we were looking for oscillators and pardon oscillator which is used in most of the circuits analog system as well as digital is a VCO shown here which is a tuning LCO oscillator and here the capacitor is essentially created out of a diode which is called vector because a variable capacitor with voltage or variable reactance or very cap the other word if you know a p-n junction depending on whether it is abrupt junction or it is linearly graded or exponential the reverse bias capacitance can be given by zero bias capacitance divided by 1 upon 1 plus Vr by 5b where 5b is the built-in voltage of the junction Vr is the reverse bias and m is the factor which is decided by the kind of junction I have for example abrupt junction is half graded is one-third it may vary from 0.35 to 0.5 depending on the grade you get get constant you get there typically in most cases 0.35 or one-third is true because the exponential function in a long range acts like more like a linearly grades but it is not 100% true because if it is a error function profile it may be slightly different Gaussian may even little different than exponential so please take it that values are normally provided by the technology people for their device if it is half then it is much easier to find 1 upon c square V is a straight line so the slope is the m factor okay so now with this in this case the diode the Vr essentially stands for the reverse bias 5b is the built-in potential which is for the given junction of source drain in the substrate that's the same diode I'll use that may have the typically 0.7 volt or 0.65 volt kind of built-in voltage and so I just have to vary the control voltage to get variation in capacitance and remember larger the voltage I apply smaller is the capacitance so the range up to which I can do is from the CJ0 to a lower capacitance that is higher frequencies so at the at CJ0 it has the lowest frequency and as I increase voltage the frequency will also increase because capacitance will decrease 1 upon 2 pi root LC so C decreases frequency increase of course for a too large a voltage breakdown may occur a normal PN junctions in a CMOS technology we have a breakdown of 6 to 10 volts beyond 5 volt normal devices do not permit more than 5 volts I can make diodes which are as they are called power rectifiers can stand 5,000 volts but this is not a power rectifier okay so it's a diode which is out of and normally even each PN junction is surrounded by an n plus region which is called guard ring which does not allow currents to spread out the reverse current okay so some other technology someday but this is what essentially and so it limits the breakdown for very low values so typical voltage which you can apply is 5, 6 volts and no more so the variation with this whatever is possible that's the maximum range tuning range which this CMOS technology will allow you for the VCO the little bit of maps be of interest which we already done but I repeat it again for the same clarity this is called mathematical model of VCO we know if I write a voltage V is equal to Vm sin omega t or cos omega t omega t has a unit of phase that's what it is omega t so one can say that d5 by dt is essentially omega rate change of phase is essentially the frequency or angular frequency so if I plot 5 versus t and if it is this kind of relation exist it will be a straight line that means the frequency is constant and corresponding to this you may have a sinusoid which may have a peak voltage of Vm here this is Vm sin omega t or cos omega t depends on where it starts at 0 or it started half way okay so this has a frequency decided by you can see the way it is the phi actually represents the frequency is that the phi t curve essentially represents the frequency pi 2 pi 3 pi 4 pi correspondingly d5 by dt is constant here so is sinusoid actually has the same frequency so you can see d5 by dt here 1 1 and 4 2 pi there will be one sinusoid and it repeats now if I have two signals V1 and V2 which have different frequencies omega 1 and omega 2 or has two phases phi 1 and pi 2 if you look at this just to prove what I made statement this has a higher d5 by dt or this has a higher phi 2 has a higher d5 by dt then pi 1 slope is higher there so if you can I can do the same thing here for pi 2 pi 3 pi for each such angle I figure out the frequency and you can see from here for d5 by dt higher this point is on the left compared to the lower one which means the frequency of d5 by d5 2 by dt will be larger you can see from here this moves has a larger frequency compared to this one so essentially slope of phi decides the frequency of operations this fact we actually utilize in PLLs that is what we do phase and frequency are related so if I can control phase then I can control frequency that is exactly what we are looking at so this figure this is this point clear to you what I said that if I have d5 by dt larger or smaller it essentially means the frequencies larger or smaller corresponding to it and that can be depicted if you have drawn this of course this is very trivial this you can always draw two lines put 5 pi 2 pi points and you can see the frequency here is lower compared to this which has because larger d5 by dt will have higher frequencies this is just to prove that point which I said and given in many books including Rojavi, Boyce Baker and everyone so the statement I am making d5 by dt omega is a valid statement okay and to therefore we can represent any phi t curve this is t curve into its equivalent omega curve okay so we say this is a slope then it has a frequency omega 2 higher slope it has a frequency higher than omega 2 which is omega 1 as long as this slope is maintained frequency is omega 2 let us say same phase same slope again occurs so you go down to omega 2 again it rises for the same slope then if it is different it will have a different frequency so this and this are essentially same so mathematically if I say d5 by dt is omega so integral of pi phi is equal to integral omega dt plus integration constant which is phi 0 which is called initial phase t is equal to 0 in a VCO we have done this expression earlier that omega out is omega 0 plus some constant of the VCO KVCO into V control this is the principle of VCO now we