they are of marriage. Two, Jimmy Madison. He's got his signature on the bank's charter. And I doubt that he'll want to see it go down and defeat. If he succeeds in keeping only half of the party in line, it will surely be that counts all pins in the plowed congressman will never yoker. Jimmy Madison won't lead us, Judge. Farewell's right. There's not a word in the Constitution that would suggest the idea of a bank to even the most fertile imagination. Yet they create a bank. And there's still not enough. The experiment is pushed further and further and further still. The sovereignty of our state is assailed with a threat to stupor but its most vital and essential power. The right of taxation. Gentlemen, you've all heard of the famous Fig Tree of India. The Strangler Fig. Its branches shoot from the trunk, spread, drop upon the ground, take root, and become trees. For which again branches shoot and spread and propagate and extend themselves until all available soil is covered and everything perishes in the steadily darkening shade. Even while Congress debated Virginia's motion to repeal the bank, hearing began on McCulloch v. Maryland. Charles Pinkney argued in behalf of the bank. It's been said that the Constitution does not contain the wood bank and that therefore a federal bank is unconstitutional. Could anything be more absurd? Congress under the Constitution may provide foreign support to Navy. Would it make any sense to say just because the word steamboat is not contained in the Constitution that therefore the use of steamboats by the nation's Navy is unconstitutional? Your Honors, the statute book of the United States is filled with powers derived by implication. Congress has the power to establish a postal service. Would anyone here question that it entails of necessity the power to establish post offices and post loads and even the power to punish the offense of robbing the males? Lighthouses, beacons, boys, and public peers are all established under the general power to regulate commerce. They're usefulness and a propriety. Have they ever been challenged? The power to lay and collect taxes will not execute itself? Congress must devise in all detail all the means of collection. A federal bank is such a means. What justification I ask you is there in saying that it is any less useful and any less proper than lighthouses, beacons, post roads, and post offices. On February 25, 1819, the motion to repeal the federal bank in Congress was defeated. Thirty yeas against 116 nays. A week later, Chief Justice John Marshall rendered the unanimous decision of his court. The Constitution of our country in its most interesting and vital parts is to be considered. The conflicting powers of the government of the Union and of its members, as marked in that Constitution, are to be discussed. And an opinion given, which may essentially influence the great operations of the government, no tribunal can approach such a question. The rank is, and I quote, a convenient, a useful, and an essential instrument in the prosecution of the government's fiscal operations. It's therefore constitutional. And the Maryland tax law? Unconstitutional. What's the argument? Article 6 of the Constitution. If the Maryland law were valid, I quote, then the declaration that the Constitution and the laws made in pursuance thereof shall be the supreme law of the land would be meaningless. The United States bank, everything. State sovereignty, nothing. The federal government will now keep growing and growing until Supreme Court must be stopped. Appeal to the people, majestic and irresistible power be invoked. I'm willing to place my rights and liberties in the hands of the state of Virginia. It's a government of men who are my neighbors. Men who know me and mine, as I know them and theirs. Men in whose election I participated. The federal government, with which they try to saddle us, composed of men most of whom I've never even heard of. Men over whom I have no control, whatever. Men who are completely ignorant and perhaps even indifferent to my most vital interests. The federal government, thank God I never will. I reply to what? We cannot too earnestly press on our readers the following exposition of the alarming errors of the Supreme Court of the United States. We are awfully impressed with the conviction that the welfare of the Union has received a dangerous wound. Reaching so close to the vitals is seemingly to draw the heart's blood of liberty and safety. That's comparatively kind. A Philadelphia advertiser accuses us of impure power and exorbitant ambition. This is the Richmond Enquirer. The article's by Hampton. Spencer Rohn? Spencer Rohn. State rights, he tells us, are the bone work of freedom and independence. State rights. The man doesn't know the history of his own country. State rights. We want our freedom and independence, not because of our system of government, but in spite of it. It was the insistence on state rights that drove us to the brink of disaster. And had not the will to fight and die for liberty united the American Army, we would have perished. I know it. You do, yes. But consider, my friend, your faith in the Union. To what do you owe it? Impassioned sermons? Logical reasoning? You owe to necessity. Unity taught you the value of unanimity, unity, common purpose, mutual support. Valley Forge. Princeton. Monmouth. There's where you learn. Paying for the knowledge you now possess with suffering, anguish, agony of body and soul. Where are the men then that oppose you now? Thomas Jefferson in his library. Spencer Roan on a school bench. Patrick Henry, George Mason, Samuel Adams. Not one of them bore arms. United we stand, divided we fall. For the Spencer Roans of this country, these are mere words. For you, it's a fact which cannot be denied.  This fool, not accepted. You're quite right, my friend. A love of the Union, as I shared with an army of brave men. Men from Massachusetts, Virginia, Georgia, Pennsylvania. Men who talk me to see America as my country. Congress is my government. Men who I haven't forgotten. I know others have yet to learn and learn it in the manner in which you did. In his opinion in McCulloch v. Maryland, John Marshall established the reality and vitality of the federal government. At Valley Forge, the American Army almost perished because the states would not honor their commitments. The Supreme Court had now made certain that the Union and its central authority would never again be in such crisis. The whole would never again be endangered by a lack of cooperation from its parts. John Marshall, writing for the Supreme Court in McCulloch v. Maryland, undertook to produce a justification for the supremacy of the federal government in the powers granted by the Constitution. Persuasive enough to last through the coming generations. In this, he succeeded.


