on another adventure. On our way to the truck we have a trailer waiting for us that is going to Calgary, Alberta. It's a little over a day's drive from here. I've got to be there tomorrow at 1 p.m. and it's about 24 hours comfortably to get there so it'll be a little rushed this trip. I waited a little bit longer than I probably should have to get going but I'm still on time. I'm still on schedule. I just won't have as much of time to stop for long extended coffee breaks on the way there. We'll just have to give her a little bit. That's okay. We'll get there. It's not like we got to chain anything down or strap it down or tarp it right. Now we're back on van division. All we got to do is go hook up and go. Man that is so nice. It is so nice. I have a whole new appreciation for it. It's just you hook up and go. That's it. That's it and then you don't got to worry about it all the way till you get to Calgary. You don't got to stop and make sure anything's falling off. You don't got to tighten the chains, tighten the straps. You don't got to make sure your tarp isn't ripping and stuff on the corners. Now you just you just go. You just hook on and you just go. You just send it all the way there and when you get there all you do is you open the doors. So enough about that. We got to get going as soon as we can here. The office wants to see me before I head out. I'm guessing to give me special paperwork or instructions. I believe I'm meeting another driver there in Calgary and I've got to help him with the unloading process because it's not as simple as just swinging open our doors. We have multi-level trailers and we deliver a whole bunch of stuff that requires a little bit of muscle and work and effort to deliver. It's not like I'm doing nothing. I'm not just a door swinger, but I'm mostly just a door swinger now. Yeah. That's okay. I'm shameless. Just a door swinger. Steering wheel holder. It's a nice break. Once I get there I have to help the other guy I believe and unload both our trailers which is cool with me. That's fine. And we'll see what happens from there. I don't know. I booked off two weekends from now. So in two weeks my dad is coming down. My father-in-law is coming down. My buddy Rick's coming down. Obviously my wife's going to be there. My mom's coming down and we're all going to install that back door in our house.  It's a little bit of a job. My dad has a long history in carpentry. My father-in-law has some history in that as well I believe. So they know what they're doing and then me and Rick or the young guys we're the muscle. We'll just pick up and move everything.  So then we'll have our ceiling done on our veranda and the back door done. That's two projects done early summer. It's not even summer yet. And we're off. We're on the Winnipeg freeway. It has stop lights but it's free to drive on it. For me anyways I mean someone's obviously paying fuel tax so I guess it's not even free to drive on. Winnipeg they really love their traffic lights and now I'm stuck in the left lane because I haven't been able to get over to the right lane. I shouldn't be in this lane with the stop light. But here we are living the dream right. So we've got to get around Winnipeg here and get on the trans-Canada westbound our way towards Calgary delivering to a brand new golf course. West side of Calgary. Looks like it's going to be a pretty fancy place when it's all finished up. These guys like those guys I hate being one of them that's in the left lane at the stop light. There's a little heads up a little tip from Trucker Josh. You ready? You don't get many of these. When there's a stop light if at all possible stay in the right hand lane if you're a truck. Leave the left hand lane for the cars and pickups to get past you. They all got places to be also and they're faster. They got better acceleration. So let them get all passed and then we're about passing people for that. But you should stop in the right lane at a stop light if at all possible. Sometimes as you saw there it just doesn't work out. Gotta do your best. This guy's got a nice tractor on the back of his trailer here. I need a new lawn tractor. I was hoping to get one next summer. Guess we'll see. We'll see what happens. It's my life motto lately. We'll see what happens. Well we're not going anywhere without some coffee. It seems like everybody else has got the same idea here or what? Convenience store in Oak Bluff. Not just a convenience store. There's a Timmy's in there. Incognito. I don't know how many people know that. They don't have very many signs advertising that there's a Timmy's here. They just set up these new pumps here. Looks like they're still working on them. Looks like they just repaved this lot which is super nice. Too bad people still parked just all over the place. Just wherever. Pull in. Put her in park and go inside. This is Canada. It's the way we do things. Apparently. It's not the way I do things. I'm gonna back into a spot here beside this guy who actually knows how to park. Saddled up, buckled in, locked in so we won't fall up. The doors are closed on the trailer. I've got my Timmy's. Got a BLT sandwich and a honey curler donut. I got my weasel. It's gonna be a good day. I did this truck for about three weeks now and I've been living in it for like two and a half weeks on our last trip there. Still reeks like cigarette smoke in here. I must have gotten used to it last trip because I thought that it was all gone. I guess I just was in here for two and a half weeks. I guess I didn't smell it as bad. But I got back into the truck just now today. Loading my stuff. I'm getting ready for this trip and all that smell was back. Oh man. And I looked closer on the walls and the slaper of the of this truck. There's an orange film, like an oily film on all of the walls. I gotta wipe down all of the walls in this truck now. They must have been a chain smoker or something. Like smoking two cigarettes at once, you know? I don't know how you smoke that much inside a confined space. Like this truck isn't that old. Like to put a yellow film.  A yellow film? And this dashboard too? The whole sleeper's got it also. This whole truck is caked in like cigarette tar.  