have a oscillator output which is say let us say given by Vm cos phi t so I represent cos phi from here in this expression okay so I get Vm capital Vm maybe you can take because I use small m again so if I write Vm cos integral omega out dt plus phi 0 so I now say the output voltage of a oscillator has this kind of representation is that clear if this is what you agree then this is what you should also agree okay why are we trying to do we want to figure out and this is very important that is why PLS are used in fact our worries are if let us say this control voltage which I am going to apply is not constant right now for example if I substitute this okay I think I made cos omega okay I will have to write now cos this omega out in here also so maybe I do that first so if I have this V capital M cos omega 0 KVCO integral V control dt plus phi 0 this is the expression I will get for V out if we control is constant then there is not much an issue okay but if this is not constant and noise over its so let us say generally the way it is expressed assuming right now phi 0 is 0 initial phase is 0 V control has Vm cos omega t as its voltage which is a CMOSI controller okay which may be overriding the DC value of V control. Now if that happens I substitute for V control Vm cos omega m t here in integral expand it integrate and expand it and leave some terms which are smaller so I get it is V capital M cos omega 0 t V 0 sin omega t KVCO Vm you can expand and get this kind of expression just put this integral here expand small term be neglected and you get this now if you see now I can further do little adjustment here and this can be then written as Vm cos omega t minus KVCO Vm Vm upon 2 omega m into this cos omega this is omega 0 plus omega m term and omega 0 minus omega m term okay if omega m is not present this whole time will go away and what you are expecting would be essentially see so control is constant you have a excellent oscillating frequency at omega 0 but if V control varies you have two other frequencies surrounding it which are called side bands these are essentially noise bands okay so some energy will be lost in side bands okay. So in many cases how do I retain control voltage constant or noise free that is essentially what we are saying we will do it through PLS is that clear so this whole issue of mass was shown to you that if there is a change in control voltage that reflects in side band power which is lost to you because remember if this is not present all the power would have spectrum would go to omega 0 if not part of the power will go on the side bands now this is very some in real life and one must actually see that your frequency does not change okay of course there is a word which of course when it comes I will talk to you later so is that clear why I am I am trying to see that why it should be some locking has to be done for the reference which I am creating and that is done through a system which is called phase locked loops okay of course they have many other features we will see one of few of them as far as this course is concerned this is good enough PLL may not be of course except for the bonus part of some small queries no mathematical theory because a huge area I can actually spend please 6 hours to 8 when 9 hours only on PLL designs by the most of the Indian so-called startup or industries in Bangalore Hyderabad Noida essentially are making PLLs of different varieties different IPs they create that their major bread and butter so do not think PLL is very trivial okay PLL is very very strong chip which so many people need at different applications so is that point clear that there is a sideband power loss if control voltage is not retained constitute so I start with phase locked loops as I say for most of you people may not be aware but this was invented as early as 1930 so it is not a very new thing or something phase lock loop was the word was known and even circuits were made as early as 1930 however the first digital first IC PLL came in 65 and first digital PLL in which digital signal were locked appeared in 1970 by the same year 1970 even sinusoidal or analog PLL were observed or actually made and similar time there were another PLL was used in optical signals and they were called optical PLLs so it is not just electrical signal phase lock loop does not have to do about electrical signal any signal you somehow phase it back adjust it you get it called PLL locking okay so these are something where you can use it to lock the V is VCO frequency I want VCO to be console whatever frequency I am using that should be constant VCO may generate something but I want that frequency should be constant of my choice I decide what is my frequency using VCO and PLL I can actually synthesize I can increase the frequency or divide the frequencies so it is called frequency synthesizers and almost every mobile phone or every television or every other kinds of receiver pagers telephony optical transmissions everyone uses PLLs in one way or the other and I keep saying a small company called core actually have 80 IPs produced last year on PLL just take a small company of 24 people of which four of IITB students and they produce 80 PLL chips as an IPs so you can see the business itself only for that company small company is on PLL so think don't think this is trivial this is very money-making system right now the typical definition of a PLL since I am not teaching this as a part I did not prepare heavily for every word of it as I say if you nearly need some maybe next semester make signal course you insist that they should teach you there if she or she who doesn't want to be there I will come and teach this is very important area for me I like this many of my students are developed is PLL so I will like to actually tell you how what's the problem PLL is essentially a feedback system that sort of a control that means it must have some feedback control it compares the output phase with the input phase please remember phase and frequencies are related is that clear so do not think that phase connection is this the comparison is performed by what we call as phase comparators FC up we will say phase detector first and that will compare as well so you call PD or FD FD is