One of the most important things for any business in the world is the branding of the business. It helps in many different aspects of the business, in aspects of returning customers, prices that you can increase and even how many people will find your business on eBay or Google search results. In this video I will show you exactly how to brand your eBay store at the right way and I will show you eight different methods to do that right and I will also explain you why it's so important to do that and how to do that with really cheap prices and without spending a lot of money. Short intro and we are starting. Hello everybody! So in this video I want to talk with you about branding one of the most important things for any business. I don't know why eBay sellers are missing this part and why they don't do that when it's so easy and so time effective. It's so important to waste this small amount of time and really, really small amount of money to improve the branding of your store because it will improve your store so much. I want to show you in this video how to do that right but first let's talk about the effect of the branding of your store. So first of all branding of your store will bring you more returning customers. All of us know that one of the best sales is a sale for a returning customer. It's the cheapest customers that we can get to our business. So if the customer will remember the name of our store next time when they will find our store somewhere in Google on eBay or even they will just remember it from your visit card or something like that they will go and buy from your store instead of your competitors. That's the first reason why we would brand our eBay store. The second reason is because it will rank us higher on eBay's search results because when people are knowing us better, if someone knows us better they will click on our listing and then eBay will understand that people are really searching for our brand and our store instead of our competitors. So it will rank us higher and we will get more sales. The last thing here and one of the most important things is the pricing. If our store is branded we can price our products much higher. We can put higher prices, make more profits because people already know us and understand that this store is a professional store and this company we want to deal with them because they give us a great customer support and different aspects that will help us to increase the prices and will help people to trust us and buy from us. So let's jump into the eight methods how to brand our eBay stores. Step number one, the template of our listing. So this one is I guess that most of you know what I'm talking about but I will go over it shortly because this one is critical. I just opened the random product on eBay and what we can see here for example that we don't really see here something branded or any beautiful template. So that's a bad example of how it should look like. But let's write here I don't know a toy for example just to find something which looks better than what we just saw. This one also a bad one. As I said before I don't know why people don't spend enough attention to this but templates are critical for your store. So let's jump and see how we can improve this thing and really put a good template for our store. What I will do is I will go to Fiverr. I will write here template for those of you who don't know Fiverr is a marketplace where it can just hire someone to do a specific job for you. And here we can see a lot of different offers. Let's just add the word eBay here. And we can see here different professionals who offer to build a template for us. I wouldn't choose someone cheap but I would choose someone by the amount of their feedbacks. We also can give some recommendations which you can find on our blog post that I will attach below this video. So what we see here is different people who just offer different templates just go there and you will find someone who can build a great template for you. See the prices will go between $20 to up to maybe $50, $60 per template but I would really go for something which is around $20 build one template for myself and then stick with this one. Before I do the template I would really recommend you to also create a logo for your store which can also be done on this side. So if we cover the logo and the eBay template we already have two things that are specific to our store and we really make us different than our competitors. So eBay template and we can also write eBay logo or store logo or anything like that on Fiverr and just find someone, pay him and create something branded for our self. Before we create the logo and the template we should also create the cover for our store. So if I go to any store here on eBay, I click on it, here at the top we will see this banner. This banner is also something that should be branded and you can also find it on Fiverr. So I would order from the same person the logo, the banner and the template and you can even discuss with them for a better pricing for this type of job. So after we have these three elements in case of designs we already ready and we can already start and adding them to our store. So after that we will see something which will be much more beautiful here, we will see here a store logo, banner and if we go to any of our templates or of our listings we will see there the right template. By the way, if you bought a template most of the service providers on Fiverr already know Autodesk. So just give them your login details to Autodesk, you can even give them an access of a VA and then tell them to add a template for you in the system. All what they need to do is to go to uploader, add new template and most of them will already know how to use our template builder and integrate the template for you in the system and in this way you will not even spend time of integrating the template because they will do that for you. So now let's jump to the branding trick number 3 and this is the third thing that is really important for us and this is the description here. So have the logo, banner, template, now we need to explain who are we and what is this story about. So I would write here something which we really go to the heart of our buyers and explain them why this story is so important for us, why they will get the best customer experience with you if they work with you. For example, this is a store of my entire family and all of us managing this store together to provide the best service for you because that's what we love and that's what we are making the living from and this will really give the confidence to your buyers to buy specifically from you because think about yourself from whom would you buy from someone like this seller who just writes a based in China, his store name and that's all or from someone who writes there really