In a previous video, we discussed the RPIE model of public relations and the E as you may recall stands for evaluation, which is a very important aspect of public relations in the entire process that we evaluate things. And so in this video, I want to just talk briefly about some of the basics behind measurement and evaluation and the importance of those things and some of the things we might factor into those considerations when performing measurement and evaluation. So first of all, let's talk about the very basics, the goal of measurement. What are we doing here? What's the purpose of all this and what are we looking at really? So we start with the goal of measurement of we have to factor in our output, the output of ourselves individually and of our team and whatever's going into this campaign. What is the output? What is the efforts that are the efforts that have gone into creating this campaign and implementing this campaign? What is this cost that's not only in dollars but in people hours, the amount of work that we've had to put into it, and just the brain power and all that kind of stuff. And then so what has been the productivity and the cost of that productivity for our organization? So that's our output. What have we created? In other words, as a result of this campaign or for this campaign. Then we look at outcomes. What are our outcomes in this situation? What are we getting out of it in a very real sense, in a tangible sense? Are we seeing increased profits, increased awareness? Are we seeing any of these things? So what was the end result of that? Of that output? So we consider what was the output and what were the outcomes of that? And then we have to kind of then evaluate that and say, okay, considering the output that we put in, the things that we put into this and the output that we had, the productivity that we had, and the results of that, the outcomes that we had as a result of that output. Let's evaluate whether that was worth it, did it all balance out? Did it pay off in the end? Was it a worthwhile investment of our time and energy and mental focus and all those things factored into it? Were the outcomes sufficient to justify the output, in other words, and did it match up? Did our output match up what we hoped we would accomplish through those outcomes? Were we able to really achieve the goals that we set out to do? So we need to look at all of this and more as part of evaluation. It's really a holistic process. So then when we think about kind of the sources of measurement, how do we go about measuring these things and where does this information come from? Traditionally, we would look at things like mentions. In other words, just any time our organization or that idea, whatever it is we're trying to promote appeared in some sort of especially traditional media in a newspaper on a TV show or something like that. Anytime there was a mention, we would put a tick mark. And that's one mention. That's one thing towards a guy. And so people might have, we want 500 mentions or we want a thousand or whatever, they would have this goal in mind. Just to be mentioned, anytime your name appears, whether it had anything to do with that, really with what you were talking about or whether it really impacted and moved the needle towards positively or negatively. It didn't matter as long as you were mentioned. That's it. It was just a very strict policy of where you mentioned. We would look at airtime. What's the amount of airtime we're getting on media that measures things in that way, like radio and television? How much airtime are you being given by these things? Are they talking about you for five minutes or 20 minutes or whatever? So we would measure things through airtime as well. Again, it didn't matter if it was good or bad, it just was airtime. Impressions. Now impressions are how many people are getting eyeballs on this, on the different media. So an impression might be, you might be mentioned in a newspaper, right? Let's say your, your, your program or your company or whatever it is you're promoting is mentioned in a newspaper. So that's one impression. Somebody whoever gets that newspaper, that's one impression. They see it, they read it, but then maybe they pass it off to a friend. And that's another impression that we try and measure how many times, you know, not just was it printed in this many copies of the newspaper, but how many people would see those newspapers or that magazine because these things get passed around, right? You know, just one magazine in a dentist office may get a lot of looks as people are waiting in there. So, so impressions, how many impressions are we getting? Again, not measuring, you know, what were these impressions? Were they good or bad? Did it help us achieve our goals? Things like that. Just how many eyeballs we're on are the name of our organization or the program or whatever it is again that we're promoting. And then somebody came up with a sort of a complicated, you know, a more sophisticated way of measuring this called the advertising value equivalent, where AVE is it's known. And this basically measures how much would this cost if we were to buy, if we had to buy this kind of advertising number advertising, you're purchasing that space and you're purchasing those mentioned public relations.  So in other words, the number of mentions, the amount of air time, the number of impressions, how much would that be worth if we calculated it as a paid cost through advertising and what's, so it's the advertising value equivalent of the work that we've gotten. Now, again, this just looking at strictly the number of mentions, air time impressions, things like that are calculated into this, not the quality, not the type of impression positive or negative or whatever. So we need to remember that this is strictly quantitative, right? And that's, that's sort of the problem that all of this, all of these traditional measurements, not only we're focused on traditional media, right, traditional media, meaning they were developed on the time, but you can measure these things fairly easily in newspapers and television and radio and so forth. It gets a little more complicated when you get into new media, to social media and things like that. It gets a little tougher to track these things. So that's one issue. But, but also we're looking strictly at these things. We're looking at quantity and not qualities we've discussed. It doesn't matter if these mentions are positive or negative or if they're, you know, really on a, on a, on a major platform or on a minor one, or it doesn't matter if it's mentioned, it's mentioned. And that's it, right? That counts. You put the tick mark up there and, and that counts just as much as it counts just as much as getting mentioned in your tiny little local papers. It would being on, you know, the NBC nightly news or whatever. Those are the same things. If it's a mention, it's a mention. But we know that those don't carry the same amount of quality. They don't necessarily came to carry the same amount of weight. One is not the same as the other. So these types of measurements do not measure quality. They're only measuring quantity. And that's an issue. So, so really we're moving away from these types of traditional measurement because they just don't provide us with the information that we need to know whether or not our efforts are really paying off. So we need to approach this with more of an aspect of a funnel, right? Thinking about a funnel where we just dump everything in there and then out the, out the bottom end, when it's all switched together and comes out at the bottom, then we have our evaluation. We pull in so much more information, not just a limited amount of information, but we pull in everything we can drop it into the funnel. So we're looking at not only here, we're not looking, not only quantitative, but quantitative and qualitative forms of measurement. Quantitative focused only on the numbers, of course. It's measuring numbers, which is good. That's good information to have. But we also need to look at the qualitative aspects of this. Is it reaching the right audience? That makes a difference. Is it, you know, what kind of mention is it? Are they making fun of us on a late night show? Or are they, are they talking positively about us on a, on a news segment or in a newspaper or whatever? So what's the trend there? Are we at joke or are we being taken seriously and getting some positive traction out of this? We need to factor those things in as well. So we need not just the numbers, but the qualitative perspective. So we need to dump all that in the funnel. Have all that go in our funnel. We need to know it's positive or negative. We need to weigh these things differently. We need to know both. We can't just ignore the negative and only present and follow the positive. We need to know about both, but we do need to measure their impact differently. We need to understand the impact that these things are having based on whether or not they're positive or negative mention or negative, you know, connection through, through this measurement. We need to look at things like social media engagement. How much are people engaging in this topic and engaging in our topic? The topic we want them focused on. And again, not just the number of mentions, but how deeply are they connected to this? Is this turning into a movement? Is it something that people are just throwing away as kind of a joke and mentioning it in that way? We need to have to measure those things, but we need to be aware of social media engagement and also how much are people engaging with us now? Are people engaging with our organization as a result of this? And are we seeing an increase in the amount of traffic that we're getting through that? So social media engagement is an important one. We can look at things like good information from search engine results. Again, not only the number of searches that we're seeing on this particular topic or on our organization, but what types are they? And what kind of results are they getting? And so we can, we can throw that in the funnel as well. Let that go into our funnel. Inquiries from the public and from media. Are we seeing an increase in that and what kind? And again, measuring not only the number, but also the qualitative aspects of that, are they positive or they negative? Are they seeking greater connection and greater understanding? Or they, uh, it is not quite so friendly toward us. And we can look at, of course, the bottom line, we can look at sales and or service activity, depending on what your organization does and what you're looking for, what you're hoping to, to push with this program. Do we see a bump in sales numbers? Do we see a bump in profit through our services or whatever in our requests for our services? Uh, and, and so do we see an impact in that way? Not just quantitatively, but qualitatively as well. So we throw all this in this and much more. And we put, we just have to let it all go in the funnel. And then again, consider it all through this, the systematic way process that we, we can develop. And then at the end, we have our evaluation. What comes out at the end, we can, we can assess more, uh, holistically and not just based on strict quantitative measures, but what's the, the quality, right? Sometimes you hear, uh, for people, especially in, for example, the podcasting world, say it's not a matter of how many downloads you have. It's not a matter of, you know, are you the most heard podcasts in the world? It's a matter of, are you reaching the right audience? Right?  And you're developing those kinds of connections, deeper connections. That's what we want in public relations really. It's not just about the numbers. It is about the numbers because we want more people to hear our message, but it's also then about the quality of those connections. And that's what these give us when we put it all in the funnel. Those are the things we ought to be evaluating. Now, of course, evaluation is a, is a much larger process in and of itself. We do this assessment and analysis. We, we then look at performance and how we can improve it. Then we gather the results and offer feedback to our, to both to ourselves and to anyone who is connected with the project and what we can do better, what we can change, if anything, what we need to shift. Right? So evaluation is much more than just determining where to get your information from. There's, there's a lot to it here. And then as I mentioned, developing that process, how is it that you are going to strategically evaluate and measure these things and do so consistently? So there's all kinds of things involved with evaluation. We've really just scratched the surface a little bit here to, to define the importance in a sense, but, but I do want you to bear in mind again, this is all part of the process. This is kind of the circular process. So once we do evaluate then, once we have our evaluation, then we can factor that into our next round of research and in preparation through our planning for implementation, which we will then evaluate again. And it just keeps going and going and going. We keep evaluating these things. And there's almost always something we can do to improve or adjust or evolve as things move along here. So we need to be continuously evaluating any effort, any public relations campaign or effort or, or proof or process or movement that we're, that we're involved in needs to have evaluation as a part of that to then feed into that research area and kick things off all over again. If you have questions about measurement and evaluation in a public relations campaign, please feel free to email me. I'd love to hear from you there. In the meantime, I hope that you do have a new appreciation and understanding for the role of measurement and evaluation in the success of any public relations effort.