called frequency detectors P stand for phase detector and together we call PFD phase frequency detectors normally phase detectors are sufficient but much more accuracy and much longer range capturing if you want you may need a PFD that also can be a fully digital circuit which is called charge pump method some other day okay so phase comparator is essentially what we are looking for I suppose some of you are communication so you must be aware of these two terms but for micro electronic student it should not be Greek and Latin so let's see what is a jitter and what is a phase noise this is something which I always want to tell people there is a confusion and there is not a clear understanding between the two though they are similar if not same so please our major worry in all NLM designs are occurrence of jitter or equivalently saying occurrence of phase noise it is very difficult to handle these jitters or phase noise at very high frequencies and we are working these days on gigahertz is that correct we are working on gigahertz and at those frequencies this is very difficult to handle at lower frequencies this typically I might tell you there is a word which is common anything below 1 megahertz the change in frequency or change in phase is called drift and in if you are a my timer we used to call wonder wandering so now it has changed to drift but anything beyond 1 megahertz it is actually called jitter or phase noise depending on which way we explain it please remember even on the board if you have chips and interconnects PCB for example these two parameters as I say essentially similar but not same they are very important in board designs so not now remember the board design of 90s or 95 have become chip designs of 2000 plus okay now you are integrated more but the same issues which were occurring and the board has now come on silicon itself so the design issues are same as we earlier looked into board designs so let me tell you what exactly is these two words which comes into our mind jitter and phase noise I will not derive the expression for this how to derive one from the other look from some Google paper you will get it let us say we have a pulse of 100 megahertz and let us say duty cycle of 50 percent that is square wave so we believe that if it is 100 megahertz pulse the pulse period should be 10 picoseconds we believe that actually and it alternates at every 5 picoseconds it should come in every 5 picoseconds but this is only if you think you are right that is ideally it should happen that and if it does not the difference which is going to come is essentially called jitter so one I shown you this is your ideal pulse which you are expecting this is the period okay now what happens in actual transitions they can be early transition or they can be a late transition okay so the maximum early to late transition width in time is called jitter there is a early transition there is a late transition the maximum difference of early to late transition is called jitter okay ideally what should be jitter 0 I do not want any all transition to occur at 50 percent duty cycle if I fixed it okay at T by 2 but if it die on what is the range in which this can change the and any time change essentially we will say t plus delta t or t minus delta t which is equivalently saying in omega terms there will be a change in phase for that omega t plus something means time shift means phase shifts have occurred so jitter essentially gives you phase shifts those who are communication again they know much more about this but from micro electronic side few more words are important for both jitter and determine this phase noise if you have written on as I said these are I mean these are interesting part and I do not want to spend hell of a time on these but I wish I would have time enough to really teach you a PLL something you know in digital I like to teach memories for long same way here I want to teach PLL but somehow my course was so organized by me I know time left to PLLs and I was told by mixed signal people they do teach that so hopefully they will in case you take that is also a elective in case you need you can all other people all NL of people all digital people need a PLL come what me irrespective if it is only digital we say DLLs but DLLs also one other name called DL lock DL block so there is a difference there also please do not confuse with DPCR DPLL and DLLs some books do not differentiate okay is that okay or this is trivial so jitter is the maximum spread of time in which signal can shift from high to low or low to high is what we call as jitter there are two kinds of jitter seen one of course is deterministic the other is always the random one typical deterministic jitters are crosstalk two lines close by signal going across one can have mutual coupling between the two and depending on the direction of signal going it may have larger coupling or a smaller if they are opposite in direction there are larger coupling they are in same sense lower coupling forward crosstalk reverse crosstalk forward is easy comparative to maintain reverse crosstalks actually boosts the values too much and difficult to organize them of course then there are EMI electromagnetic radiations interference as the word goes this EMI radiations may come from the next line which is resonating at high frequencies or may come from other systems around in the block okay other chips can actually have this or in a dub of microprocessor or such thing other company including my power supply may actually emit EMI's EMS so if there is an EMI signal path we actually get into jitters and same way word is if not electromagnetic even the noise simple noise can be coupled between the two because of mutual couplings so there will be noise surrounding which may actually over read the EMI radiations coming from outside they are similar but different sources and finally there are two digital people are most worried that in a block of circuit you are lot many inverters are lot many days all of them switch one go okay out of eight let us say you acquired or eight eight in one and eight switch together they may lead to two major worries there we called power supply droop and ground bounds that is the leader will shift up power supply