something specific which is really unique for them and you really feel that you're dealing with a real person who cares about you. So this is something that is critical when we covered all this stuff, we can jump into the next step. The next step and this is the tip number four for branding your eBay dropshipping store and this is the gift message. When you dropship from Amazon, AliExpress, Walmart or any other supplier, you have an option in your order to add a gift message. Now if you think about that, this is our time to give our customer another reminder that we are the person who sends him the product and now they will be happy because they got the product. Now, mostly if you do dropshiping from Amazon for example, they will be in this moment super happy to get the product fast and then they will remember your brand as something good. Now, let's see how it works. If you go to Amazon or Walmart or any supplier, when you make the order in the last step, you just put the gift message. If you work with automated orders in AutoDS, you just need to go to orders processor, click the edit button and then choose here the gift message and right here, thanks for buying from us and remind them the name of your store. For example, thanks for buying from us, leave all store, we wish you to enjoy the product or anything like that. But remember to remind them from whom they bought the product. So if you add the gift message, it's another opportunity for you to remind them that hey, we gave you the product, please remember us and also you can write here please leave us a feedback on our eBay store. Just for example, then they will also remind that they need to go and give you something nice back because it's important for you. I would even spend more time in the copy of this message so I can write there or something like it's really important for us. It will change our life if you put a positive feedback for us. Step number five in branding our eBay store. So branding is not only about texts and about images or templates or a cover picture. Branding starts and finishes with customer support. Same as we do in AutoDS and we always focus in giving the best customer support that's important for any business. Same for eBay store and eBay also values this a lot. Maybe you heard a lot about people who got suspended on eBay. Now mostly the reason is just bad customer support but it's also very important for branding. So to give the best customer support you need to create templates for messages for yourself. Templates that really had some copywriting something which will really be written with a good language, good English and will be clear for your customers and show that you're a professional store. If you work with AutoDS customer support system you can integrate their messages templates for messages and then with the click of a button send it to your customers. So that's what I would recommend to you. Go to customer service, click on view and reply and then here in the bottom you can add messages templates. When you add the messages templates here make sure that for the signature of any message you use your store name. For example thanks and then your store name. Also remember always to contact the buyer using their name. So to do that what you need to do is just to put full buyer name here and then with the click of a button AutoDS will use the name of the buyer when you send this message. So this is something which is really critical and I really recommend you to spend a lot of time and a lot of efforts and focus on improving your customer support. If you do a good customer support the customers will remember you and this will also affect and improve your branding. Tip number six always stay in the mind of your customers. Again same as we did with the gift message. If you work manually remember to send follow-up messages to your customers. Hey I already sent your product it's on the way to you and it will arrive within x time or hey here is your tracking number. You can follow it here. You can track your tracking number here. And in the end the third message will be hey I know that you already got your product and I hope that you're happy with the product and the service that you got please leave us a positive feedback. Positive feedbacks for sure will also improve your branding and your eBay store. How to do that automatically if you use AutoDS go to the monitors page then go to orders processor and then just click here messages to buyers choose the messages that you want to send to your buyers automatically and it will be sent to your customers. The next tip step here is the tip number seven.  So when you list products to eBay make sure that you add there a small watermark that shows people that this is your store. This is something that is not a will not make a huge difference but all together will make the big difference. If you work using AutoDS go to settings just add a watermark here upload the picture and that's all. After that for any of your products you can with the click of a button add this watermark to all your pictures and that's all. This is really highly recommended and it will make your photos and pictures look different from all of your competitors. It will increase the chance that people will click on your listing and for sure it will also improve your branding. The last thing and this is the eighth step to brand your eBay store and this is the social media. We wrote about it on our blog post about branding which you can also read and we already talked about what I said in this video in this blog post and this is the social media. You can read eBay's FAQ about using social media but shortly what I recommend you to do is to create Instagram, Facebook, Pinterest, Pages for your eBay store and list there your top products. Share some information about your store share some information about the products that you list your store in this social media. Now it's not something that within one day you will get a lot of followers a lot of traffic to your store from this social media but after some time if you really put efforts in this and put focus on improving your social media networks for your eBay store first you will get assets you will get assets that will which will stand with you for the long term it will help you if you create more stores for example if right now you have only eBay store but soon you will also open a Ucomar store or Shopify store or Amazon store it will still stay with you and will be part of your brand. It also gives much more confidence to your buyers to buy from you when they see that this is a real brand that has some networks and some more channels where they can follow you and learn more about you. I really recommend you to take all these eight tips that we already talked about let's go over them really quickly and see what we talked about so we talked about templates we talked about the logo and the cover we talked about the store description the gift messages the customer service which is super important custom messages to buyers and the watermark the social media and all this together will give you huge results and you will see huge increase in your sales for the overtime what I recommend you to do is just go to the orders page in auto.ds export the orders and check in google sheets or excel in your computer how many returning customers you see right now after that two months after you branded the store check this again and you will see a significant change in the amount of returning customers that you see in your store. I hope that you like this video don't forget to subscribe to our youtube channel share anything that you would like to know about dropshipping in the comment section like this video and share it with other ebay sellers and dropshippers see you in the next videos bye