You can follow along with this presentation using printed slides from the Nano Hub. Visit www.nanohub.org and download the PDF file containing the slides for this presentation. Print them out and turn each page when you hear the following sound. Enjoy the show. So this is lecture 24 on large signal response of PN junction diode. Now if you remember that we are using the PN junction diode as a prototype of a very simple device. You can only simpler thing would be a homogenous chunk of semiconductor and which is basically a register and we know how to calculate resistance and other things. And this is the simplest one because you have a n type doping and a p type doping just two pieces a junction and we are going through this exercise of think the finding out how this device responds. So in equilibrium we draw the band diagrams of the Poisson equation and how saw how the built-in potential and how the depletion weight and all those things how they come about. We have talked about DC. The DC was a lot of discussion right because when you apply a bias we found that although the current is asymmetric positive bias it has a type of current which is exponentially rising with voltage and the negative bias it was saturating but there were lots of very interesting regimes. One was this trap assisted or defect assisted low voltage regime diffusion limited regime ambipolar and similarly on the reverse bias side we talked about Zener tunneling and Avalanche breakdown right. So all pieces are very interesting and if you understand them this forms almost a comprehensive list. In the last class we talked about small signal response that beyond the DC if you in addition catch a signal from air let's say you are listening to a radio station and then you have a diode then you have a DC voltage which is your battery to it you know your triple A or double A battery but in addition you pick up this microvolt amount of signal from the air and how would the circuit or the diode in equivalence respond to that small voltage that we found right we found that there are diffusion capacitance for minority carriers majority carriers there was junction capacitance and of course the conductance that depends on the bias point. Today we will be talking about this large signal response this is more like digital signals that you have let's say 1 volt and instantaneously you turn it to minus 2 volts let's say logic level 1 to 0 or go the other way around go from minus 2 volts let's say to plus 1 volt and if you make this transition too fast then what you have learned before wouldn't apply exactly and that is what would be the discussion topic of discussion today. So I will start with a charge control model and I will explain how that comes about we will start by talking about the turn of characteristics which is going from logic level 1 to logic level 0. Now remember logic level 0 doesn't mean voltage 0 logic level 0 might mean voltage of minus 2 volts for example this is just two separate largely separated voltages and we'll talk about a little bit turn on characteristics and then we'll conclude consider a diode in a circuit and the voltage source instead of being a triple A battery is actually transitioning between two voltage levels voltage level 1 maybe a volt and voltage level 0 which may be minus 2 volts let's say any voltage any specific voltage. Now the diode is in series you are measuring the current and if you just think about the diode itself you will get this IV characteristics right it is biased at a certain point and you can see the P side of the device is connected when it's logic 1 connected to the P side N to N side and so it's forward biased and so you can see the blue dot on the IV characteristics indicating that there is a finite amount of current flowing if it is at logic level 0 through the diode. Now if you gradually turned it off you know over a period of seconds then what would have happened that at every instant the diode would have adjusted to the DC potential almost and it would have gradually followed this curve. It is that the last point is let's say minus 2 volts every point is sort of inquires the equilibrium it knows the IV characteristics so beyond the DC calculation that we already did if the transition is slow then we don't really need anything more although the transition is not DC it is almost DC at every point however if you make the transition very fast let's say in your computer these things runs as tens of gigahertz in a nanosecond if you change it that fast then all in a sudden you will see that it cannot really follow this path what it is going to do is follow that red dotted path that instantaneously it will flip the current and flip the current you can see that immediately going keeping the voltage the same why the voltage remains the same I'll explain in a second but what is going to do from the positive current you see where y-axis is positive it immediately will flip the flip the car direction of the current as the voltage source wants the current to go the other direction it immediately responds to that dictate that current should go the other direction but then you can see for a while the current remains almost the same as the voltage is decaying off from a positive voltage gradually going to zero and then for a little bit it has the final final descent to the final final equilibrium point of course the final equilibrium point has to be the same because that's the final state what I'd like to explain to you today is the physics of this that why it takes this particular path under what conditions and how to understand that that's the purpose of this lecture now if you want to look it at it in a slightly different way you could plot the voltage and the current as a function of time you see this is voltage versus time on the right hand plot with time as a parameter so every point here you could stamp a time but in addition you could split it up also you could plot the voltage as a function of time and current as a function of time do you see that the the right hand side and the top drafts essentially contains the same information let me explain look at the the yellow points the yellow points are the voltages before this transition occurred I had a forward bias you can see on the left hand side the voltage versus time curve I have also a forward bias positive current and that's called I sub f you know f for forward now if you switch it very quickly again then you can see you will have this green circle the green circle is the current that has dropped down and you can immediately see also in the current versus time plot that the current has switched from I f to IR and it has done so instantaneously there's no time in there right so you can see almost instantaneously but for the voltage look at it the voltage the green circle is sitting on top of the yellow square so voltage has not changed now that's strange voltage is the same current going the opposite direction I mean how can that happen so we'll see that and then finally you see that great triangle great triangle is when the voltage has gradually decayed to its final value essentially going to voltage equals zero and on the left hand top side you can see the triangle and similarly but for the current look at this going from the green circle to the red arrow or a triangle the current has more or less remained the same now that's very strange and we like to explain that now let me explain some terminology so that I can help you guide through this concepts by the way when you do 0 to 1 minus 2 volts to plus 1 volt again it is going to take a non-trivial path is not going to follow the steady state DC characteristics and that's shown here in blue dotted line now a few quick definitions the definition is the we'll call this time T sub s storage time is the time when the current essentially remains the same during its transition current remains essentially the same we'll call that T sub s and for many circuits many minority carrier circuits mean sorry minority carrier devices like APN junction diode this time is a dominant time this is the storage time and I'll explain why they call it storage but it is only typically true for that minority carrier type devices that this time would belong and dominant then there is this TR the TR time is when the voltage has gone to zero and it's gradually swinging in back to the equilibrium reverse bias point you know gradually going down that's the T sub R now T sub R for this device will not be as big but for many devices as we'll show short key barrier diode majority carrier diode in that case that's the next class TR might become the dominant one and the total time is TRR which is called the reverse recovery time this is the time it takes for the signal to go voltage to go from positive side to the negative side now why do I what why am I interested in this time because if you try to flip the current or flip the voltage faster than this time your circuit isn't going to work so you calculate this time and design your circuit slower than this so that the voltage can reach the final point without any trouble okay now I have to solve this equation now that's going to be a challenge you can see Poisson equation I have to solve it from minus plus 1 to minus 2 volts now that's not something that's very good this time I cannot say n is n not e to the power j omega t it is not the signal coming from your 9 20 a.m radio signal with a micro volt from the air this is going from 1 to minus 1 volt or minus 1 to plus 1 to minus 2 volts I cannot drop the entity well I cannot really do much with this so I will have to stay with this and solve this it turns out that indeed on the computer you can do that people do that often but I can simplify this and that will in fact give me a lot of information a simplification of this where I get rid of the space coordinate of this equation and I explain to you how the way if we can get rid of that then I will have instead of those two complicated equations I will have this very simple first order differential equation and similarly instead of this whole transport equation drift and diffusion and all those things I will have this very simple equation you know it's approximate but for the transient what are you going to do if I had to solve this partial differential equation back of the envelope your real your envelope has to be pretty pretty large in order to contain all this calculation so these approximations are called charge control equations it is an approximation when you have large signal time transient you do so I will explain to you how this comes about but let's first talk about the what is happening in the device and how does this current flip without voltage flipping how does it do that so you see let's me assume that I have forward bias this diode do you see why it is forward bias you can see the Fermi levels quasi-Fermi levels has been split by that amount and quasi-Fermi level on the n side assuming the right hand side is grounded the left hand side has been pushed up forward bias minority carriers have been injected now in this particular case I have assumed that there is recombination on the minority carrier side how do you know that because this curve in xt is actually exponentially dying off had there been no traps then it should have been a straight line going across okay but then what happens now if I all on a sudden go from vdc from the dc voltage to a reverse bias voltage right so the Fermi level on the left hand side will go down significantly immediately in that case this is what's going to happen the current will go down a little bit and then the charge will gradually its charges gradually disappearing where is the charge going the charge is going to the other side getting back where it came from and part of it is recombining with the traps and with the majority carriers so you had a big build up of charge and gradually discharge is going away and eventually this charge will all be gone and you will get to the reverse side but one thing I want you to see do you see what is happening in here although initially the total amount of charge was exactly the same right when I turned it off look at the slope on the left hand side the slope I have changed the slope although I have not changed the charge more or less but since I have changed the slope at that point going now