voltage may go down okay these are also essentially deterministic they may lead any change in anything will lead to jitters the other of course is random and in general if you are from micro electronics we always look into the upper part which we think we probably have some control if you are a communication plan he is very happy here or she is very happy here no control so she is very happy he or she is very happy random is essentially maybe because of the temperature maybe because of process variation maybe because of the interface states different interface states okay and since it is random most likely it follows Gaussian in nature Gaussian distribution it picks up and since there can be more than one jitter sources average value if you have to calculate is called RMS jitter please remember these are like a noise so noise is added up the same way this is also added up so jitter is something this of course deterministic jitters can be off drift whatever it comes we can offset it we can some compensation we know how much so we compensate partly for example if you want cross talk between any two interconnect line put a ground line okay space extra space but every signal line is surrounded by shield which is the ground line in normal cable you have shield on a chip there is no shield so you actually every alternate line is a ground line okay so only link between ground no signal on that that's how coupling could be minimized anyway at the cost of both size or silicon size the second part is phase noise which is as I say it's a related term but not same so if you have a variation in signal timings they can also be represented in frequency domains and normally they show a Gaussian distribution of this kind this is let's say iron oscillator whose power is shown here against frequency if there are no jitters or there is no noise all the power should have gone to the Taylor frequency which is my center frequency f not okay that that time oscillate will oscillate at that frequency so no issues fine everything but if there is a distribution like this as shown here some power is actually given to adjacent frequencies which results in sideman just now I showed you this same word shown here so now we define a phase noise out of this you can see what I do it at this frequency of whatever bands it has come at 0 plus f1 fm here I take a bandwidth of 1 hertz and figure out what is the power density and then integrate all the power which would have actually I got integration of total this power and ratio of the 2 is called phase noise is that figure drawn as I said this is not necessarily part of our course per cent design but good designers must be aware of everything this other than things do not work we do not know what to explain it may still not work but at least you should be happy it's not working because of this okay so that because word is how we know about okay and this spec is specifically normally given to we see how much phase noise available allowed so it's not that this is not a spec this is a spec so phase noise is defined as power in 1 hertz bandwidth of offset frequency that is 0 plus fm is the offset at that one 1 hertz bandwidth if you find the power there divided with total power of the carrier then it is called the phase noise and it's always expressed as db with reference to carrier divided by hertz dbc per hertz so we must actually design like an error if you are solving a chemical analysis what is the way we do it within this truncation error or what is the error bar we say okay truncate things so a pll be a particular error met top of the scope will take you what is the permissible phase error 5% 1% 0.5% you decide design okay that much time it will go through loop and will actually settle actually 0.5% sorry most permissible phase error is half percent now there is a circuit which is shown below which is more like a pll we have a summer here we have a low pass filter and we have and we want to have output frequency same as center frequency we see as output frequency should be the same as and there is a variation in input frequency from the center frequency so as soon as you that small delta T occurs this loop will operate and will bring center frequency to close to VCO frequency or rather opposite the VCO output will be exactly same as your reference output or frequency want even if jitter there are few other words which of interest to some this sigma part is essentially is what it does by a detector phase no no this delta T is in the omega form 0.5% that is at the phase for the center frequency whatever is the phase acceptable to use half that is let's say I have 1 mega half percent equivalent phase whatever is allowed their lock should stop let us say 1 mega half percent changes 0.99 megahertz 0.996 megahertz we don't want to go beyond further to make it 1 megahertz so it lock should stop there ideal it should be 0 it should lock exactly at that frequency but it may not because the components can never give 100% locks but that should be permissible for you jitter also give a little different statement there is a word which they say cycle to cycle jitter for example here it is D plus delta T when the next time it is T plus delta T to okay first of course is RMS value so average value of that is average RMS not average RMS value is normally taken for peak to peak or RMS two values of jitters are measured then there is called accumulated jitter over a given time after certain cycle how much is the net jitter occur to you it's called accumulated jitter for example here you can see now it is small small for a band this may be large enough a jitter and that may change your final phase itself okay so that is the accumulated jitter is also specified 5% okay of course then there is a jitter in duty cycle distortions 50% may become 49 51 that also can create more problems so these are essentially as I said terminologies in PLL books or PLL chapters if you read in a analog book as I said we are not going into huge detail of that some other day some other time for some other people okay so here is a phase detector part which essentially is shown here you have two signals V1 V2 which passes through a phase detector and create an output and the way we actually are looking