I am a Ph.D. student at Electrical Engineering Department IIT Bombay also I am a teaching assistant for this course. I am working in the area of RF and microwave. So today I will be taking a lecture on microwave diodes. So let us start the lecture. Firstly I will give you the brief outline of this lecture we will be starting with semiconductor materials then we will talk about n type and p type of semiconductor materials after that we will discuss about p-n junction diode then verector diode, short key diode, pin diode, tunnel diode and finally, gun diode. So let us start with semiconductor material we know in any atom electrons can occupy only discrete energy levels. Now if two or more such type of atoms are brought in close vicinity then the electrons at the similar level should shift to the higher energy level. Now many of such atoms are if brought in the close vicinity they form energy regions these regions are called S bands. Two of the bands are the conduction band and the balance band and they are separated by a forbidden region. This forbidden region is also known as the energy band gap or forbidden gap. The band gap defines a significant role in defining the conductivity of the material. Now the materials are divided into three types first one is metal then semiconductor and insulators. So in case of metals the conduction band and the balance band overlap with each other. So an electron can move from the balance band to the conduction band at 0 Kelvin. In this case electrons play main role in the conduction. So the only type of carriers are the electrons. So this is a materials which has only one type of charge carriers that are electrons. The next type of material is insulator. In case of insulator the band gap between the conduction band and the balance band is relatively high it is of the order of 4 to 9 electron volt. So electron cannot move easily from balance band to the conduction band. It requires a sufficient amount of energy to move an electron from the balance band to the conduction band. So they are not a conducting material. The next type of material is the semiconductor material. The band gap in the semiconductor material is between the insulators and the metals. It is of the order of one electron volt. Now at room temperature the electrons gains sufficient energy from the thermal energy so that they can move from the balance band to the conduction band. And when a electron moves from the balance band to the conduction band it leaves behind a hole. Now if you supply some energy in this particular case this vacancy is filled by another electron. So it looks like that the movement is also taking place because of holes. So in the semiconductors there are two type of charge carriers holes and electrons. Now the concentration of holes in any band is defined by the Fermi energy level. So Fermi level is an energy level which would have 50 percent of probability of occupying at any instant of time. Now I will talk about the semiconductor materials which are used by the industry. So the most commonly used semiconductor material is silicon. The band gap for silicon is 1.12 electron volt. For germanium the band gap is 0.66 electron volt. For gallium arsenide it is 1.43 electron volt. For indium phosphide it is 1.27 electron volt. Now among these semiconductor materials silicon is the most widely used semiconductor materials and most of the electronic devices are made using silicon materials. And few of the active devices are also made using the semiconductor material but they are not suitable candidates for the microwave frequency range because they suffers with the problem of minority charge carriers storage which will not provide the desirable performance at the microwave frequency region. Now if I see these two type of materials they are the compound semiconductor materials. Now if you see the energy gap for these materials are relatively high but they offers the significant advantages over these two materials like they provide low noise figure, high power handling capability and they can operate up to very high frequency range may be up to terahertz. Now if I want to increase the conductivity of the semiconductor material, so the semiconductor material conductivity can be increased by adding the small amount of impurity in the semiconductor materials. So there are two types of impurities which can be added to semiconductor materials. The one of the impurity is the n type of impurity which belongs to valence 5 group. So let us take an example of an atom from valence 5 group. So phosphorous is the example from valence 5 group. If we add the impurity of phosphorous in a silicon lattice, now we know in case of phosphorous it contains C5 electrons in its outer most shell. So these electrons form the covalent bond with the silicon lattice that can be seen from this particular figure and the fifth electron is loosely coupled to this lattice. Now at the room temperature, this electron gains the sufficient energy so that it can move from the valence band to the conduction band and it is negatively ionized. Similar case happened in case of other impurity atoms. Now when the impurity atoms are added, the amount of impurity atoms are generally lies between 10 to the power 18 atoms in per centimeter cube region. So if you see in these n type of materials, the impurity atom have a tendency to donate the electrons. So that is why this impurity atom is called as donor. So in this n type of materials, electrons are the majority carriers and holes are the minority carriers. Now the Fermi level in these type of materials is shifted towards the conduction band. I will show you Fermi level in the next slide. The next type of material is the p type of material. When you add the impurity from valence 3 group, for example, if we add a boron atom which belongs to valence 3 group, now we know in case of boron in its outer most shell, 3 electrons are there. So