the current will be going in the negative direction so it follows the dictate that the current must be going in the negative direction simply by just nodding its head a little bit in that direction in the opposite direction because dndx diffusion coefficient multiplied by dndx is the current so all I care about is not the n n could be anything so long I allow the dndx in the right direction current will be flowing in that direction so you can see that by keeping this profile my current will all be going it will be a constant and going in the negative direction although the charge may be huge and actually be corresponding to a forward bias charge okay so this is a plot I will be showing you often the idea is you should see that this is a time sequence of the charge that is sitting inside the p n junction inside the minority carrier as you are going from the forward bias to the reverse bias now this is the equation transient equation I want to derive that charge control equation I will explain how first of all it's minority carrier right so I should always be able to take out the electric field as I said taking that out is a little subtle and I have explained to you you should learn it once so that later on when you drop it off you sort of know that you can go back and explain to a student but for the time being minority carrier side majority carrier holds the potential I drop the electric field so I have the diffusion term now on the diffusion term I have this n naught which is the equilibrium density well n naught does not depend on time I get that rid of that and I have delta n which is whatever the charge you see on the top right hand side the charge profile this delta n is a function of x and is a function of time you can see that the top side it has changes with space and also changing with time do you see why there should be a second derivative with respect to the diffusion coefficient of course because you insert the expression for j sub n and that's what you have and if this is essentially a small injection condition then is in the shock lid hall term becomes delta n over tau sub n right when you have put a small amount of charge in so that's what you have delta n divided by tau sub n that's the shock lid hall condition it's a partial differential equation still not probably easy to solve but let's see whether we can do some more this we could do let's say we take that delta n multiplied by q and a and delta x and then integrate from 0 to wp 0 to wp what is that that's the minority carrier region on the p side right and so that I'm just integrating the whole thing now if you integrate now that whole quantity q a delta n well that's changing with time right do you remember it was a big initial triangle and it was gradually going down so of course that's changing with time let me call that thing whatever is inside area under this curve q q is changing with time of course but I have integrated over wp and the wp is from 0 to wp is end of this region so that will be my area under the curve and so therefore I could write do you see a whether I could write this q is the whole thing and d dt for that will give me the first term dq dt that's no problem now what about the second term the diffusion term do you agree how I have written the second term in this particular way look at this the second term was a second derivative with respect to x so those the second derivative I have written as dx and dx and then I have cross multiplied with dx that will take care of one dx so I have a differential of q a delta n right and if I have a differential can I not integrate it out this is a differential I I can always take that differential and integrate it out and that you will see that says that I have the first term is the current that is going out from the right hand side and the second term with respect to diffusion coefficient which is current coming into the into this box that's the first and second time and the last term well that's the recombination term q n divided by 1000 now you have seen this type of integration before why have you seen this do you remember the delta function business the second derivative anytime in the Schrodinger equation when I gave you a delta function you had to integrate it across a delta function and the two sides you had this first derivative on one side and the first derivative on the other side that was separated by the discontinuity well the same trick here I haven't done anything else you just multiply dx and integrate it out okay there is a typo I can see that w n should be w p on the top side okay but you get you get the idea so the current so what does this equation say well this equation is telling me this equation is telling me that the charge that is building up in this box is equal to the current that's coming in from the left hand side you see x equals 0 that's the current that's coming in and the current that's getting out x equals w p and so the total amount of charge that is building in is the equal to the net amount of electron that is flowing in that's why it's called charge control and of course a certain amount of charge is going away through recombination do you see that q divided by tau n term that is the amount of charge that's getting out so only thing I have done and this is a general trick by the way anytime you have a differential equation short engine equation diffusion equation any equation that you can have second order partial differential equation if you want a big signal transient you can do do this in any case in any problem it's nothing to do with this particular problem but it's a general physics problem or general mathematical trick okay so I have a beautiful simple equation now I may be able to solve something so let's look at the turn off characteristics I'm making an equivalence on the left hand side I'm going from 1 to 0 and to reflect that similar situation in a you know undergraduate circuit type context look at this right hand plot right hand top plot I initially have the p-n junction forward biased with the voltage v sub f and you look at the position of the switch the switch is connected to the forward bias diode right then once a time t equals 0 the switch goes from the forward bias the battery and goes to immediately to the right hand side to getting connected to the reverse bias there battery do you see why it's called reverse bias because look at the negative terminal of the battery that is connected to the positive of the positive of the diode so it's reverse bias so if I can understand this circuit right hand top circuit then actually I have understood the left hand circuit and that's what we are going to do so let's take a look I have to solve this equation in that in that top equation or top figure context at top right context and see try to calculate the storage time the red t sub s is what I am after t sub r will be a little complicated so we will not get there for this device t sub s is what we are after now t less than 0 of course the equation is given by this now do you see whether you agree dq dt that's fine if I sub f well there is a forward current flowing dc forward current flowing so my i diffusion is i f and that was not dependent on time it was a dc thing so that's what I have now what was this dq dt it was steady state was there any change in with respect to time of course now there was a constant profile sitting there so dq dt would be 0 before I have started switching there is no change in change in chart and so the dq dt is 0 now the question is that why would the current remain the same after the transition also that's that's what I'm going to explain to you a little bit later now one thing I'm going to let me before I go there one thing is this current is going to remain the same do you remember in the last class when we are talking about this small signal response we had a register a diffusion capacitor and a junction capacitor now can you change the voltage across a capacitor instantaneously you cannot right that will require because it's half cv square if you change v instantaneously then that will require infinite amount of energy so you cannot change the voltage instantaneously across the capacitor and so and thereby since you cannot change the capacitance therefore you not sorry cannot change the voltage therefore you cannot change the charge as well because q is c multiplied by b c is a constant v you cannot change between 0 minus and 0 class and therefore q you cannot change also so from here can I write this that for t less than 0 dq dt is 0 steady state i f is whatever current I was flowing in the forward bias case I know the initial bias 1 volt I know the current so I have that and so q at 0 minus it is going to be i f multiplied by tau sub n cross multiplied dq dt is 0 okay now the charge cannot change right because the voltage across the capacitor cannot change total integrated charge cannot change so q 0 minus is equal to q 0 plus so that's fine I'm trying to solve that equation during the transient period so I'm setting up the boundary condition you know boundary condition anytime in the circuit you have done this many times so I should really be level at this point okay so how do I solve this equation then now t greater than 0 t greater than 0 the current is the equation is now dq dt equals minus ir now why is minus ir because you see it's a reverse biased diode the current must be flowing in the other direction whatever the vj is whatever the junction voltage is what is the maximum that it can be in the forward bias side equal to the band gap right it cannot be larger than the band gap because the vbi the maximum voltage of vbi the whole barrier it can be if you dope it on both size degenerate then the maximum barrier it can be is equal to the band gap so whatever you have let's say you have a close to 0.6 0.5 0.6 volt and then if vr is minus 2 volts then you can just look at the circuit and immediately realize that given a r the current in the output circuit must be flowing in the negative direction it doesn't matter what the diode wants to do given that diode can only have let's say 0.6 volts in plus vr let's say is minus 2 volts the output current in R must be negative going in the negative direction so the diode has no option but to supply the negative current it it doesn't want to change the voltage fine but it must supply the negative current otherwise the circuit will not be satisfied and it can do so easily so by the way this current and I'll show that this current so long the vj is smaller than much smaller than vr that current through R will be simply vr divided by r right that's a small voltage diode voltage so in that case the current is approximately a constant not fully a constant approximately so ir is a constant and so this is a first order differential equation everybody can solve it right so you just cross multiply divide and then what will be the equation what will be the answer from here do you think it's some sort of log that will come out and the time on the other side will have a certain amount of time on the other side okay and when you integrate you will get an expression like this you can see the log right and then you can see the two boundary conditions q at 0 plus that's on one end and q at p sub s end of the storage time that's the another end right now this point is very important to understand and this is a conceptual thing that why ir can go in the opposite direction and I have explained that in a few minutes ago while not changing the charge too much between 0 minus and 0 plus you see all it has to do all it still has to do is can keep the charge almost the same but change the slope on the one end a little bit and that immediately gives it the requisite current minus ir and as it is losing the charge gradually over a period of time it just keeps the slope exactly equal to the value that the circuit dictates the circuit through the resistance are once a fixed negative curve and so it will just keep that profile okay all right so how much time then I have I still haven't solved the problem completely except if I make this assumption you see in the beginning I had a lot of charge forward biased diode it was exponentially delta n exponentially went with voltage and it was gradually dying off millions of electrons sitting in the minority car historic at the end when the