That's just... Oh it makes me mad, you know? Like I said, I got nothing against smokers. But if it's your own vehicle, your own your own house, I understand. It's your stuff. Who cares, right? But I get into this truck and I gotta wipe down. Like they did offer to have it detailed and I said I'll just detail it myself. So some of this is on me. I could have had someone else do this for me. But I didn't realize how bad it was gonna be. I don't know how much you have to smoke to leave a film on everything like that. But it's gotta be quite a bit and it's all the way in the back and on the roof in the back. I'm so glad. I'm so glad I haven't developed that habit. I'm so glad. If you have, hey that's up to you. But imagine what your lungs look like, right?  I got some good friends of mine. My cousins that I hang out with all the time smoke. I don't care. That's what they want to do. This doesn't bother me if they have a smoke while we're hanging out. And if they want to go outside and have a smoke, I'll usually go outside with them to hang out with them, keep them company while they have their smoke, right? That part doesn't bother me. It's just I'm just, it's a habit I don't understand. But I also acknowledge I don't have to understand everything in this world. Well, this is the first trip across the west in this truck. She's doing good. Smooth as glass. Just sailing. Like a sailboat just gliding across the smooth waters. Pretty much, pretty much. Some of you have asked what this thing dangling over here is. I think it's supposed to be the mic for the onboard telephone system. And it's supposed to be stuck somewhere, but obviously the sticky stuff on the one side came off. I'll have to fix that sometime. Keep forgetting about that. Saw a couple of you ask about that. We're here in Saskatchewan, Saskatchewan, Saskatchewan, Canada. We're going past Whitewood here on the way west. Look at all the bugs in the windshield, eh? And it's not even evening yet. You just wait till the sun starts to go down. This is nothing yet. There's nothing. We can try to wipe this off if we want to. Not enough washer fluid in the world for these prairies. Doesn't do nothing. We'll have to stop and actually squeegee them off. But 10 minutes later, they'll be back. So I have 971 kilometers left to go to Calgary. That's about 10 hours of driving. So about 600 miles. Somewhere in there. We're making as far as we can tonight yet. We got eight hours and 22 minutes available to us on our clock. We did get a reset. I was home for four days actually. I was only planning on being home for two, but the way things worked out, we were home for an extra two days which worked out really nice for me. Because I got a lot of work done at home. I got that veranda ceiling done. For the most part, you saw it there, right? I have to finish the venting on the outside edge yet. But I got the big part done and it took a lot longer than I thought it would. A lot longer. Took four days. I thought it would take a day and a half. Took four days. But I am also an amateur and I didn't know exactly what materials I was going to need. So I had to run into town twice to go get new materials and exchange some that I bought that were wrong. But we got it done. Now we're rolling on. We'll be busy for the rest of the month. Like I said, got to deliver this load to some fancy golf course west of Calgary. And from there, I believe I'm heading up to Edmonton. And we have a load there waiting for us. Not sure where it's going. Not sure where it's going. But I'll pull it wherever it needs to go. So we're directly above the western edge of North Dakota. And a couple of hours will have passed on to Northeastern Montana. If you're wondering where we are according to the US map. Just above North Dakota, Montana. Just on the Canadian side, eh? Nice and green up here now though. Look at this. Golf courses are open.  Pretty much back to normal for the most part. As normal as it's going to get, I think. Which is good. I hope things start getting busier again. They'll probably be a little while before they allow concerts and stuff like that. But that is what it is. You all know the story. You're all living it. We're all living the dream right now is the Whitewood Auction Livestock sales. You want to buy some cows? That's where you go. I'm going to pull in in Balcony. Balcony Baloney. That's about... Oh, actually that's quite a ways up yet. Another couple of hours. We'll see what happens. We'll see what happens. See, this highway was built along that railway there. That railway is what joined Canada, our west coast and our east coast. Way back in the day under Sir John A. McDonald, the founding father of Canada. He united the country coast to coast with that railroad right there. Very important railroad. And now we got a highway parallel to it. Very important highway too. I mean how would this golf course and Calgary get their stuff if we didn't have this highway here? I mean you could send it by rail but that would probably take two weeks. Whereas I can get it there in a day. This thing, this highway makes it a lot better. This guy went, ooh, nice W9. Very nice. Very, you guys want to see it? Very nice. He waved at me, I didn't wave back. My bad. Too distracted by your nice Kenworth. Guy's hauling a lot of weight, I bet.  There you go, he's on. Gotta get back over here. My Algoni Baloney.  But hey, you want to be all fancy. Turn right in 100 meters. I know Karen, I know, we're not. I'm off course, I know. Turn right. No, we're not gonna, I am turning right. You want me to go over to the field over there? Look at this poor truck stop here. It got killed by the Flying J over there.  Big corporation came in and crushed it to the ground and curb stomped it. Poor guys. This road for 22 kilometers. I like the Flying J. I do, I just, I do know, I know the consequence is that we gotta sacrifice a lot of small business for it. And that's the sad part. And I know I'm one of those guys that loves Walmart. I'm one of the, I'm part of the pack. I know I'm just a sheep. But I don't get why they get to be open, but everyone else has to stay closed. It's too dangerous to go anywhere else. It's too dangerous to be on the beach. Go over there and stand in line at Walmart. It's safer there. I don't get that. I don't know. Continue on this road for six kilometers. I'm glad this whole thing is just about over. At least here anyway. It was never really bad here on the Prairies. We never really got the worst of it. Nice truck. Very nice. Very nice, how much? So we're gonna go park in a parking spot and then I gotta wash this windshield off before we leave. I'm not getting fuel here though. Or maybe I should. I'm under a half a tank now. You know what? Yeah, let's just go get fuel. We're here. Let's do it.