right now is the phase difference which is delta phi and the average value of this V out should be linear now definition because this is one which is going to control the VCO frequency which is the control signal of VCO okay typical phase detector could be as simple as an XOR gate if you have two signals V1 V2 in the square form you can see at every this is an XOR so whenever they are not same values the output go one otherwise there are zeros since there is a jitter between these two at this frequency this is 0 but this is 1 so it rises it becomes 1 at this point again this is 0 but this is 1 so again against comes down so there is a pulse a small width pulses or markers come depending on this jitter you have and you will see once this kind of output voltage this then you take an average of this is that correct how do you take average filter okay so we will get only average value of that that value you feed it to be controlled and adjust your free is that okay the point is trivial but that is what I just copied from Rosary some other things this is of course is trivial as I said this is the DLL part essentially this only simple digital phase lock loop which is shown here okay there is also a problem of jitter in there is a jitter in signal and jitter in phase lock loop so we have a second loop the stability so there are issues and issues okay the four cases that I have discussed if between the two V1 V2 there is no change in phase so only at the you know for a very short duration transitions occur so the output also transits because this even if we say it is 0 it is not never 0 so it is marginal water so it gives markers how if it is pi by 2 as it is shown here 50 percent so for this time 0 but half the time there is one so you get an output of square wheels of this kind is that correct 50 percent of time you can see here this is one this is one so 0 but this is 0 and this part is 1 so wherever 1 0 occurs or 0 1 occurs XOR will give 1 okay so correspondingly you will get such purses and you should what actually have to do is the average of this okay is your control voltage integrator also can do the same okay then you have pi opposite phase opposite markers the transition wherever goes strongly negative we will show a mark on that if it is 3 pi by 2 it will give a different frequency part in this and you will get again pulses okay so depending on the skews you have you can always get the output and this output when average can change the VCO frequency and bring it back V2 and keep comparing between V1 and V2 so that finally they lock to a close by value up to one cycle yes one cycle phase range is this phase detection is possible and range is also clock locking is also possible more than 2 part it is second clock starts no no lock starts it does not pick up they should follow this model retongue model so before we quit PLL there are few interesting things about PLL which analog PLL use or analog signal processing people use is they inject a sinusoid signal into reference input which is the frequency at which you want the reference signal the internal oscillator means VCO lost the injected signal into reference that is what you want whatever this it should lock to that there is a frequency difference between reference and injected signal is proportional to the K of the VCO all right if it is locked it goes to 0 and internal sinusoid then represent the filtered version of the reference sinusoid and that is what you are looking at that you use as your output of a VCO is that clear x simple g-gmc filter case gmc oscillator k sath gm-gmc means what compensating the RP value okay yesterday I showed in a negative resistance this okay here is the PLL base PLL for a CMOS technology this is your VCO-gm was VCO yesterday I already discussed with you these are the diodes which essentially receives the control voltage this is that average RRC filter I just showed in a LPF this is that average RRC and this is your phase detector your reference input the frequency at which you want to lock the input this is your VCO you tune it to this close to this frequency feed it back compare it in the output here is locked to the reference or if you must have that there is no P channel device anywhere still called CMOS because technology CMOS the VCO is the control is coming from the phase detector averaged out so this essentially why I say PLLs are very crucial for real life requirements because you want to hold this frequency to a constant value before you use it into any particularly RF applications okay where is called image is very strong there and you will actually it will pass through the digital side and that may actually huge noise your capacitor requirement for a to D converter will be very large so it is very difficult to maintain large capacitance is in chip and therefore always you will write to reduce down down frequency from the higher ones and you do not want images to move through so no DC signal should go out okay so very important that it settles to a frequency exactly some other day some other time before we quit this today last introductory part which is again as I say not the part of the course but I think you should know before you quit switch capacitor circuits are very very popular in a to D converters or many of the filters okay like you can even make a ladder filter LCR filter using switch capacitors why we want to change everything to capacitance because we know the resistance and inductance are always troublesome in taking area than accuracy capacitors are well within my control so I prefer all circuits to work with capacitors so here is something very interesting let's take a case this is your resistance your voltage V1 your voltage V2 one of them is higher let's say V1 so V1 minus V2 upon R is high ohm's law or R is equal to V1 minus V2 by I or V1 minus V2 what is current charge per unit time charge per unit time but what is one upon time frequency charge is essentially Q times something and total charge will be decided by the capacitance available there some way into frequency something of this kind not exactly so I have an idea that I can replace R's a CV crown either CVC so I can replace a resistance by a capacitance this is my thinking this is what essentially it means