charges have all gone away then it's a reverse biased diode on one side I have ni square divided by n a and another side I have zero because in the reverse bias side the boundary condition requires that that's zero and so I essentially have no charge left you know ni square over n a in silicon let's say 10 to the power 18 dope I have 100 minority carriers and so one end I have 100 another end I have zero I have minuscule amount of charge in the beginning I had millions of charges as a result I can get rid of this q t sub s because that's the final amount of charge I'm left with and if I do that then I have a equation which is actually very simple you see ir plus if why does that if come from do you remember q at zero plus is equal to q of zero minus and q of zero minus I relate it to the forward bias current so ir plus if divided by ir now there is something very interesting here so do you realize that if you forward bias the device very hard if you forward biased it very hard then it will take a long time for the charge to go away because tau sub s is how long if the charge how long it required for the charge to go away and if ir if is very large you forward biased it very hard it will take more time that makes sense right you can see that that immediately makes sense tau sub n when you have a lot of traps is tau sub n larger small small right tau sub n small so when you have a lot of charges it makes sense that charge will decay very fast it makes sense right as soon as because this was a lot of area under this curve and if you have a lot of traps then it will go away very fast if tau sub n is not very large then it will require me a lot of time because all the electrons has to go out through the door the other door meaning the other side of the junction nothing is going out through the majority carrier side on the door acceptor side and so it will take a lot of time now this is a very important point tau sub n because generally traps are bad we don't want traps right because it is non-ideal characteristics and all those things but when we want ultrafast switching many times people intentionally put in traps in the minority carrier side because by putting that in you can see that you can turn on and off this diode very fast and it will i'll show you later that it behaves almost like a majority carrier device at that time if you put a lots of tau sub n and that's why this is a very important circuit trick that people put it by hand in order to analyze the devices okay all right what about the turn on characteristics or the turn on voltage transient well if you want to do the voltage you can again start looking at the total charge q sub n instead of integrating between 0 to t tau sub s you know that's what we did in the previous equation you just integrate between 0 to any given time t so not all the way to t sub s but any given time t you will get the charge q sub n and once you know the charge you can get the voltage how much voltage is how will you get that you will put this charge in in n p 0 and t so this is that charge so you will just put this charge back in n sub p is zero that's the minority carrier n i square divided by n a so you know how much the diode is forward biased and from that you can calculate what the forward bias voltage must have been so again you can calculate this and characterize this transition from the red triangle in the v a car to the green circle where it gradually turns off so when you go home make sure that maybe you can put it in a mat lab or in your calculator see how this works out put some value forward bias current you know a milliamp maybe a reverse bias current maybe a micro amp put it in and see whether you can actually calculate these things this is something I will not explain but what I want to point out that if you worked a little harder not too much hard then you can also calculate this storage reversed storage time at this t sub r and the t sub r has this complicated relationship but you can see you know them all right you know if what was the forward bias current in the beginning IR well that was a final final reverse bias current t sub r is unknown also p what is that that's the recombination time you had more traps the recombination will be more you can put this whole thing in and you can see how you can calculate the t sub r the error function well I am sure you have forgotten but you can look it up and the point is that once you express it in a very simple form you can calculate this the point is that you can do it so we will not do it for the time being and you can sum them up and look at the total current and you can see that in most of the time the t sub s the t sub r is typically very small you can see the dotted line and the solid line in general and so therefore the simple calculation we made is fine for the time being is fine no need to understand it in detail but if you really wanted to understand it you can look at these book at page 117 and then we can move on from there but for the for the time being we will not get into that that detail turn on characteristics again that's very simple turn on characteristics let's say you're initially you had a voltage and you now from a reverse bias this time you just want to turn it on and go to the forward bias and if you wanted to go in the forward bias what do you do well one thing you can say that at t equals infinity whatever it is that t equals infinity is going to be steady state again so if it is steady state and you also know at t equals infinity the current will get to the forward bias whatever the steady state forward bias current is i sub s and dq dt at t equals infinity is zero right steady state again because you have transistor turned it on steady state and so therefore at time t equals infinity your current is i f tau 7 right that makes sense because that will be the steady state current and then again the charge will exactly now go in the opposite direction it will start with essentially zero as soon as it's forward biased although it doesn't have the full amount of charge it will tilt the potential so that it can keep supplying the forward bias current and you can see why the slope of the profile is essentially the same dndx at that point gives you the same forward bias current i f and this will go on until it reaches steady state and so in the forward bias case do you realize why this i f must be the same because the output circuit wants the current to be the same and therefore i f is the same and again you can integrate it out no rocket science here this is the result of the integration because you started from time t equals zero therefore it looks a little bit simpler does this final answer look about right when t equals infinity when t equals infinity what will happen to the exponential do you think that will go away so of course at q at t equals infinity they must be equal to each other right and t equals infinity i already know this i sub i sub f multiplied by tau multiplied by tau tau sub n right that's i derived it in the last slide and so you can see that over time in the beginning when t equals zero current charges zero t equals zero exponential gives you exponential of zero gives you one one minus one is zero so in the beginning you don't have any charge makes sense right and then when you have t equals infinity forward bias current is gradually filling this tank up you know this storage tank up and gradually you will have the full final potential so you can calculate how the charge would behave as a function of time now on few other applications of how this charge control model that you have just seen used to do large signal transient how it can be effectively used to solve many other important problems so one of them which is very important is calculating this diffusion time by this charge control method and what I mean by that is that assume that a device is forward biased an electron has just been injected on the left hand side let's say of the device just at the age of the minority carrier and then this carrier will spend some time within this minority carrier region before eventually being collected by the right hand contact the question is how long does it take for the electron to go from the age of this region to directly to the other contact how long does it take and that's the diffusion time because the electrons are moving by diffusion now if this recombination was a dominant thing then of course you expect so you expect that the electrons would come and directly will recombine with the holes below and that will be whatever is the response time right because that is how long it takes for the electrons to go but if you do not have traps and as you can see this triangular profile is saying that we do not have traps because the second derivative of diffusion equation is zero ax plus b equals zero ax plus b equals the carrier concentration so no traps and in that case what the electron does is is sort of this this issue that it takes an electron takes many path and eventually gets out and everybody takes a different path why does it go back and forth phone on scattering ionized impurity scattering so it scatters back and forth many times before it goes out and the question is how long does it take now although the path looks complicated a very simple formulation of the charge control can actually help us answer this question so here I do not have any recombination so I will drop that term now the way I can answer this question about how long it takes is effectively to assume that in the beginning I had a certain amount of charge and then I dropped the voltage I turned the voltage off and if I look how long does it take for this charge to decay away from this minority carrier region away from this region altogether and restore equilibrium that would be the amount of time the electron effectively on average everybody has different time on average how long it takes for the electrons to get out so you do something like this you will say that right after zero plus time c equals zero plus when the voltage was turned off I had a certain amount of charge and at t equals infinity well the charge will be very small right because that's the equilibrium charge and the time for this charge effectively requires to drain it away which is draining it away to the right hand side the contact at that I will call the tau diffusion so I can calculate the dq dt as a difference of initial and final charge divided by the time it takes for the charge to drain and the diffusion current now this I could drop because it's a small quantity and as a result I could write the tau diffusion is equal to this charge initial charge I had divided by the current but you realize the charge is simply the area under this triangle half the ordinate multiplied by wp wp is the base so that's the total amount of charge q in the beginning and the current is simply q dn dndx the derivative but derivative is same everywhere here this is straight line so that will simply be delta np divided by wp and the amazing thing is that it tells you that on the average how long does it take for on the average how long does it take for the electrons the red electrons to bump around and get out of this region and you can see it goes as wp squared so the length of the minority carrier squared divided by 2 dn now why does it have this particular formulation you can easily answer that question actually because you can see that I can write it approximately as wp which is a distance and dn divided by wp is a diffusion velocity right and so essentially you have this wp squared divided by dn that's what you have and why there is a half well half because some of the particles are sort of in the end in the beginning close to the right hand side some close to the left hand side and on the average you have a transit time which is sort of a mean of this time because not everybody is starting on the left and going out right for this formulation and so that gives you a formulation of the diffusion time simply by using the charge control method there are more complicated ways but this is the simplest now you can also do another thing very conveniently with the charge control method which is to calculate the ac dc diode current without having to go through solving all the minority carrier equation you know matching boundary condition we do all those