Coming to you from our GIS studios, I am Anitya Antoine and this is your Midday News Brief. The Ministry of Tourism, Information and Broadcasting, Culture and Creative Industries in its quest to bolster the island's tourism industry is extending its expertise to the taxi sector. Minister for Tourism, Information and Broadcasting, Culture and Creative Industries, Honourable Dominic Fede indicated that a lot of opportunities go unexplored due to stakeholders not taking advantage of available technology advances. The initiative, according to him, will be very beneficial not only to enhance St. Lucia's tourism product but also to empower business owners, especially those in the sphere of village tourism. Honourable Fede explained that one such initiative will provide the kind of assistance needed by these owners to give their businesses the competitive edge. As World Know Tobacco Day approaches, global partners are bringing attention to the harmful and deadly effects of tobacco use and second hand smoke exposure while seeking to discourage the use of tobacco in any form. The tobacco epidemic is one of the biggest public health threats the world has ever faced killing more than 7 million people a year. More than 6 million of those deaths are as a result of direct tobacco use while around 890,000 are the result of non-smokers being exposed to second hand smoke. The Ministry of Health and Wellness recently launched its campaign for World Know Tobacco Day 2019 in partnership with the National Commission on Chronic Noncommunicable Diseases to bring attention to the issues of tobacco use in St. Lucia. This year's campaign is significant for the National Commission on Chronic Noncommunicable Diseases as it seeks to target the youth. The World Health Organization recommends that governments and communities prioritise tobacco control in order to achieve sustainable development goals target for one-third reduction in noncommunicable disease premature mortality by 2030. The chair of the National Commission on Chronic NCDs Dr. Owen Gabriel said the most effective measure to improve lung health is to reduce tobacco use and second hand smoke exposure, however the potential of tobacco control for improving lung health is highly underestimated. World Know Tobacco Day will be observed on May 31, 2019 under the theme tobacco and lung health. The Registry of the Supreme Court St. Lucia in collaboration with Compete Caribbean is campaigning for the use of Alternative Dispute Resolution, ADR, on mediation as the preference for resolving conflict. As such, a campaign has been launched which seeks to increase the availability of and access to mediation services under the legislative framework in St. Lucia. Chartered Accountant and Trained Mediator Andrea St. Rose says that an environment where there is a process in place for settlement of disputes is very good for business. The campaign will allow for engagement with SMEs, including manufacturers, farmers, service providers and other business owners about how mediation services can be made more accessible. This has been your media news brief, thank you for watching.


Today we are having the 23rd lecture continuing with passive filters that already discussed the first order and second order low pass filters using passive networks. Let us continue with that it is important that we understand the first order and second order in order to nicely get an intuitive aspect of any higher order filter design. So, first order and second order low pass filters were the ones that were discussed in the 22nd lecture. But whatever maximally flat magnitude characteristic was the feature that was emphasized in filter design and maximally flat delay these are the 2 important characteristics that you would like to have for our filters or the amplifiers or I mean whether they are RF amplifiers or RF amplifiers or the base band amplifiers these are the characteristics we would like to have for these. In some cases we would like to have better noise attenuation property which are characteristic of Tebyshev and inverse Tebyshev filters particularly inverse Tebyshev filters wherein we can locate certain zeros outside the band to get rid of narrow band noise color noise. Elliptic filters again narrow band noise can be very nicely removed and we can permit certain amount of steep characteristic which is steeper than inverse Tebyshev filters for the same order using peaking or ripple in the pass band. So, the ripple in the pass band ripple in the stop band are elliptic maximally flat in the pass band ripple in the stop band are the inverse Tebyshev ripple in the pass band okay is the characteristic of Tebyshev but about is maximally flat in the pass band. So, basis filters are the corresponding filters where maximally flat delay characteristic is got. Now when we discuss passive filters we had considered RC, RL filters and RLC filters now we will further go into an understanding of these passive filters we saw that by having a magnitude characteristic of this type corresponding to maximally flat magnitude characteristic Butterworth filter the numerator polynomial is just a constant it has only denominator polynomial and it has only the highest order which has a coefficient as far as x squared is concerned x squared or x to power 4 x to power 6 like that these are all Butterworth filters. Then we would like to have certain amount of ripple in the pass band then it can have 1 minus k 1 x squared or in the numerator 1 plus k 1 x squared for the second order filter characteristics 1 minus k 1 x squared plus say 0.21 x to power 4 or something like that and numerator can have no polynomial in x or you have numerator polynomial which is 1 plus k dash x squared divided by this kind of denominator polynomial or you can have k 1 and k 1 dash both existing this being positive this being negative that will further enhance that. So, in a sense the kind of characteristic that the Chebyshev filter has is something where peaking can occur. So, if it is only can constrain attenuation it can be 1 minus k 1 x squared kind of thing then when you have 1 minus 0.25 x squared here you can locate a 0 for example at x equal to 2 that is the point where we have let us say a neighborhood noise transmission occurring okay. So, we want to get rid of that or this may be the 50 hertz noise in a biomedical signal right. So, we want to get rid of that fully because it is large in magnitude. So, then we can locate a 0 in the numerator polynomial okay. So, that at a certain point in the frequency domain it goes to 0 of transmission. Now that particular 0 along with a k 1 coefficient which is negative which is greater than okay magnitude than this is going to be if this 0.25 this is 0.5 it is equivalent to having no constant denominator and 0.25 here minus 0.25 here same thing. So, that means actually it is going to peak there considerably okay. So, that means it has a steeper attenuation characteristic