so everyone what we do okay let us say there are two switches which are driven by Phi 1 and Phi 2 Phi 1 and Phi 2 are clocks which are what kind non overlapping okay so maybe I should draw a triangular banana check you okay actually rise time 0 near the if you want further you can do like this okay so essentially I am saying there is a dead time in which both signals are 0 both lots are 0 of course the period is same from this to this or from here to here whichever way you look at the period is same okay so here is a Phi 1 Phi 2 non overlapping clocks and let's say I have a input voltage given here V1 input output voltage expected there are actually put by me is V2 do you see it is I am trying to replace the resistance by this network is that clear V1 V2 V1 V2 which may are high I am replacing with two transistors switches and a capacitor if you have it done I will give the maths on that okay so when the Phi 1 is high and therefore Phi 2 is 0 okay so what is the charge on the capacitor Q1 is CV1 if Phi 1 is high Phi 2 is guaranteed low so Q that is the capacitor is charged to potential V1 and holds a charge of Q1 which is C1 V1 second time I close Phi 1 and make Phi 2 high so during dead time it is retaining the charge of C1 V1 after some time my Phi 2 starts the problem why I kept that time because I do not want charge to be not reaching its maximum I want that charge to be retained as the fixed value of DC which I put V1 okay now on the Phi 2 was high the charge on the capacitors from this side you can see this is V2 and this is your capacitance so this is like a switch closed okay this is like a switch open so now this tries to charge this capacitor depending on initially it will decide what the new charge should be but assuming the charge which it should go if initially there was no charge should be CV2 however it both are one by one so the net charge on the capacitor assuming C1 V1 is higher is Q1 minus which essentially is C V1 minus V2 in one clock cycle of the phase Q1 minus Q2 is the average charge current which is flowing through this charge divided by time so this is the average current which is essentially equal to C V1 minus V2 divided by T but we know from our earlier theory current is essentially V1 minus V2 by or S or whatever R switch capacitor equivalent may be we will say it the equivalent resistor have amper so V1 minus V2 by R that is the current flowing through this so if I equate this the switch capacitor is T by C or equal to 1 upon F clock so if I know my two phase clock and I know its frequency I can create a resistance of 1 upon Fc equivalently is that correct before we quit we make a simple filter so it will be C Rc time constant is C2 by C1 or C2 by C into clock okay 1 upon clock R is 1 upon Fc so if I want Rc into C2 then it is C2 by C into 1 upon F clock you can see from here I can create any filter between these capacitors and an integrating capacitance also I can put switches there any resistor I want an amplifier I replace that resistance by a capacitor switch and then the ratio of capacitance will give you gains so I can make an amplifier I can make an integrator because I do not put R there I put only C I get an integrations so I have I can create every circuit of opium which requires R can be replaced by a switch capacitor what is the advantage because capacitance are the easiest to make in MOS technologies or even bipolar technologies compared to every other resistor or any other values you want to fix okay it is partly digital because switches are there and that is where the problem started before we quit no reason to explain but this switches are not ideal okay they create hell of an issue one problem is which everyone should know whether it is digital analog circuit non-circuit if when it is on there is a charge in the channel okay when you make f0 you expect this charge to collapse so where it can collapse either at the source end or at the drain end yeah charge has to be withdrawn but there is a capacitor sitting here okay so the next value of set lege churro is co kisita saia dekhazhaya ki yeh yaan jane ke pehle ek is a kuch aur circuit so chokya bana factayen jokie so echo transistor daltayen jiska source drain short karna or is ki agar phir kappa So the final voltages are not exactly known depends on the frequency which you operate. This is another problem much probably this feed forward, feed forward, backwards problems are very difficult to solve but can be minimized. It is called Ekor method, it is called CMOS, partly solved. The third problem is KT by C noise and that KT by C noise always exist. So switches being non-ideal, the issues of non-ideality play a role in any switch capacitor systems. But otherwise they look to be very promising, they look to be very promising. Okay, so this finishes whatever I wanted to tell you in this course, not that it is enough, not that it is less but this is enough for this semester.


The Linux Foundation, Noriaki Fukuyasu. Good morning everyone. Thank you so much for attending the Open Source Summit Japan. On behalf of the entire Linux Foundation staff, I would like to welcome you to Open Source Summit Japan 2023. We are really excited to have you here. Particularly for those who are coming over to this event from overseas, I really would like you to take your time to explore the town and experience the culture and tradition of Japan after you fully attended entire sessions in two days. Before we get started, first and foremost, I would like to say a huge thank you to our sponsors, especially our diamond sponsors. Let me click. So, especially our diamond sponsors, Automotive Grade Linux, and our platinum sponsors, Fujitsu and... Wrong button. There we go. Okay. Again, thank you. Our platinum sponsors, Fujitsu, Honda, and Sony. So, we will not be here without your kind support. Thank you so much. Also, I would like to thank our program committees who actually reviewed all the CFPs that were submitted. When I asked them to become the program committee of this event, some of them asked me how many CFPs they have to review. And I said maybe 100 or 200, but I have to admit I lied. There were like 450 of them in two weeks. But nevertheless, they have done such a great job reviewing the CFPs. So, I