they forms a covalent bond with the silicon lattice. You can see here and at the fourth position, it has a tendency to accept the electrons from the adjacent covalent bond of the silicon. Now at room temperature, it again gains sufficient energy so that it accept the electrons from the adjacent silicon lattice and becomes positively ionized. Now the vacancy is created at this particular place. This vacancy is again filled by another electron and the hole will be created at that particular location. So it looks like that the movement of hole is taking place. In these type of materials, holes are the majority carriers and electrons are the minority carriers. Now these type of impurity atom have a tendency to accept the electrons. So they are called as acceptors. In these type of materials, the Fermi energy level lies near the valence band that I will show you in the next slide. Now if the n type of material and p type of material are brought together, then they form a junction that junction is called as a p-n junction diode. Then you can see that in case of p-region, the Fermi energy level is near the valence band. In case of n-region, the Fermi energy level is near the conduction band. Now when these materials are brought close to each other, they have a tendency to make a equilibrium. So we know in case of p-regions, holes are the majority carriers and in case of n-region, the electrons are the majority carriers. Then these carriers will try to make the equilibrium. So hole from the p-region will try to diffuse into the n-region and electrons from the n-region will try to diffuse into the p-region and they will leave behind the positive ions in case of n-region and the negative ions in case of p-region. Near the junction, they forms a space charge region which builds the electrostatic potential and this electrostatic potential further refuses the diffusion of electrons from the n-side to the p-side and it also refuses the diffusion of holes from the p-side to the n-side. Therefore, in equilibrium, there is no flow of current due to the built-in potential. The built-in potential is defined by the impurity atoms or the doping profile and the type of material which is used. So the built-in potential for silicon lattice is 0.7 volt and for germanium it is 0.3 volt. Now I will talk about the operation of this p-n junction diode before going into the operation mode. Just see the IV characteristics of this diode. Now I will talk about the operation of this diode using the IV characteristics of this diode. So when the p-n junction is connected in forward bias mode that means if the positive terminal is connected to the p-side and the negative terminal is connected to the n-side, then it will repel the holes away from the terminal and it will again repel the electrons away from the negative terminal. So they will try to reduce the depletion region. So that can be seen from this particular curve. So when the forward bias voltage is greater than the built-in potential or the n-voltage, so up to this point only the reverse saturation current will flow which comes into the picture due to the electron hole pair generation. So when the forward bias voltage is greater than the built-in potential the current flows in this particular circuit. When the forward bias voltage is much greater than the thermal voltage which is defined by the kT by Q and that is 26 millivolt at room temperature. So when the forward bias voltage is much larger than the thermal voltage then the currents increases exponentially. This can be seen from this particular curve and the current of this particular curve is represented by this expression. This is known as this Shockley's current equation. So here you can see if Vt is less, if V is much greater than the kT by Q then it will increase exponentially. Now if I bias this Pn junction diode in reverse mode that is if the P region is connected to the negative terminal and the n-side is connected to the positive terminal. Now the terminal will attract the holes toward the P region and the positive terminal will attract the electrons towards the negative terminal. So the depletion layer width will increase and it will restrict the flow of current. So you can see in reverse mode there is a very less of current which is equivalent to the reverse saturation current. Now if we increase the reverse bias voltage to a sufficient large value then the current increases suddenly. Why does this happen? Because for this particular voltage the electrons gains sufficient energy so that they knock out the electrons from the outer orbit of the atom and the current increases. The reverse bias voltage can also be increased further. There is no harm in using the Pn junction diode above this reverse bias voltage but make sure that there should be a connection with the resistor so that it should not damage the diode. One more thing one should keep in mind while using this diode in this particular region that it should not exceed the maximum current because if it is to be brought in below breakdown voltage then it should be operated in the normal region. So that is the thing that one should keep in mind when one is exceeding the general breakdown voltage. I will talk about this diode circuit model. So the diode will be represented by a non-linear current source in parallel with two type of capacitance. The one capacitance is the junction capacitance and the another one is the diffusion capacitance. Then this should be connected in series with the series resistor which accounts for the losses in the depletion region. Now this diode is to be packaged so the packaging losses should also be considered. So the Cp capacitor is included to account for the packaging capacitance and this Lp is considered here to account for the bonding wire inductance. Now how to make this particular diode? To make the diode lightly doped n type of layer should be deposited on heavily doped n type of substrate then the p type of layer should be deposited on the n type of layer. Now to make the electrical connection with the circuit the metallic contacts are provided at both the ends. These are the metallic contacts you can see. These metallic contacts could be of tungsten, aluminium, gold etc. The next is where these type of diodes should be used. So there are various applications in which these diodes can be used. So diode can be used as a rectifier, voltage regulator, switches, power limiter, digital gates, clipping, clamping etc. Now depending upon the application one should choose the diodes. Now before going into the practical diodes I will talk about the representation of this diode. So this diode is represented by this particular symbol. Here this terminal represents the n-ode and this terminal represents the cathode. Now the forward current will flow in this particular direction. So it supports the movement in one