things in the about two or three class ago about remember region one two three four all those complicated things you don't have to do any of this charge control will almost give you an answer for that very quickly for example this way so we are looking at steady state so dq dt is zero and i diffusion is the current that's coming in which I don't know and want to calculate but by the way this tau sub n if I don't have any recombination I just told you that tau 7 is equal to tau diffusion because that is how little it takes for the electrons to get out not through recombination but by diffusion so I put that in and so I can write that the diffusion current whatever that is is equal to q divided by tau diffusion and if I put it in then you will see the q is again half the ordinate and multiplied by the wp which is the base but this time the q is actually proportional to the voltage exponentially proportional to the voltage remember that was the boundary condition that we did for as a function of voltage fn minus fpe that gave me the quasi-farm level separation and excess charge so I can put that in tau diffusion I just calculated and do you remember this equation the final one dn divided by wp and i squared divided by na and the exponential of the whole thing that was the that was the diode current right but I don't did it just in two lines instead of having to go through all those complicated derivation this is really easy but of course you have to really understand the problem in depth before can use this type of two line derivation that requires practice and this is an exact expression that we actually got from the previous case okay and very quickly then we talked about large signal response is of great importance in digital switching of course I gave you a very simple example but in reality when you have a CMOS inverter a MOSFET turning on and off the resistance and output resistance capacitance those are more complicated so we'll have to reapply many of the things that we learned in actual situation but for the time being it gave you some idea this way of solving differential equation by charge control which is to get rid of the space derivative by integrating over a certain region is very powerful technique it's a general mathematical technique has got nothing to do with electrical engineering per se anytime you see a second order differential equation with time derivative built in you can always use this and impress your professor that you can you can do this but this is a general way and it's really very very powerful and finally the boundary conditions for these problems are required to be carefully done t equals zero minus and how it couples to t equals zero plus what happens to charge at infinity sometimes you will see charge goes away so you can drop the infinity term sometimes the charge builds up to a steady state then you shouldn't drop the the boundary condition right so this has to be it has to be carefully done and if it is done carefully this simple differential equation is very powerful you can do a huge number of things while using this okay


All right. Welcome everyone. We look at the fourth key to supernatural ministry today. We'll pray and get started. Let me just open up with a word of prayer. Let's pray. Heavenly Father, we thank You, Lord, for this time. We thank You for the wisdom of Your Word. And Lord, we believe that You're building us up, Lord, line upon line, precept upon precept, and helping us, Lord, strengthen our inner man. And God, move, O God, in the manifestations of the gifts of the Spirit. Father, we ask for Your grace. We ask for Your strength. We ask for Your favor, O God, and Your blessing upon this time of discussion, Father God.  We thank You. We worship and honor You in Jesus' name. We pray. Amen. Okay. So coming to the renewed mind, we all know that God is so much greater than us, so much higher than us. And the way He thinks is different from the way we think. The Bible teaches us in Isaiah 55. We must be familiar with that passage where it says, right, like, Your ways are not my ways, Your thoughts are not my thoughts. So God definitely has thoughts which are way higher than our thoughts. So here is the question. When we talk about the supernatural in our lives, if we keep functioning with our level of thinking, we won't be able to move in God's supernatural. So that is why we must aim for God's way of thinking. And the Bible teaches us that there is something known as the renewed mind. Or it's God's way of thinking that each of us needs to develop, which will help us walk in victory, which will help us walk in the power of God. When we study about the kind of mindset that a believer can have, there are three different mindsets that the Bible grows light on. First is for us to have something known as the natural mind. Natural mind is the normal, logical, rational mind that every human being has. So the decisions that we make through the natural mind are limited to our five senses. When we don't have information beyond the five senses, we are not able to, you know, decide. So that is the natural mind. Is there anything wrong with the natural mind? No.  And the Bible talks about this natural mind. But then, you know, there is also a reference to something known as the spiritual mind. Let us read one passage where there is a mention of both of these kinds of minds, natural mind as well as the spiritual mind. It is in 1 Corinthians chapter 2 verses 11 through 16. So if someone is there, you can please read the passage out aloud. 1 Corinthians 2, 11 through 16. For what man knows the things of the man except the spirit of the man which is in him? Even so, no one knows the things of God except the spirit of God. Yes. Now we have received not the spirit of the world, but the spirit which is on God. Now we might know the things that have been given to us by God. These things we also speak, not in words, which man to himself teaches us, but which the Holy Spirit teaches, compare the spiritual things with the spiritual. But the natural mind has now received the things of the spirit of God. But they are worshiped in him. No one can even know them because their spiritual isn't. But he who is spiritual gets to solve things. Yet he himself is rightly judged by no one. But who has known the mind of the Lord that he may struggle? Well, we have nine of cards. Okay. So there is a distinction here where in verse 14 we read about the natural man. And what does verse 14 say? Natural man does not receive the things of the spirit of God. For they have foolishness to him. Nor can he know them because they are spiritually discerned. So it implies that the natural mind is limited to the natural world. So what are some of these? It says things of the spirit of God. So the things of the spirit of God are the truth of God's word, the revelation of God's word. And at times God causes to do things which are beyond the natural realm. You know, when we look at things like miracles, when we look at things like supernatural divine healing. For the natural man, for the natural mind, it's very difficult to grasp. That's what Paul is telling here. He's saying that the natural man does not receive the things of the spirit of God. For they have foolishness to him. Because logically there'll always be a question, how can this happen? Think about the wedding of Kena where people ran out of wine. Jesus were to propose this or share this idea with the people and say, okay, don't worry, we will have more wine. Miraculously, you just fill all the pictures, the jars with water. It will turn into wine. If we were to share something like that, do you think people would have accepted it? The natural mind, what would the natural mind say? If Jesus said, okay, bring water, we'll make wine out of it. Yeah, it's impossible. Jesus, it's impossible. Don't play with us. These are all the comments which people may have presented because in the natural thinking, these miracles are not practical. They are not possible. So the natural man cannot receive the things of the spirit of God. But what does it say? These are spiritually discerned. So there is an aspect of spiritually discerning matters. Now how do we spiritually discern things? We normally spiritually discern when we are thinking on the basis of a renewed mind. So there is an option, even for a believer, there is an option. See normally, let's say, I'm just putting a percentage to it, but that's not the accurate person. It's 60% of the day. We just live by a natural mind. We just manage our life on the basis of natural mind, logic. Okay, this is the time that I have. This is the way I have my schedule. I'll do this, I'll do that. If petrol is less, I'll put petrol.  But there is that other aspect where God may want us to expect his intervention. Now if I function 100% with the natural mind, I cannot accommodate what God wants to do. Because for the natural mind, it's too big. Or in other words, the natural mind is very limited. We always question, right? I mean, there are so many questions in the Bible. We can look at the miracles and say, but how? Even Genesis, God created. He said, like, there be like natural mind would be like, seriously? Is that how he created the world? I can't accept it. But the spiritual mind can discern and it can receive the way in which God works. So for a believer, it's so important to strengthen the renewed mind. So we'll talk a little bit more about the renewed mind. But there is a third category. Anyone? What is the third category of mind that the believer can function with? Natural mind, spiritual mind or renewed mind? Third one, carnal mind, correct. But isn't that quite sad that a believer can... There is an option to function in the carnal mind for a believer. If we are not careful or if we are not submitted to God, then there is that risk of functioning with the carnal mind. What does the Bible have to say about the carnal mind? So the Bible says that the carnal mind is an enmity with God. Romans chapter 8 verses 5 through 8. Let's look at that passage here. So I'll read it. It says, for those who live according to the flesh, set their minds on the things of the flesh. But those who live according to the spirit, the things of the spirit, for to be carnal minded is death. But to be spiritually minded is life and peace because the carnal mind is empty against God. For it is not subject to the law of God, nor indeed can be. So then those who are in the flesh cannot please God. So what can we understand about the carnal mind? There are some pointers or hints over here. One is carnal mind is enmity against God. That means what the carnal mind wants is against what God wants. What does God want? God wants his name to be glorified. God wants his kingdom to rule and reign. Then God wants us to, we could say, walk in the spirit and not in the flesh because over here it says, those who are in the carnal mind, they will please themselves. Verse 8 says, those who are in the flesh cannot please God. So when we are in the flesh, what do we end up doing? It's all about self-seeking. It's all about our pleasures, our needs. And Galatians chapter 5 also talks about the fruit of the flesh. So we have an idea, bitterness, anger, all kinds of evil is what is associated with the flesh. So when we say that a believer is working with the carnal mind, these are the priorities in the carnal mind. Self, pride, jealousy, lust, anger. So it's like fully opposite. Now natural mind is valid. God has given all of us a natural mind. So we can function with the natural mind as a believer. God doesn't say anything about that. There's nothing wrong. But a carnal mind is a no-no. When we are a believer and we have a carnal mind, that is something God does not want. Because it is opposite to what God desires from our lives. And then of course, you know, comes the spiritual mind or the other word that we use is renewed mind. The familiar scripture is Romans 12. We all know that, right? Romans 12 verse 12. We not conform to the ways of this world, but we transform by the renewing of your mind. Okay? That you may prove that which is the acceptable will of God. So what is the renewed mind? What is the renewed mind? Would you like to describe it? A renewed mind? The renewed mind is where we add our thoughts. Our thoughts are completely changed. Okay. Transparency. So we