at the pass band H that is the elliptic filter. Now coming to first order high pass filters we have this with R and L. So, earlier low pass means R and C now high pass means you just replace the C by L then it becomes high pass right or we can have C in series and R in shunt here. So, that at high frequencies this becomes a short and output is going to be equal to input okay and at low frequencies it is going to decouple the output from the input so it is 0 of transmission. So, the 0 of transmission exists at DC okay and therefore and it is going to go towards 1 as frequency goes to infinity here this particular inductor is going to make the DC appear as 0 here and at very high frequencies it is going to be an open and the output is going to be equal to input. So, both have the same characteristics okay if for example the RC time constant of this network is made the same as L by R of this network that is RC is made equal to L by that means if a capacitance C exists you select an L equal to C R square right then these two will have exactly same characteristics which is 1 by 1 plus S by omega say bandwidth. So, this will be omega bandwidth this is the 1 over omega bandwidth is RC time constant or L by R. So, this is the nature of first order high pass it is easy to design. So, V naught over VI is SCR by 1 plus SCR for the RC network and it is SL by R divided by 1 plus SL by R. So, the magnitude function squared is this okay into conjugate of this in a domain where you have put S equal to G omega so when you put S equal to G omega this becomes the magnitude which is omega C R square divided 1 which is nothing but our normalized frequency capital omega X is equal to capital omega hence forth we will use this because this is the way we have started our filter theory right. So and it is X square by 1 plus X square which is what you have as X equal to omega by omega naught or omega by let us say bandwidth. So, the normalizing frequency is the bandwidth of the low pass or high pass which right whichever it is that is the normalizing frequency omega naught in this case is 1 by RC if it is a RC network. That has been plotted here this is the magnitude and this is the delay function right. So, the delay function goes to point 5 of this and magnification because it is square root it goes to 0.7 here because it is square root. So, the delay function is just there is no delay here actually there is a pi by 2 okay minus this delay okay as the phase shift the phase shifting function it is pi by 2 minus tan inverse okay X okay which is differentiated and that is how we get this function from the tan inverse X function design of high pass band pass and band stop filters can be done starting from the corresponding low pass factor type that is an important theory that we would like to discuss today that how frequency transformation can be easily used to convert a low pass prototype into an equivalent high pass okay or given a high pass how to convert it into a low pass prototype and do the design in the low pass domain. So, since we know all the filter types can be easily designed in the low pass domain we can after converting we can do the design in the low pass domain and to convert it back to the required high pass band pass or band stop filter topology. Now one such transformation for low pass to high pass for example is 1 by 1 plus X square okay is the low pass tongue okay where it is equal to 1 at X equal to 0 and goes to 0 at X equal to infinity. Now do the transformation from low pass to high pass that transformation is X is change to 1 by X so X square changes to 1 by X square right. So, we have this now becoming equal to X square by 1 plus X square that is what is plotted here and you can clearly see that at this point okay it is 0.5. So, it finally goes to 1 so this is the transformation how does this transformation work in terms of a passive network that we would like to use ultimately. So, let us say we want to design ahh first order high pass filter with F naught equal to 40 hertz okay omega naught then becomes equal to 2 pi into 40 which is 80 pi let us design the first order low pass filter prototype okay with omega naught equal to 80 pi and then using the transformation will get the characteristic and also in terms of the network we know what to do that is the C let us say omega C equal to omega okay into ahh omega by omega naught which is 80 pi. So, we get this therefore from this for a C equal to 1 micro farad for R of 5.7 K we get this 40 hertz cut out for the low pass prototype and high pass filter okay is also going to have the same bandwidth okay that is this one will be having its upper cut off frequency this one will be having the lower cut off frequency at the same point okay if L is made equal to CR squared how did this come about because we know that our earlier experience that as far as the time constants are concerned they must be made the same that means L by R is equal to C into R. So, the choice of L is based on this CR squared so it gives you 15.7 Henry's which is too huge a value realistically to have as a circuit particularly now right and therefore even in older days about 40 years ago this kind of inductance is too bulky to be used with electronics of ahh even 40 years ago. So, this has been simulated okay using ahh active networks and RC networks okay. So, that is one way of solving this problem of ahh size as far as the inductor is concerned. So, inductor was the first component to be rejected in electronics okay at baseband particularly. So, it is too huge now let us consider building up of a second order RC low pass filter that can be done theoretically using two first order networks in cascade that means actually we have one RC low pass filter cascaded to another RC low pass filter let us say it is R1C1 and this is R2C2 then the transfer function is very easily written as DC transmission is 1 so 1 by 1 plus rest of the things are functions of S okay and this coefficient should be such that the whole thing is dimensionless that means if this is frequency this should be time constants okay. So, first time constant with just one capacitor is R1 into SC1 okay this is one integration you can say 1 by SC1 R1 is one integration with one capacitor this is the other integration okay that current goes the all way to these R1 plus R2 and then into C2. So, C2 coefficient is R1 plus R2 as far as this is concerned as one integration using individual capacitors then double integration it means it gets integrated to this and then through this right is coefficient of SC2 so you have SC1 R1 into SC2 R2 which gives you SC2 R1 C2 R2 this is the easy way of straight away writing down the transfer function of most of these networks okay. So, Omega naught the normalizing frequency here SS squared by Omega naught squared okay so Omega naught by comparison becomes 1 by square root of R1 C1 R2 C2 and Q this is S by Omega naught Q normalizing. So, please