would like to say a big thank you to all the program committee who helped building this wonderful program. And also, please bear with me for a few more moments. There are a few more housekeeping items that I have to go through. First, I would like to... Everyone to come visit the sponsor showcase, which is in the whole A. I am sure you have seen it on the way come up here. We have the sponsors booth there. And also, one important thing is that's the place where you can find your coffee and snacks and seating area. You can actually chat with your open source community friends. So, I encourage you to stay there as much as you can while you're at the event. And also, the Wi-Fi info and the link to the conference schedule is on the back of your badges. And also, there's a schedule show up on the signage board throughout the venue. And also, we are going to have a woman and non-binary in open source lunch today at 12.45. And it's open to all of our women and non-binary attendees. And in order to come to this lunch, there's no pre-registration required, so you can come to the lunch. And, you know, this is basically the first served. And the lunch will be at the Sosai patio at a hotel called Soutetsu Grand Fresa Tokyo Bay Ariake Hotel. I repeat it. Soutetsu Grand Fresa Tokyo Bay Ariake Hotel. And in case you forget the name, please just come to the event registration desk and they will help you. And also, we are going to have the sponsor showcase booth crawl, which is starting from 6.10 in the 10 minutes past 6 p.m. And that's where you can... In order to show the booth of the sponsors, but also that's the opportunity for you to, you know, working with your open source friends that are coming to this event. So please take that opportunity. And finally, but not least, we have an event called of conduct that everyone attending has agreed to abide by and that we enforce. So, you know, it's a long sentence, but in short, basically, you know, everyone should feel welcome and included to participate in this event. And I would like everyone to treat everyone with the respect and professionalism. And if you have any concerns, please visit the registration desk and you know how the event team will help you. So with that, I would like to kick off the event. I would like everyone to help me to welcome our first speaker of the day, Executive Director of the Linux Foundation, Jim Zemmling.


We've seen that Hartree's method provides a good approximation to the energies and configuration of electrons and atoms. However, when we try to extend these ideas to molecules, we run into some challenges. The central field approximation is key to the success of Hartree's method. Treating the net force on each electron due to the nucleus and the other electrons as always directed towards the center of the atom greatly simplifies the problem. In a central field, the angular behavior of the wave function is the same as for the already solved case of the hydrogen atom. All that remains is to solve an equation in the single radial variable R. And, as in the case of hydrogen, each orbital is characterized by a set of quantum numbers. This allows us to enforce the exclusion principle by simply assigning different quantum numbers to each electron. However, the central field approximation is not generally applicable to molecules. The net attractive force on an electron, due to the pull of two or more nuclei, will not be spherically symmetric about some central point. And the repulsive force, due to the other electrons, even when treated in an average sense, is also unlikely to have spherical symmetry. Because of this, we will not be able to reduce Schringer's equation to a single radial variable R. This leaves us with a computationally much more challenging problem. Moreover, in a non-central field, the angular momentum of individual electrons will not be conserved. Without angular momentum quantum numbers, we cannot enforce the exclusion principle by simply assigning different quantum numbers to different electrons. This is a fundamental issue that we need to resolve before we can move forward. So far, we stated the Pauli exclusion principle along the lines of no two electrons can be in the same quantum state. But one of the postulates of quantum mechanics is that the state of a quantum system is specified by its wave function. So rigorously, the exclusion principle should be a statement about the wave function. Let's label the spin of an electron by a discrete coordinate S that has two values, up or down. Then for a two-electron system, the wave function would be a function of eight variables, the x, y, and z position coordinates plus the spin coordinate for each of the two electrons. To simplify the notation, let's represent the four coordinates of an electron by a single boldface coordinate x. Then our wave function is psi of x1, x2. And this gives the probability amplitude for finding electron 1 with coordinates x1 and electron 2 with coordinates x2. Consider the configuration where electron 1, which we color orange, has coordinates a, and electron 2, which we color green, has coordinates b. The probability of this configuration is specified by the magnitude squared of psi of a, b. If instead it was electron 1 that had coordinates b and electron 2 that had coordinates a, then the probability factor would be magnitude squared of psi of b, a. Mathematically, these could be different states of the system with different probabilities. And if instead of electrons we were keeping track of macroscopic objects like billiard balls or planets, these would definitely be different distinguishable states. The state of Venus being closer to the Sun than Earth is very different from that of Earth being closer to the Sun than Venus. But electrons, as elementary particles, are indistinguishable. We can't physically label or paint them, and given the uncertainty principle, there is no way to talk about the distinct path of electron 1 versus the path of electron 2 inside a molecule. The most that a measurement of a two electron system could tell us, even in principle, is that there is an electron with coordinates a and an electron with coordinates b. So, these probabilities must be equal. The behavior of a physical system cannot