give this, how many money is there? We made a God piece to have a pure mindset. Yes. Yes. So to have a thought process, the way God thinks. Okay? And what you said is correct. She said that to have a pure mind. Because that's how God's wisdom is. We read about it in James chapter 3, where God's wisdom or God's thinking, it's peaceable, it's righteous, right? So it will produce a good fruit. That is renewed mind. Now, why are we using the word renewed? No, it's basically like a renovation of our minds, where when we come to know Christ, we come with our background, we come with our usual ways of thinking, usual patterns, we use the word patterns, because sometimes they have patterns. It's not just easily you can't remove one thought, because it usually has, how do you put it? It's like a little more strong in our minds that you can't uproot it just with one thought. Sometimes you have to uproot several thoughts to get rid of that pattern that we are experiencing. But it's a process. So we go through that renovation in our minds by removing carnal thoughts, by removing worldly thoughts, selfish thoughts, unbiblical thoughts, what the Bible has to say regarding the same matter. So, for example, if you take, for example, success, we may come with the mindset once we are born again that what is success? Success is being popular. Success is making a lot of money. Success is making people follow you. So maybe we have that mindset, but what is a renewed mind? You have to look at success with God's definition. What is God's definition? Servant leadership, humility, being submitted to God and being a blessing to the people. So you see a contrast there. So then it's just a simple example. In that one matter, we are seeing that there is a carnal way of thinking about that same issue, but there is a renewed way of thinking about the same issue which comes from God. Now, with regard to every subject in our hearts, we need to have renewed thinking. So it's a lot of hard work. It's about journeying with God day by day and somewhere we ask the question when we are born again, why aren't all believers perfect or nice? When we interact with believers, we come to know, oh, there are these perfect parts, but then there are these still unformed parts. Why is it so? See, we're all going through the process of being renewed and that's the journey we have to make. And as we make that journey, eventually for various aspects, our mind will be renewed. The way we think about the matters will become the way God thinks about the matter. And we cannot underestimate the power of thoughts. This week, Pastor Jay Kumar talked about thoughts and he said how even one single thought, he had some good facts that he shared, the speed at which we think, the number of thoughts that we think. But thoughts will determine our actions. Actions will determine our behavior and behavior will determine our lifestyle. So everything starts with one thought. Even if you look at Adam and Eve, you will become like God. Oh, okay, we'll become like God. One thought, it led to what? The fall and the whole thing. So we cannot afford to have even one thought in our minds, which is not the way it is in God's mind. So these are the risks that we run. So we talked right now about three things. We said a natural mind, which is okay, which is good. We have to function in a natural mind. Carnal mind, we should definitely not function in it because it's against God. Third, renewed mind, which obviously we will develop over time.  It doesn't work like that. We have to make the journey. That's when we will be able to see God working in our lives. So now, coming to, why are we talking about the renewed mind in the supernatural, keys to the supernatural ministry? See, when it comes to the supernatural, if we are limited to the natural mind, we can't move in the supernatural. Okay. There are two instances given in our notes here. One is the time when in John 6, there was a need for food. So there were crowds waiting and you know, Jesus wanted to feed the hungry crowds but there was no food. Okay. What exactly happened in this particular incident and the other incident which is shared in our notes is from Matthew chapter 14. Okay. When Jesus tells Peter, come and the Peter comes and walks on the water. Now in both of these incidents, we'll see the way people are thinking. So let's first go to John 6 verses 1 to 13. Then someone read it like quickly. Yes, John 6. And Jesus went up on the mountain and there he saw the disciples. Now the Passover of Christopher James was new. Then Jesus went up his eyes and seen a great multitude coming where he said, we're sure you've read that. But this is such a test in both of these incidents. In one of these two, Philip Anthony, 200-dynamic word of God, is not sufficient for them that everyone in the family wanted to see something and he was telling it to his brother. There is a lot of fear who has fire-body rules and just a lot of fear among so many. Then Jesus said, make the people sit down. Now fear was much faster in the face so the men sat down in the number of 5,000. And Jesus looked and when he had given fans his view to them, they had given disciples and disciples to those sitting down and my person had finished as much as they would. So when they were filled and set with disciples, the other of the parents had remains coming out in his house. Okay, great. Thank you. So we see a miracle happening over here. But look at the mindsets. There are two people. One is Philip. One is Andrew. Okay, Simon Peter's brother. So what's happening now? There are the multitudes. How many people are there? The number is 5,000. Okay, 5,000 people. Now, okay, fine. So now the question that Jesus asks Philip, he says, Philip, where shall we buy bread that these may eat? But this he said to test him for he himself knew what he would do. So he's asking Philip, Philip, tell me where shall we buy bread? There are 4,000 people. So how many, at least how many loaves do we need? Logic, natural mind. Come on, let's do some calculation. 4,000. Okay, fine. So 4,000. Let's see. Bikes. Okay. 8,000. 8,000. Okay, fine. So if we say more than that. Okay. Okay. So basically, women and compared to men, more than that, right? Yeah. So I don't comment double than that. This is getting complicated. Let's just assume.  So 10,000 loaves of bread we want. We're assuming each person will have one because they are very hungry. Okay. Now let's just 10,000. So if you say 10 rupees per loaf of bread, how much money do you want? Yeah. One lakh. One lakh rupees. So Jesus is asking firstly, that's the one. You need money. Okay. Secondly, he's saying where shall we, which bakery shall we go to? They should have, right now they should have 20,000 loaves or 10,000 loaves of bread. Practical issues. Very logical. He's saying Jesus, 200 denari worth of bread is not sufficient. Okay. Whatever that denari was worth in those days. He's saying that only is not enough. Now, what will we do? So he's thinking like us. We need at least one lakh rupees, which bakery, even if we swiggy, like will it reach in my life? We're thinking all those logical questions. Because the task is too big. Okay. How to solve this problem now? But, you see, it's good, not bad. Nautical thinking is being applied, natural mind is being applied. But you find Andrew, he is bringing to Jesus a boy with five loaves and two small fish. What is he thinking? What is Andrew thinking? I don't know. Because we can understand what Philip is thinking. He is working, functioning with a natural mind. A logical mind. But Andrew, he is mostly functioning with a renewed mind. Now, we don't know whether he has seen Jesus earlier. I mean, we don't have any recorded incident. There, you know, personally, there was a multiplication of bread that Jesus did with the disciples or what? I don't know. But the amount that he knows Jesus, he knows that miracle is possible Hey, Jesus is here. Don't worry. Okay. Definitely something is possible. If Jesus is telling us we have to do this, there must be a solution to this problem. That's why in the first place he is proposing that we must feed these people. So, Andrew has a renewed mind. The possibility of the supernatural Andrew is able to envision that. So, it's just for us a contrast of two people who are functioning with two kinds of minds. Natural mind, which is not wrong at all. But what is the problem with the natural mind? Very limited. We get stuck. Especially when it comes to God's work. Because if we know anything about God from time to time, his assignments are impossible. Okay. You're like, how to do this? I don't know how to do this. But, it's only when we walk by faith that we can do it. We think about Moses. Come on. Bar the Red Sea. Leave thousands of people. Joshua, cross the Jordan. Bring down the walls. You know, overcome the enemies. More, so many people. Every one you take up, you know, Elijah, Elisha, John the Baptist, Jesus, Paul, Peter. There were so many incidents in the lives of God's people that when you see the things that took place at supernatural, there's no logical explanation that we can provide from the natural. But how did they manage to walk in the supernatural by faith? The help of the renewed mind, which told them there is a possibility. We're dealing with God here. He can do the impossible. So that possibility of believing for the supernatural will only come from the renewed mind. And that's why we need to develop that renewed mind. So Andrew was thinking with a renewed mind. He knew, you know what, the solution for this problem of whatever, you know, 10,000 loaves of breads we need right now, it is a miracle. And Jesus will give us that miracle. So let's take the little, I'm sure he can pray, bless, give thanks to God, break it and it will multiply. And look at the miracle that took place. Gather up the fragments that remain so that nothing is lost. Therefore, they gathered them up and filled 12 baskets, 12 extra baskets. I'm smiling because just yesterday I saw the answer sheet of one of the children's church kids. And this question was asked, what did, this statement, gather up the fragments that remain so that nothing is lost. Jesus said, so what do you think happened with the remaining bread? So the child had written, Jesus asked them to pack it for snacks. But you see there was abundance. There was not just a miracle but extra. And I was just amazed how the child is thinking, okay, maybe they packed more for snacks. But with God, you see, unless we come with that childlike heart, we'll become limited. We can't walk with God. Think about Peter now. Okay, Peter walking on the water. So now we need to go to Matthew, Matthew 14, verses 22 to 33. Yeah. Yeah, one more person could read this passage quickly. Matthew chapter 14, reading from verse 20. Immediately Jesus made the disciples get into the boat and go on ahead of him to the other side. After he had refused them, he went upon a mountain by himself. When evening came he was there alone but the boat was already considerable distance from the land. By the waves, because the wind was against it. During the fourth wars of the night, Jesus went out to the walking on the lake. When the disciples saw him walking on the lake, they were terrified. They said and cried out in fear. But Jesus immediately said to them, Take courage, it is I who not realize that. Lord, it is you that have to come to you from the water. Come, Jesus. Then Peter got down out of the boat, walked out of the water and came towards Jesus. But when he saw the wind, he was afraid and he had to stand and cry out. Lord save me. Immediately Jesus reached out his hand and called me. He said, why did you do that? I think we can stop here. We can see how again there is an impossibility where Jesus is already walking on the water and even the disciples see him and then Jesus says but immediately Jesus spoke to whom? To Peter? Who did he speak to? Everyone. He spoke to everyone. He spoke to them saying, be of good cheer, it is I do not be afraid. Maybe once Jesus spoke like that they came to know, oh yeah, this is Jesus. We are familiar. This voice is Jesus' voice. But it was only one person among the disciples who had that possibility thinking, immediately he said, Lord if it is you, command me to come to you on the water. Unbelievable. How can anybody even ask that question? I think there are other disciples. Nobody asks Jesus that question. But Peter is saying, so that shows that he is functioning out of a renewed mind because he is thinking of the supernatural. I can walk on water. Lord, if it is you command me to come to you on the water. And thank God, Jesus is very gracious and he says, come. So Peter steps out of the water. He walked on the water to go to Jesus 1st 30. But when he saw now, what is happening? There is a switch. The switch of the renewed mind went off. But the natural mind came on. Suddenly, this is crazy. I am on water. And there are winds. It is boisterous. How can I be walking on water? This is not logical. So he switched to the natural and now he started singing. So sometimes it happens to us also. We start on a supernatural journey with God like Abraham. God told me, in between switch of renewed off supernatural, what am I doing? Where am I? Can I really do this? Why did I make this decision? We just come to that place. But the point is, we have to journey with the renewed mind all alone. Then only the supernatural is possible. So what did Peter do? He switched to his natural mind. Obviously, natural mind will tell you it is not scientific. Peter, excuse me Peter it is not scientific to walk on the water. Don't you know? You have to sink.  