remember our lecture here this C1 R1 plus C2 into R1 plus R2 C1 R1 plus C2 into R1 plus R2 is equal to 1 by Omega naught Q so Omega naught being equal to this then from that you can get 1 over Q as square root of C1 R1 by C2 R2 square root of C2 R2 by C1 R1 if this is to be made that is Q is to be made very high let us see then we have to maximize this one way of maximizing this Q is minimizing the denominator polynomial because all these things are occurring in the denominator of Q okay this is what 1 over Q. So, this is required to be minimized okay. So, that means R1 by R2 can be selected such that this is very small these are all positive so R1 can be selected to be sort of much smaller than R2. So, that means R2 is large compared to R1 then we can ignore this then you have this as X plus 1 over X kind of thing so which is going to be minimum at X equal to 1 that means when C1 R1 is equal to C2 R2 so the test minimum value for this is equal to 2 it cannot go lower than that in a passive network of this type if it is made second order filter then you cannot have Q okay greater than half it cannot be even made equal to half it is always less than half. So, you do not use okay higher order filters okay particularly second order filter with two Rc networks or two RL networks you will can prove that the same is true with two RL networks LR LR okay. So, it is impossible to get Q greater than half or equal to half. So, what do you do you that must use RLC networks for getting any Q you desire. So, the best circuit for getting higher Q is a resonant circuit this is nothing but a series resonant circuit this has been studied by you in networks right and we have also analyzed this circuit earlier in the previous lecture. So, what happens we can therefore write the magnitude of this from our previous experience as 1 by 1 plus magnitude squared is 1 by 1 plus 1 over Q squared minus 2 into X squared plus X to power 4 where X is omega by omega naught and omega naught is the resonant frequency okay omega naught is nothing but 1 over root L into C okay this is equal to 2 pi into F naught. So, we have omega naught as this and Q equal to 1 over omega naught CR if you write down the transfer function the transfer function is something that you can readily write it is going to be 1 over SC by 1 plus okay SC into R S S squared LC. So, you will notice that Q is equal to 1 by omega naught CR if this is S squared by omega naught square. So, this can be written as okay. So, this is S squared by omega naught squared this omega naught squared. So, this is nothing but 1 okay. Now by making Q equal to 1 over root 2 the coefficient of this can be made equal to 0 okay. So, then it becomes 1 by 1 plus X to power 4 that is the square of magnitude or it is called Butterworth. Now if you do the transformation of X squared okay to 1 over X squared with the bandwidth remaining the same the Q remaining the same it simply becomes 1 by 1 plus okay 1 over Q squared minus 2 into X to power minus 2 plus X to power minus 4 which is the high pass function with the same Q equal to 1 over root 2 maximally flat that means Butterworth. So bandwidth of both are the same again. So, second order low pass filter example so 40 hertz is the bandwidth. So, you can say L is equal to 15.800 again you see that it is too huge okay for maximally flat response Q equal to 1 over root 2 so R becomes 5.62 while the C and R values are reasonable the induct value is too big to be accommodated normally and we have to convert it into high pass of the same order with Q equal to 1 over root 2 so we just put X squared as 1 over X squared so we get the high pass filter characteristics with L dash equal to L C dash equal to C omega naught equal to 1 over root L C Q is omega naught into C into R. So, we get this characteristic which is that of the high pass and the enter key is this right. So, it is 1 minus the low pass is the high pass 1 minus low pass. Now going to band pass filter band pass filter is a combination of low pass and high pass filter characteristic obviously it should be at least second order because the low pass or the high pass characteristic comes into picture first. So, we have a band pass characteristic this is the high pass characteristic comes first and then the low pass characteristics so cascading high pass with low pass results in this kind of behavior so it can be just done this way but we have already mentioned that if it is the same kind of network for example C and R like this R R and C like this does not matter both are band pass this comes first and that right. So, there is another interesting network which also this is used in what is called wind bridge this is also a band pass. So, if for example this is for all these network the transfer function is the same what is it SCR divided by 1 plus 3 SCR R 1 is equal to R 2 so we get and C 1 equal to C 2 that means Q of this is going to be equal to 1 by 3 I told you that the highest Q it can have by design is less than 0.5. So, these are all pretty useless circuit for most of the general filter characteristic that we would like to generate that means we should be able to get a Q which is anywhere from low value to very high values low pass to band pass transformation. So, the X in this case is going to be replaced by X is going to be replaced by X minus K squared by R this is going to be the same as X squared minus K squared by X as depicted here. So, X is replaced by X minus K squared by X then the entire characteristic gets shifted to where X was 0 that gets back to X equal to K here. So, this is the shift from X equal to 0 this maximally flat magnitude square characteristic or the Butterworth characteristic of first order gets shifted to X equal to K with the same bandwidth right. So, you can see that so, we have substituted here is 1 by 1 plus X squared becomes X squared minus K squared by X whole square. So, that is the transfer that is plotted here. You can see this this is 1 by 1 plus X squared and this is 1 by 1 plus X minus 25 by X okay that means K is equal to 5 K squared is 25. So, you can see that it is peaking the speak at X equal to 0 has been transferred to X equal to 5 and the bandwidth of this is unity let us say it is normalized with respect to the bandwidth and the same bandwidth is replicated here after the shift. So, that is 4.5 to 5.5 bandwidth. So, this normally has the negative side getting replicated at X equal to minus X equal to minus 5 okay X squared equal to 25 there. So, X equal to plus or minus 5 this gets replicated. So, the bandwidth remains the same as that of the low pass prototype. Design a second order band pass filter with center frequency equal to 5 kilo hertz let us say and the bandwidth of 1 kilo hertz. Design first order low pass prototype for a bandwidth of equal to bandwidth of the band pass filter which is 1 kilo hertz. So, the low pass prototype should have a bandwidth of 1 kilo hertz. So, we have selected okay