direction and this is called as the unipolar device. In ideal case it will only support the current flow in this direction and it will not allow any current to flow in the reverse direction. Now the diodes can be defined into two types depending upon the their current rating and the power rating. So the diodes are divided into two categories small signal diode and the large signal diodes. So the true examples have been taken for the small signal diode. So IN 4148 and IN 914 are the diodes for the small signal diode. The specifications of these diodes are given here. You can see from the current rating the current is relatively less. These diodes are a good candidate for switching applications or for clamping. The third type of diode that is IN 4007 is a power diode that you can see from the specification of this diode. The current rating is relatively high. So it is more suitable for the applications like it can be used as a power diode or rectifier. So one should choose the diode according to the application. The next diode that we will talk about is the vector diode. Now if we see the p-n junction diode and if we try to see the reverse bias behavior of this diode it shows a very interesting property. Just to explore that particular behavior just connect the p-n junction diode in a reverse polarity. So that the positive terminal is connected to the n region and the negative terminal should be connected to the p region. Now if you increase the reverse bias voltage the depletion layer width will increase. So you can try to relate this geometry with the capacitor. These two regions n and p regions will be analogous to the parallel plate capacitors and this will be analogous to the parallel plates of the capacitor whereas the depletion region is analogous to the insulating material between the capacitor plates. So now we know in case of parallel plates capacitor the capacitance is given by epsilon A by D where D is the width of the insulating material. So if we increase the reverse bias voltage the width of the depletion layer will increase. So the capacitance will decrease. So therefore with increase in reverse bias voltage the depletion region increases and the capacitance reduces. Now the capacitance of the vector diode is given by this expression here V is the reverse bias voltage, phi naught is the belittle potential and gamma depends on the doping profile. So gamma is equals to 1 by 2 or 1 by 3 for abrupt or the linearly graded junction. Here Cj0 is the capacitance corresponding to 0 bias condition and it will be maximum. Now this particular diode is represented by this particular symbol. Here you can see this is similar to the PN junction and in series the one capacitor is added. So this represents the symbol of the vector diode. Now there is a very important characteristics of vector diode and that is the Q factor. So suppose if a vector diode is used for a application like oscillator. So if it has higher Q it will provide relatively low phase noise. Similarly in case of tunable band pass filter if the Q factor is high so the tunable filter will be more selective or the response will be steeper. So depending upon the application Q factor should be chosen. Now we know the Q is inversely proportional to the C value and the series resistance. So there is a tradeoff between the capacitor value and the quality factor. So one should choose the capacitor according to the application. Next I will talk about the IV characteristics of this diode. As I mentioned earlier capacitance decreases with increase in reverse bias voltage. So this shows the characteristics of the vector diodes. Now these IV characteristics of the diode can be altered by changing the doping profile. So there are two types of doping profile abrupt and the hyper abrupt. In case of hyper abrupt to doping profile the capacitance variation range is relatively high but it comes at the cost and low Q factor. Now if I talk about the applications these vector diodes can be used in various applications like voltage control, oscillators, tunable filters, phase shifters, amplitude modulators, frequency multipliers etc. Now again similar to the pn junction diode one should choose the diode depending upon the applications. So here I have taken the two examples of practical diode one is BBY5702 the specifications for this diode is given here. The quality factor of this diode is very high. So it is more suitable for the selective filter and the another example I have taken where the tunability range is relatively more. You can see in this case the C max to C min ratio is relatively more and it defines the tunability range. So it is more suitable for the wide band tuning range like if you want to use it in vector network analyzer or a spectrum network analyzer then the diode will be more suitable. So one should choose a diode in depending upon the application. The next type of diode is the short key diode. So the short key diode is similar to the pn junction diode but in this case the junction should be made using the n type of material and the metal. So in this case the n type of epitaxial layer is deposited on the highly doped n type of substrate and then metal is deposited on the n type of epitaxial layer. Now to make the electrical connection with the circuit the metal contacts have been made and this is how the structure of short key diode is made. Now we know this is the junction of metal and the n type of semiconductor. So the depletion region will be less in this case. So this provides relatively low built in potential or low turn on voltage and due to the less depletion region it provides relatively fast switching and less reverse recovery time. So what is reverse recovery time? So reverse recovery time is the time taken for a diode to switch from on-staff to the off-state or vice-verse. So in case of pn junction diode this time is around 5 to 200 nanoseconds, however in case of short key diode this time is of the order of 1 nanosecond. But there is a disadvantage of this diode it suffers with the high reverse leakage current and low breakdown voltage due to the low depletion region. Now if I compare the IV characteristics of this diode with the pn junction diode from these IV characteristics you can see it provides low turn on voltage and it is of the order of around 0.3 to 0.4 volt and you can see here the reverse leakage current in this case is very high. It is of the order of micro ampere however in case of pn junction it is of the order of nano ampere and the breakdown voltage for this diode is relatively less. So this is the drawback of this diode. Now if this diode is to be designed for the vector applications the doping profile should be altered accordingly. Now if I talk about the circuit model this the circuit model of the short key diode is similar to the pn junction diode. The only thing is there will not be any