But God, Jesus was gracious. Thank God, even when we are in a place where our faith is shaking more than him shaking his faith is shaking so he is sinking at that moment and Jesus gives out his hand and he saves it.  Keep your mind, continue to walk with the renewed mind, continue to walk with faith. Then only you can make it happen. Or then only you can see the miracle. When we are switching like this it doesn't help. So that's the importance of a renewed mind where a renewed mind is one which will help us exercise our faith in God. It will help us truly believe. Because we are looking at a supernatural God with God all things are possible. So renewed mind says, yes I can expect. Yes, a miracle is possible. Yes, healing is possible. So a renewed mind will help us behave. So from the natural whenever it is required we need to learn to function in the renewed mind. So make that a practice. So what will the renewed mind do? The renewed mind will ask for a miracle. Even though naturally, logically it's not possible the renewed mind will say why can't I pray for a miracle? Why can't I ask God to do this? That needs to be in us. Somewhere I think we miss that. So that's a key that expectation that ok God can do a miracle. Let me ask for a miracle. So that is important. That is the key now. The renewed mind will think of a possibility of the supernatural and you know the word of God will help us operate in the supernatural and yeah to just develop this in our lives is what is useful. So just going a little bit back to that passage we read from first Corinthians 2 what is the renewed mind? We will try to understand that a little bit more. See the renewed mind comes from the word of God but in this passage we saw in verse 11 it says the Holy Spirit knows the mind of God and the Holy Spirit is able to convey or let us know what God is thinking. So in that case what we must do is obviously the natural mind cannot accept that but our renewed mind can know the heart of God and when our renewed mind can accept the heart of God regarding that matter we will be able to move in the supernatural. So regarding all matters we can ask God what are you thinking? What are you thinking? What are you saying about the solution to this problem? What are you saying about my destiny? What are you saying about my ministry? What are you saying about my health? So when we start to ask questions like that what's led by the Holy Spirit will grasp what God has in his heart and then we start to agree with that and then we start seeing the miracle. So I think I have shared the gist of what I wanted to say but any comments from your side regarding the renewed mind it's something we must also really put into practice every time to say God what are you saying because we may feel limited we look at a situation and we say it's not it can't happen. So when we are led by the Spirit I'm sure we will be able to trust God, believe God because it's coming from the heart of God the Holy Spirit knows the mind of God and the Holy Spirit is revealing to us this is what God wants this is what you see what is the picture that you are seeing what is the vision God is giving you what is all that it's all from the heart of God prophecy it's from the heart of God so when we know what is there in God's heart it makes it easier for us to believe that that's what God wants and so let's perceive it So always maintain a renewed mind no questions then we can close with prayer today we can take a question in the next class too think some more about this subject okay alright so sure let's pray and let's close then but I would request somebody from the class to pray so yeah please lead us Jesus God we can be a little further this time of learning O Lord Father we thank you for teaching us about the new things Jesus right now O Lord Father as we have learned O Lord Father Jesus we ask you Holy Spirit to help us O Lord Father to live and to walk in a renewed mind O Lord Father in the mind O Lord Father that is in alignment with your word and with the truth of who you are Jesus O Lord Father help us O Lord Father not to be behavior in our case but help us O Lord Father to stand firm O Lord Father in who you are in our lives in the faithful O Lord Father Jesus of which we are O Lord Father everything that we have learned O Lord Father Jesus help us O Lord Father not to forfeit but help us O Lord Father to take with O Lord Father to meditate on it and to live by it Jesus of which just give you all the glory and honor for everything O Lord Father in Jesus O Lord Father Amen Thank you Prince Thank you everyone Thank you for connecting to this class God bless you and have a good week


The last time we'd been there was for a father-son fishing trip. At the time, I had no desire in this bonding experience. I'd grown up resenting him as prior to that day he had shown little to no interest in me or trying to bond with me. It was, however, one of the few pleasant experiences I had with him before his tragic death at this very location. I'd heard the news that very day he'd gone on a fishing trip with some friends of his and their bodies had been discovered on the lake shore by another family. It appeared that they died from drowning, but that never sat right with me as he'd always been an exceptional swimmer. Unfortunately, there was no evidence to support foul play, but I didn't accept that. I demanded answers. The day I arrived at the cabin, it hit me hard how much I actually missed the man that I had resented for so many years. Through that one shared experience, I'd gotten to know him so much more and it never felt closer to him. I'd looked forward to doing it again, but unfortunately, that opportunity was taken from me. As I unlocked the door and walked inside, memories of that day hit me like a train. By the time I'd finished unpacking, my face was soaked in tears. There were stone remnants of our previous visit, such as the plates we'd eaten, our catches neatly stacked on the kitchen counter, and an old singing animatronic fish mounted on the wall. Later that day, I went out by the lake. I stood at the exact spot where his body had been discovered and gazed out at the large open body of water. Something out there killed him. I just knew it. It wasn't some unfounded theory that I had out of nowhere either. I had heard the stories. There was an old urban legend about some giant fish that live near the center of the lake. There had never been any concrete evidence other than some supposed sightings by less than credible individuals, and my dad was one of the biggest skeptics. I, on the other hand, was terrified to go out to that part of the lake so he made sure we didn't venture out that far during our trip. As an adult, I decided to put my fears aside. I knew that if this monster did exist and it was responsible for the deaths of my father and his friends, I wanted its carcass on my wall. After setting up my boat and packing supplies and a variety of weapons such as a speargun, a machete, and even a 12-gauge shotgun, I ventured out. After reaching the center of the lake, I turned off the engine and waited, speargun in hand. I figured I might as well make the most of my time and pulled out some fishing gear and cast a line. With any luck, the beast itself might take the bait. As terrified as I was at the prospect of the lake monster being real, I was ready for a fight and eager to take it down. Time passed with no luck other than a few small catches. I was about to give up and head back for the night when there was one final strong tug on the line. I tried my best to reel it, but it wouldn't budge. I initially thought that maybe it got snagged on something down there, but the line shot away from the boat at an unexpected speed. The force of the pole snatched the fishing rod right out of my hands. I quickly reached for my speargun, ready for a fight. Everything was still and quiet, not a single sound other than my breathing and the atmospheric sounds of the lake itself. Suddenly, the boat shook from an impact just below it, as if something swam at a high speed and rammed right into the bottom. I held on, making sure I didn't fall in, knowing if I did, I'd be at the mercy of whatever this thing was. I peered over the side of it and saw a large shadow was circling me. Soon, it approached me, and a slimy scaly hand reached out and grabbed the side of my boat. Panicked, I attempted to start the engine, but it kept sputtering. Another hand popped out and the creature pulled itself up, revealing the monstrosity that undoubtedly had killed my father. It looked somewhat like a man, but its skin was green and scaly.  Its eyes were glossy and blinked horizontally with slimy eyelids. I screamed in terror at this sight and aimed my speargun directly at it. I fired, piercing the creature directly in its core. It let out a gargled cry as it fell back into the water, black-colored blood pouring out of its dying body. I tried the engine again, and finally it started running. Before I could take off, however, more pails of scaly arms reached out and grabbed one side of the boat. They were trying to tip it over, but before they could, I reached for my machete and started hacking at the arms. A couple of them managed to pull their upper bodies out of the water, but I swung at them too, decapitating each of them. One managed to catch my arm with its tentacles, and I could feel the sharp pain of the beak tearing into my arm. I reached over and grabbed one of the spears and jammed it directly into the creature's eye. It finally released me, and it squealed in pain. I got the boat going, leaving the monsters behind. I looked at my arm, and I could tell that it took a good chunk out of it. I got to shore, grabbed my first aid supplies, and ran into the cabin, locking the door. After disinfecting and wrapping up my arm, I called the local authorities. I tried explaining what I'd experienced, but they didn't take me seriously until I unwrapped my arm and showed them the huge chunk that was taken out of it. I left that day, and I've never went back. Last I heard, there was a search team that went out to investigate, but just like my father and my friends, and almost myself, they never came back. I ended up going to the hospital for my injuries and was given some antibiotics to prevent any infections. I don't think they work though, because there's something wrong that seems to be resulting from getting bit. Last time I checked on my arm, I noticed the surrounding tissue was starting to change color and texture. I can't seem to stay hydrated, and last night I went to splash my face with some water in my bathroom and noticed something odd about my face. The color of my irises are getting pale, my skin is changing, and I've noticed tiny holes forming on the inside of my lips. I don't know what those things were or how they got that way. I don't know if there's some type of cryptid, the results of chemical mutation, or the host of some kind of aquatic virus. But I think I'm turning into one of them.