in this case omega equal to 1 by RC this is the bandwidth as 2 pi into 10 to power 3 selecting 1 micro farad we have appropriately chosen R as 159 so that the bandwidth of this comes out as about 1 kilo hertz here that is 0.7 because this is square root of the magnitude okay the 0.5 becomes 0.7 or 7. So, then we can note that if you sketch this this way this bandwidth corresponds to exactly okay the 1 kilo hertz that we have designed it for right as the low pass prototypes. So, this is the simulated result okay and it is exactly located at 5 kilo hertz this is what is called the low pass to band pass transformer. Please remember this fundamental thing it is the RC that determines the bandwidth okay if this is remaining the same it is 1 over RC which is also the bandwidth okay of the so called band pass filter okay this just gets replicated this way. Now low pass to band stop transformation okay again if you start with RC right you have to let us just go back to this and see how this particular thing is designed basically we have a low pass that we start with this is C and R. So, this reactance is substance is SC so S E is replaced by okay SC plus 1 over SL what is it this is an admittance okay originally SC okay it is replaced by SC plus 1 over SL which means actually its frequency dependence is J omega C. So, this now becomes equal to J omega C okay into minus 1 okay over plus 1 over J omega L or this is J omega C into 1 minus right what happens here this becomes omega C has been taken out so it is omega square L into C okay this 1 over LC is really is what is called 1 minus okay omega naught square normalizing frequency right. So, this is the this CR is the one that determines the bandwidth okay of the low pass prototype and this is the shift this is what is called as X okay that is 1 over X square for example you can call this as 1 over X square that is K square over X square okay. So, this is the centre frequency shift that means it gets shifted to the resonant frequency of the system. So, when we just put this way this is C this inductor is okay nothing but 1 over omega naught square into C that is the value of inductor. So, we can easily compute this equivalent okay in the frequency transformation and that is how we have designed the whole thing and you can see that that is what this resonant frequency is at 5 kilo hertz 1 micro farad and 1 milli henrys roughly corresponds to very nearly equal to 5 kilo hertz. So, replace the capacitor by a parallel resonant circuit replace the inductor by a series resonant circuit okay. So, that way actually a parallel resonant circuit if it is replaced by a series resonant circuit then you have a transformation of things from band pass to band stop. So, the same thing only thing is this frequency scaling effect now is the resonant frequency is 1 over 2 pi root L dash C dash okay and the original C that determines the bandwidth that gets scaled to okay C into bandwidth square divided by center frequency this normally called okay 1 over Q square okay. So, the case scaled to okay this kind of thing and the inductor is to be chained to okay L dash by 1 by bandwidth squared into C okay. So, that L dash C dash becomes equal to 1 over center frequency squared as so the resonant frequency remains the same. So, if I now chain these capacitors and inductors in this manner then the Q remains the same okay as before okay and this becomes the band stop. It is equivalent to changing X to X square minus K square by X okay to the power minus 1 now. So, first transformation is okay X to 1 over X and then that X can be chained to X square minus K square by X okay. So, the parallel resonance becomes a series resonant circuit and L dash and C dash get scaled accordingly so that the Q remains the same. So, that is the band stop characteristic exactly produced. Let us do the same thing 5 kilo hertz and 1 kilo hertz okay 5 kilo hertz is the in place where we want the notch and 1 kilo hertz is the bandwidth of the notch. So, actually design first order low pass filter prototype for a bandwidth of and is equal to bandwidth of the band pass filter. So, this is the low pass filter prototype with 1 kilo hertz bandwidth somewhere here right 0.707. So, if you extend the same thing here this is going to be again 1 kilo hertz and this notch frequency is going to be at 5 kilo hertz. The network is again same 159 ohm resistance this one micro farad gets divided by 5 square because that is the Q 5 by 1 kilo hertz okay 0.04 micro Henry's and for it to be resonant at 5 kilo hertz the inductor value is 25 milli Henry's at micro farad. So, we can easily design this scheme starting from the low pass filter prototype and this is the notch filter next. Let us consider using inverse TBCU filter as given in the figure right this is an important network now inverse TBCU filter okay means what we already understood this I want the characteristic like this let us say it as maximally flat characteristic up to the bandwidth and at this point right where I want to get rid of a specific frequency that is going to be like this let us say okay. So, this particular point is going to be the frequency at which it is rejected totally this component of frequency is rejected. So, this can be obtained by a magnitude function which is 1 minus n1 times omega squared the omega squared is now currently being replaced by us as omega is equal to X. So, that means this is our X squared so one square root of 1 plus X squared plus X to the power 4 this is the kind of characteristic like to have right. So, you can note that at X equal to 0 is going to be just 1 okay and transmission and as X goes to infinity right this is going to result in let us say if you have something like this right this particular thing is going to result in this is square root of omega to the power 4 is going to dominate as X increases to a large value. So, this also becomes X squared and this becomes very nearly equal to okay at X equal to 0 it is 1 at X equal to tending to infinity it is going to be n1 squared that is the transmission because it is going to be dependent upon n1 squared because this omega squared gets cancelled with this omega squared this is asymptotic to n1 squared. So, this is a very simple design therefore it uses just a tapped inductor along with the capacitor that is all with the resistance. So if you write down the transfer function of this again right you can note that this inductor in series with this is the resonance circuit which means it is series resonance that means actually it becomes 0 okay at a certain frequency when omega L1 is equal to 1 by omega C. So, that means omega L1 equal to 1 by omega C these two reactances get cancelled together and it causes the thing to become a short circuit. So, the transmission is 0 that means the 0 is equal to 0 of the numerator polynomial is at 1 by L1C. So, that means actually we have this the n1 okay which is easily controlled by us okay with