deficient capacitance so that is not included in this circuit model and the short key diode is represented by this symbol. This corresponds to the anode and this represents the cathode. If I talk about the applications so the applications of the short key diode is similar to the pn junction diode they are used in RF mixers and detectors, power rectifier, SMPS and clamping etc. Now again here I have taken the example of two practical diodes. This one belongs to the power diode you can see from the current and the voltage rating and this one is more suitable for the switching applications. So one should choose again the diode according to the application. The next type of the diode is the pin diode as the name says that here the intrinsic layer is inserted between the highly doped p and n junction. So the i layer is deposited only on highly doped substrate and then highly doped p type of layer is deposited on the intrinsic region. So this is how the geometry of this structure is made then again the contacts are made to make the connection with the electrical circuit. So in this case the depletion region is relatively wider due to the insertion of this intrinsic region. So in this case if I talk about the reverse bias case it will provide very wide depletion region. So the capacitance for this diode will be very less and it will be almost constant because the depletion layer length is relatively wide. So in this case it provide the lower capacitance and if I connect this diode in the forward bias then with increase in forward bias voltage first the recombination of electrons and holes will take place in the intrinsic region after that the recombination will take place in the p and n regions. So the resistance of the diode will vary. So in the forward bias it will act like a variable resistor. Now the symbol of the pin diode is represented here this denotes the diode and this represents the cathode. Now if I want to make a circuit model of this it can be divided into two cases the forward bias and the reverse bias. In the forward bias it acts like a variable resistor and in the reverse bias it acts like a capacitor whose value will be much less as compared to the p-n junction diode and then a series resistor is added to account for the losses in the depletion region. And these LS and CP are accounted for the losses due to the packaging. Now if I talk about the characteristics as I told you earlier the pin diodes offers high resistance it provides lower capacitance due to the insertion of the intrinsic layer between the highly doped p and n layer it provides high breakdown region due to the intrinsic region. So if I talk about the applications these diodes are mainly used for the applications like in variable attenuators RF switches phase shifters high voltage rectifiers RF modulators power limiters etc. Now just to show again the applications I have taken the two practical diodes. The first one is corresponding to the power diode and the second one is more suitable for the high voltage variable resistor. So one should again choose the diode according to the application. The next type of diode is the tunnel diode. So the tunnel diode is a diode where the p and n junctions are highly doped. Now we know in case of conventional p-n junction diode the conduction and the valence band are separated by a large forbidden gap when they are heavily doped the Fermi level shifts in the conduction band in case of n type of material and it shifts in the valence band in case of p type of material. So there is a mechanical phenomena which takes place this quantum mechanical phenomena is called as the tunneling. So in the thermal equilibrium the Fermi level of the conduction band and the valence band will line up. So there will not be any flow of the electrons from the conduction band to the valence band. So the voltage will increase the voltage from 0 to the voltage corresponding to the peak current then the barrier potential will decrease and the level will shift up. So there is a possibility that the electrons from the filled state in the conduction band can tunnel into the empty states in the valence band. So this can be seen from this particular figure. So as the electrons tunnel from the valence band to the conduction band the current increases. Now when the voltage is equivalent to the peak voltage in that case the maximum tunneling of electrons can take place from the conduction band to the valence band. So it represents the maximum peak current. Now if the voltage is increased further in that case the tunneling of charged carriers will decrease. So the current will decrease with increase in voltage. Now when the voltage is increased more than the value voltage in that case there will not be any overlap of these band. So the current will come to a minimum value or it may be 0. Now if voltage is increased further this tunnel diode will behave like a conventional PN junction diode and the injection current will start flowing which increases exponentially. So that is represented by this IV curve. Now if you try to make a load line, if you make a shallower load line whose resistance is relatively higher then it will cut these IV characteristics at these 3 points 1, 2 and 3. Now this point 2 is the unstable point. Now if there is a little deviation in the voltage then either it will come to 0.1 or 0.3. So depending upon the previous stage in this mode this tunnel diode are used as a memory device or the storage device but this is of little less interest to the microwave circuit designers. The another type of load line can be drawn when the R is relatively less. So it will show you the steeper line and it will cut here in the negative resistance region. So this particular region represents a negative resistance region and if you connect this circuit now with the external LC component it will act like a oscillator. So here you can see that the negative resistance region is less so it will provide low current and the power provided by the tunnel diode will also be low. So it can provide the low output power oscillators. Now if you see here in this region the current increases linearly with voltage however in this region it acts like a conventional diode. So the region 2 is a transition between the linear region and the p-n junction region and in this region it behaves like a negative differential resistance. Now this diode represented by this symbol this represents the anode and this represents the cathode. So the characteristics of this diode is that it can operate up to very high frequency range may be up to millimeter wave frequency range and it can operate up to 100 gigahertz it provides very high speed operations and it provides low noise low power consumption but it suffers with a drawback of low output power. So nowadays this is replaced by transistors. Now if I talk about the applications tunnel diodes