Hello everybody! Watch this video to find out how to recover data from a software GVNUM RAID 5RA based on FreeBSD operating system. I'll show you how to install the latest version of FreeBSD with the GNOME graphic interface, and also how to create and configure a software RAID 5 with three hard disks. GVNUM is a control utility of a logical volume manager, and this is how the VINUM volume manager is implemented in GEOM. It underwent many changes since the initial import in FreeBSD version 5. However, as of early 2020, GVNUM has been deprecated. At this time, it is seen as mostly unmaintained and inferior to ZFS for most purposes. Yet, some people do use it to organize their data storage systems. For starters, let's explore how to install FreeBSD. Just as for any other operating system, you need to download an installation image. On its official website, you can find different versions, both 32-bit and 64-bit. Download the version which suits you best depending on the amount of system memory. At the moment, the latest FreeBSD version available is 13. Create a boot USB drive with a specialized utility, for example, Rufus or Acher. Connect it to the computer where you want to install this operating system and boot from the USB drive. When the computer starts booting, press again to select the first item on the list, the installer. Then you will see the installer window, so choose Install and press Enter. At the next stage, you can choose a keyboard layout. I'll keep the default option and press Select. Specify the hostname for the server. When choosing system components, these two items will suffice for a typical server build. Leap 32 and Quartz. To select an item, press Space and OK to continue. The next step is disk partitioning. I choose UFS, Automatic and click OK. Since I have allocated a separate hard disk for the operating system, I choose the option EntireDisk. If you need to create a separate partition, choose the corresponding option. Select a partition scheme from the list, check the FutureDisk setup and click Finish. Agree to override the disk. This will raise all the existing data on that disk. After that, the operating system will be installed without any user actions, so just wait until it is complete. Give the superuser or root password and type it again to confirm. In the network settings, choose the network interface you need and press OK. Now you should give your network options for IPv4. Yes, use DHCP, yes, use IPv6, no. Use Origin, country, setup date and time. Now you should select the services which run at boot – SSHD and APD – Power ID. Select security options 3, 4, 7, 8. To add a new user at this stage, press Yes. When FreeBSD reboots and starts, you will see the command line. With too few people enjoying working with it, I will also show you how to install GNOME, the graphic interface. GNOME is a free open-source desktop for Unix-type operating systems. However, you also need to install Xorg to make the graphic interface work. Xorg is a free and open-source implementation of the XWindows system display server that allows users to organize graphic work in environment. To install Xorg, type this command. And then, yes, to confirm your decision. It starts the installation process. After Xorg is installed, you can move on to installing GNOME. Time the following command. And then, yes, to confirm your decision. The graphic interface will not boot automatically after you have installed the components. To have it booted automatically at startup, you need to change some settings. Type this command in the console. It will open the configuration file where you should add a line like this. After that, press Escape. In the window that opens, select Live Editor and press Enter. Then choose Save Changes and press Enter again. To restart the system, type Reboot. After the restart, you will no longer see the console but a graphic interface. Now type the login and password that you have given before. After the password is provided, the GNOME desktop will boot. At this stage, the installation of FreeBSD and GNOME interface is complete. Alright, we have installed the operating system and added a graphic interface for Kenwinians. Now let's explore how to build a software 8.5 with 3 hard disks connected to this PC and organize a storage for important files. To begin with, you need to identify the names of connected disks and determine which of them will be used to build a RAID system. Type the command. As a result, here is what you see. CD0 is the optical disk drive, DA0 is the system drive, and DA3, DA2 and DA1 are the disks that we will use to build RAID 5. In the card system, they are located in the folder If you are in doubt, you can check the disk size. You can do it with this command. As a result, you will see this information. Later, we will need it because this is the disk size. For your convenience, I will highlight it on the screen. Now you should create a directory where the RAID is going to be mounted. Let's give it this name – Server. After that, create a configuration file for the RAID system by typing disk command. And fill in the required information. Disk names, RAID configuration and size for every disk. Drive RAID 51 is the name for the physical disk, but you can use any name you like. Dash dev slash DA1 – the disk itself in this system. We mentioned it before. Volume RAID 5 is the name of the virtual disk, which is going to make up our RAID 5. Plex is the set that provides the entire address space. Since we are going to build RAID 5, type the following – org RAID 5. And the stripe size will be 256K, as recommended by the manual. SDR sub-disk. We will use 3 disks, 30GB each, but we'll specify the size as follows – the figure I have highlighted before. Press escape and save changes to the file. Now you can create the RAID 5 system itself. As a result, a new device will be created – slash dev slash gvnome slash RAID 5. Now you should create a file system for it. After that, let's make the vendor module boot automatically. At the next stage, the array should be mounted. As the mount point, we will use the folder server, which you have created at the beginning. Finally, restart the computer. That's all. We have built RAID 5, and let's use another command to check it. You can see the 3 disks and the new volume of the corresponding size. RAID 5 is quite a reliable solution in terms of safely keeping important data, but just like any other storage, it is not perfect. As a result of many factors, its operation may be interrupted, and some information may be lost. If your server is down, a one or several distancing in the array are no longer functional, and as a result of that you have lost access to some critical data, use a specialized data recovery tool – Headman RAID Recovery. This program supports most popular file systems and RAID times. It will read all the necessary information on the fly and rebuild the damaged RAID automatically. All you need to do is to scan it and restore the files you need. Click the disks out of the server, where the RAID was built, and connect them to a Windows computer. If your motherboard does not let you connect all of them at once, use special adapters and expansion cards. As you can see, the program has rebuilt the RAID without effort, and now it displays all the data inside it. Here is our RAID 5 with the UFS file system. Right-click on the disk and select Open. Select the scan type. For example, Fast Scan will quickly search the disk and display all the information it has found. If the Fast Scan can't find the necessary files, then go for Full Analysis. Go back to the Drive Manager, right-click on the disk and choose Analyze again. Select Full Analysis, choose the file system and click Next. In most complicated cases, we recommend searching files by their signatures, by checking the box next to Content Aware Analysis. As a result, the program will display the files and folders, which are still on the disks. Select the files you want to recover, click Recovery, and select where you want to save them. Before you save anything, you need to make sure that you have as much disk space as the amount of data you are planning to recover. Having chosen the directory, hit Recovery. In the end, you will find the recovered files in the folder you have chosen. In very complicated cases, where critical service data was erased from the disks, the program may fail to rebuild the array automatically. Luckily, for such cases, this program features a manual way for rebuilding the array in a special constructor mode. To use this mode, you need to know all the information about the damage to array. Open Rate Constructor, select Manual Mode, click Next, and fill in the array data. Select the type, block order, block size, add the disks included into the array, and specify their order. As a result, it should appear in this window. If you got all the properties right, you will see the directory tree. If you see none, it means the properties are incorrect or this information is insufficient to identify the rate. You may have to specify the offset, which tells you where the beginning of the disk is located. You can find this information with the help of Hacks Editor. When all the properties are ready, click Add. After that, the array will appear in the Drive Manager. Scan it using fast scan of full analysis and recover the files you need to restore. And that is all for now. Hopefully, this video was useful. Remember to click the Like button and subscribe to our channel. Leave comments to ask questions. Thank you for watching. And good luck.