respect to omega is really equal to say small omega by omega naught omega naught is the bandwidth it is that of the pole okay omega naught. So, what is omega naught omega naught is the series resonance frequency of this what is it? It is equal to 1 by root of total inductance L1 plus L2 into C. So, this frequency is lower than the 0 frequency the bandwidth is lower than it. So, this let us say is roughly the point at which we have this the bandwidth okay. So, the bandwidth is located when this series resonance occurs there okay the denominator polynomial goes to the minimum value that means it has a peak it has a tendency to peak. So, it can have a peak also depending upon the queue right. So, we will select the queue such that that the it is maximally flat let us say. So, that value of queue at which is maximally flat for a given problem let us work out this problem it is interesting I want for biomedical applications let us say a 40 hertz bandwidth I have a predominant component of 50 hertz present. So, I will locate this what is the 0 at 50 hertz. So, my omega 1 is going to be omega z is going to be 2 pi into 50 hertz. So, that is equal to 1 by square root of L1 into C. So, this omega z is fixed based on my desire to get rid of this as much as possible. Therefore, I put a 0 of transmission at this frequency. Then I select the queue of this network in order to make okay. So, N1 has already been fixed because of the choice for this right. So, that is the thing N1 is equal to okay this yeah because it is 2 minus 1 by Q square 2 N1 is equal to 2 minus 1 by Q square this is the way we are going to select the 0. So, that it becomes maximally flat N1 is equal to omega P pole if you consider this as the pole frequency what is it omega P is equal to 1 by square root of L1 plus L2 into C as the pole.  So, this is 50 and that is 40. So, F that P divided by F z okay P by F z therefore is 0.8. So, N1 is 0.8 square okay and you can therefore note that this when we square it this becomes square.  So, that makes the coefficient of x square and numerator and denominator same that means it maximally flat that occurs at a Q of 1.18 okay and R to make that Q equal to 1.18 is 3.34. So, I would like you to simulate this and see the characteristic of this which exactly resembles what I am showing here. So, this is the characteristic that is normalized of course of the filter that is the Chebyshev filter that I have designed now you can see if 1 corresponds to the bandwidth. So, if this is equal to 40 hertz this is equal to 50 hertz. So, it is 50 by 40 which is 1.25 scaled to the bandwidth. So, this is the filter that we have designed okay and it is going to be this kind of characteristic that we should have in order to make it work as good filter for let us say biomedical applications. It can be improved by cascading one more first order filter. So, that this gets attenuated and the characteristic looks now like this right. So, most of the white noise gets removed by one more first order that is cascaded to it and here it does not touch. So, this is the characteristic that finally you can get by having a second order filter cascaded to a first order filter. You can improve upon it. So, this is the kind of design that normally gets carried out okay buyers very easily in fact we do not need any help of higher order equations and higher order mathematics for understanding filter design. Let us now just for conclusion sake start with some random specifications right. Let us say I have a filter design that I have to do for getting rid of two major neighborhood frequency components okay in let us say baseband signal process that means I want a low pass filter okay which outside the band has two major narrow band noise components okay that must be got rid of. So, if I have to get rid of two major narrow band noise components and white noise of course. So, what I have to have minimum to start with and what is the topology how can I intuitively get this topology okay just by knowing the requirement right. So, let us start with this problem it is bandwidth is known the signal bandwidth is known let us see. So, I want to approximate it to a box like characteristic with this is the bandwidth okay this is the low pass filter I want to design. So, I have the bandwidth as let us say I will say omega naught earlier I have been normalizing always the whole thing with respect to the bandwidth of the low pass filter prototype. Now let us say this is going to be omega one noise component this is the other noise component so these are major then apart one that I have to attenuate the noise considerably uniformly. What is the minimum order that I should select and how what should be the nature of this obviously I want to locate my two zeros here that means first thing that you do is the numerator polynomial is okay containing one plus s square by omega z one square. So, write down the numerator polynomial first this may be some constant H naught one plus s square by omega z two square then the denominator polynomial right let us see denominator polynomial greater than the numerator polynomial that means this is already fourth order.  So, we have seen in the earlier this thing the numerator order if it is young or young the denominator should be at least one order higher okay so that means I have to have this as at least okay I can do better by having higher orders but this is the minimum that I require. So, straight away write down the transfer function of the required polynomial that you have to that means it can be just that this one thing can be realized by using one second order network another can be realized by another second order network and third is a first order network. So, I know that I can cascade this together and definitely get what I want after that how do I optimize the filter design obviously the location of all these poles and zeros are already fixed the poles will make it such that I should get for example maximally flat here and obviously there will be ripple here okay. So, what is the kind of ripple you get if it is maximally flat it is going to be just this and then it is going to be and because of the this order dominating ultimately it will all go to zero ultimately. So, this is the characteristic I am going to get and it can be maximally flat here that is I want to have better attenuation characteristic what should I do with it I will permit okay this cannot peak because this is going to be just going on decreasing this is a going to have 1 by 1 plus x squared under the root this one will have obviously a tendency that can cause a peak this one will also have a tendency to cause a peak so that can be two peaks okay apart from the peak at zero caused by this first order that can be two more peaks that means basically I can have it going like this okay and going like this actually it may therefore increase above this right so it may be the kind of characteristic you may be