are used as a ultra high speed switches they can be used logic memory storage devices microwave oscillators and amplifier they can also be used in FM receivers. So here I have included the two examples of practical diode and this first one is used by the Russian military for switching applications and the second one that is IN3716 is used to make the oscillators or the transmitters. So depending upon the application again one can choose the diodes. The next type of the diode is the gun diode. So this is a special kind of diode it uses only one type of semiconductor material here the lightly doped n type of material is inserted between the two heavily doped n type of semiconductor material and the metallic contacts are made to make the electrical connection with the circuit and the heat sink is provided to account for the heat losses. So we know in case of few materials like gallium arsenide and indium phosphide they have local minima in the conduction band. See one of the local minima contains the higher mobility and lower effective mass however the another minima which is at relatively higher energy level it contains lower mobility and higher effective mass. So in general all the electrons occupy the lower energy states. Now if you provide the energy to this material the electron gains the energy and they try to shift from the lower energy state to the higher energy state where the mobility is less. So as long as the concentration of electrons is more in this band the current increases. However if you again increase the electric field there will be a situation when the concentration of electrons will be more in this case which corresponds to lower mobility. So the mobility decreases with increase in voltage that means the current decreases with increase in voltage that represents the region 2. Now there will be a situation when you again increase the voltage then all the electrons will shift to this band and it will have the lowest mobility in this case the current will be minimum. So if you again increase the electric field diode will behave like a normal PN junction diode and its current will increase exponentially. So this is the IV characteristics of this gun diodes. Now if you see here this looks similar to the tunnel diode. But if you look into the operation principle of these diodes they are quite different and that is the reason that gun diode provides relatively high RF output power. So this diode is represented by this symbol. The next I will talk about the gun diode characteristics. This gun diode can operate up to very high frequency range maybe up to 150 gigahertz with relatively high output power at low cost. So nowadays many of the gun diodes are replacing the microwave tubes. They are more reliable and stable at higher frequency range. But this suffers with the low DC to RF efficiency. They are also sensitive to the temperature variations and they provide relatively small tuning range and the power dissipation in these diodes are relatively high. Now if I talk about the applications these diodes can be used in as a low and medium power microwave oscillators and amplifiers they can also be used as sensors in detection systems. Now here I have included the two practical diodes. This one is the pulse diode and provides relatively high output power and this is designed in the X band. The output power for this case is of 10 watt. And in this particular diode this is a continuous wave diode and it is designed for the carbon. The output power for this diode is 300 milliwatts which is considered as a medium power gun diode. Now just to conclude in this lecture we started with semiconductor material then we saw how the conductivity of the material can be increased by adding the impurity in the material. Then we combine the n type and p type of materials and the combination of n type and p type of material forms a p-n junction which provides a very interesting feature like rectification, switching. Then we talked about the vector diode and we saw that how this diode can provide the high tuning range of capacitance which will be used in various applications like in oscillators, tunable filters etcetera. After that we talked about the short key diode which is the junction of metal and the semiconductor and due to this particular junction it provides very high switching. So it is more suitable for the mixing and the detection. Then we talked about the pin diode due to the insertion of intrinsic region between the two highly doped p and n layer it provides the variable resistance. So it is highly used in case of variable attenuators and other applications. Then we talked about the tunnel diode which is highly doped p-n junction diode and it provides a special feature of negative differential resistance but this suffers with the low output power. So using the tunnel diodes low output power oscillators or the amplifiers can be designed. Then we talked about the gun diode and then we saw that the gun diode provides relatively high output power and nowadays they are replacing many of the microwave tubes and cavities. So with this I would like to conclude thank you very much.


Starway Stone Ward, an invasive species, has been confirmed in Cass Lake. The Forest Service announced a closure order near the Knudsen Dam to reduce the spread and prepare for treatment. Mel Meyer has more from the Chippewa National Forest. The Knudsen Dam boat access, campground and parking areas will be closed until January 1st to reduce the spread and for a previously planned construction project. The boat motors tear up the algae and then the little segments can populate themselves elsewhere. The Forest Service says that will work with the Minnesota Department of Natural Resources, which will use herbicides to kill off the species. It's not high fishing season right now. If we have to have this infestation, this is a good time to find it and treat it. The plan created by the Forest Service and its partners may look like the one used on Turtle Lake, which has had mixed results. Bruce Ansbach will be assisting both groups with the project. He also oversaw the work on Turtle Lake and the dredging process used there. So with the equipment in there, they kind of push some up next to the drift curtain and then they couldn't vacuum up right next to the drift curtain. Workers have since applied herbicides twice to kill off remaining fragments, which has worked in other bodies of water like Upper Red Lake. It actually worked really well because it's an enclosed harbor area and the stuff is practically gone. The size of the infestation provides hope for eradication. We haven't found any more, except for at the Knudsen Dam area, so that's very hopeful. In Bemidji, I'm Al Meyer, Lakeland News. Zebra Mussels, another invasive species, was found in Cass Lake in 2014. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.