able to get. So ultimately I know that it will be some kind of if it is equiple like this and rippling at this point this is the best I can do with selection of cues and selection of these different pole frequencies omega p1, omega p2 and omega p3 so I know what I should get so please know that all this peaking frequency will be close to the bandwidth so that means omega p1 is going to be let us say the first peaking frequency and omega p2 is the second peaking frequency and the q of this q1, q2 should be greater than q1 because every such thing can be concluded very intuitively this way that this is always attenuated like this and then that attenuation of this first order can be compensated for by next peaking circuit okay. So let us therefore see how it is going to be looking like so first order is going to go like this because it is attenuating continuously peaking only at omega equal to 0 right we would like to have the next one which is going to peak like this so this decrease is compensated for by this increase so it becomes maximally flat okay up to this point so there after both of them are decreasing right so at most it can therefore become maximally flat only up to this point and there after okay both of them are decreasing so it will be decreasing at double the rate right and then I have to have another peak which is higher than this okay. So that this decrease can be compensated for by this increase so it will have to be higher so the q of the second order should be higher than that of the and it is going to occur close to the bandwidth there after of course all these three things are going to cause attenuation and therefore they are going to decrease only. So this is the way we are going to have the characteristic of all these blocks individually consider and that is how they become maximally flat or they can have a ripple okay that means if this is located further close to the bandwidth this may be permitted decrease and then increase similarly this one okay can be permitted to decrease and then increase and that is how you get the ripple okay. So the q's of elliptic filters will be higher than the q's of let us say inverse tables filters okay and all these inverse tables and elliptic q's will be higher than that of the Butterworth filters blocks. So these are the intuitive concepts that you can derive out of just knowing okay about the second order and first order. So try out this as trial and error just have the second orders and first order cascaded okay and see what happens to the multiplied higher order network this is the way right higher order filters are designed and that particular thing does not require the help of any sophisticated tool or anything else okay for understanding okay. So this is the conclusion that we are going to have that passive filters are very efficient and power efficient I am saying they do not require any biasing arrangement etc and precision passive components can be easily got therefore you can actually build these filters okay very easily if you understand the rudiments of the filter theory okay. In the next class we will just see how and by active filters came into existence and one natural way of thinking filter design because most of the passive filter designs have already been standardized and elaborate tables exist for variety of filter design okay these are all in normalized frequency domain what should be the q what should be normalized frequency ratios in order of ripple of so many decibels okay etc. And therefore one ready way of converting all this into active is just to get rid of the inductor and simulate the inductor using active device resistor and capacitor. So in the next class we will see how inductor simulation can be carried out with the help of the active device primarily the op amp and resistors and capacitors inductor simulation using capacitors.


I always love the best way because our soldiers shine and can prove to everybody how good they actually are and how much they know their skills and their crafts. To show the world how good our soldiers are, I love this competition. So the value of the best warrior competition is getting them back to the basics and doing some of the fun things that they joined the Army for. And it's a great opportunity for them to experience the new qualification standards. They're new this year so we're changing over from one standard to another and so they get to carry forward the skills that they had with previous qualifications and apply them to these new qualification standards. It's important because it can represent your unit but also give you a sense of where you're at. After everything you execute you assess. Coming to these competitions and moving stage from stage is a good opportunity to keep assessing yourself. I did the ACFT this morning and now they're at the mount site doing the Army warrior tasks. So the ACFT is a new way of assessing our soldiers. These are the best warriors of each ESC and they've done the ACFT before and they've killed it. You have to know the basics to progress throughout your career and that's exactly what warrior tasks are. The most important part of the Army is these basic tasks that kind of make us a functional organization. So you must do your individual tasks good and proficient to survive in the battlefield and then you can combine that with everybody else's to do the collective tasks. And be able to shoot, move, communicate, medicate, decontaminate and sustain yourself. Spot report as follows. How are you feeling? Mine's a 10, body's a 10, feet are like a 9.5, feet are 9, mine's a 10, well my back might be 9.5. I really do love the Rock March that's a really tasking event that it significantly tests their heart instead of their body. Their body will feel it but their body will do it. If they've got the heart to push through it then that's really where they set themselves apart. It's pretty tough right now, this massive shot I'm feeling in my legs, 252, I'll take that all day. It's a marathon not a sprint so if you do bad one event you're just going to make sure you pick it up and kill it on the next one. My name is Sergeant Major Goodman, I'm a 316th ESC Sergeant. You would, can you tell me a little bit about yourself? Now what are the four rest positions? How long have you been in E-5? The Army Regulation covers the wear and appearance and they'll trade you up all the time. You've been intense, kept us on our toes, we didn't know you. The NCOC. All soldiers are entitled to outstanding leadership, I will provide that leadership. I love this competition as I said before, when I was a young soldier I competed in a soldier of the quarter and it excelled me to be the NCO that I am. These young soldiers, they are setting their standards and they are the future, they're right in their own history. They are going to be the next platoon sergeants, the next first sergeants and the next command sergeants of the Army of the Future.