depend on how we arbitrarily assign subscripts to indistinguishable particles in a mathematical model. A valid two electron wave function must have the property that its magnitude squared does not change if the coordinates of the electrons are exchanged, since this is equivalent to simply relabeling indistinguishable particles. Now, what does this imply about the wave function itself? If u squared equals v squared, what can we say about u and v? One possibility is that u equals v. Certainly, if psi of x1, x2 equals psi of x2, x1, the probabilities will be equal. A wave function with this property is said to be symmetric with respect to the exchange of coordinates. But another possibility is that u equals minus v. After all, 2 squared equals 4, but so does minus 2 squared. So, we could have psi of x1, x2 equals minus psi of x2, x1. A wave function with this property is said to be anti-symmetric with respect to the exchange of coordinates. In nature, we find two types of elementary particles. The bosons, such as the photon, have symmetric wave functions and do not obey the exclusion principle. The fermions, such as the electron, have anti-symmetric wave functions and do obey the exclusion principle. The exclusion principle follows from this anti-symmetry. For example, suppose both sets of coordinates, x1 and x2, are equal to x. The two electrons have the same spin and are at the same location. Wave function anti-symmetry then requires that psi of xx equals its negative. But there's only one number that equals its negative, and that's zero. There is zero probability that two electrons with the same spin are at the same place, which is a particular case of two electrons in the same quantum state. In general, an an electron wave function must be anti-symmetric with respect to the exchange of coordinates of any pair of electrons. This is a rigorous statement of the exclusion principle, and it forms an additional postulate of quantum mechanics. But how do we enforce this condition? An elegant solution is given by the Slater determinant, due to John Slater. In Hartree's method, we represent the wave function of a two electron system by a product of two one electron wave functions, a so-called Hartree product. Slater pointed out that this form of wave function is not intrinsically anti-symmetric, hence it does not rigorously satisfy the exclusion principle. But we can make it anti-symmetric by subtracting the product with the coordinates exchanged. No matter what the one electron wave functions are, this two electron wave function is explicitly anti-symmetric. It is equivalent to the so-called determinant of a matrix in which the columns correspond to different one electron wave functions and the rows correspond to different electron coordinates. A normalizing factor, in this case one over the square root of two, is usually included. Let's see how this works by considering the example of two electrons with the same spin occupying hydrogen 1s and 2s orbitals. We take the 1s and 2s wave functions and form the Slater determinant two electron wave function. Consider the situation where one electron is at radius a. Let's arbitrarily take this to be electron two and replace r2 by a. This gives us a wave function for the other electron, a function of the single variable r1. When r1 equals a, this wave function is zero. Here we'll plot this wave function for different values of a, which we represent by a red dot. When the second electron is far from the nucleus, the first electron essentially occupies the 1s orbital. But as the second electron moves towards the nucleus, the wave function for the first electron changes dramatically, so as to always be zero at the location of the second electron. If we multiply the wave function by the radius and square the result, we get the probability density for electron one to be at a particular radius, which has more physical significance. We can see how electron two squeezes electron one's probability distribution, so as to always keep the two electrons separate. If we have three electrons, there are three different pairs of electrons we can swap, so we have to be careful about our bookkeeping. Let's represent the Hartree product shown as one, two, three. We can swap electrons two and three to get the permutation one, three, two. For anti-symmetry, a single pair swap term should have a negative sign. We could also swap electrons one and two to get the permutation two, one, three. Or we could swap electrons one and three to get the permutation three, two, one. We can get two more permutations by swapping a second pair of electrons. If in the two, one, three permutation, we swap electrons one and three, we get the permutation two, three, one. For two swaps, we have a minus minus sign, which is a plus sign. Finally, in the permutation three, two, one, we can swap electrons two and one to get the permutation three, one, two. We get the Slater determinant by adding the two positive permutations, two, three, one, and three, one, two, followed by subtracting the three negative permutations, one, three, two, two, one, three, and three, two, one. We end up with a total of six terms, three positive and three negative. Formally, we write this as the determinant of a three by three matrix in which the columns correspond to different one electron wave functions or orbitals, and the rows correspond to different electron coordinates. The normalizing factor in this case is one over the square root of six. This is starting to look unwieldy. For n electrons, there are n factorial terms in the Slater determinant because there are n factorial permutations of the numbers one through n. n factorial is n times n minus one times n minus two down to one. The water molecule has only 10 electrons, yet 10 factorial is more than 3 million. Fortunately, we can always take our single electron orbitals to be a so-called orthonormal set in which the projection of any orbital onto another is zero and the projection of an orbital onto itself is one. In this case, the vast majority of terms and calculations with Slater determinants are zero, and we end up with tractable expressions. Hartree had developed his method using intuitive concepts. Slater provided a theoretical foundation for the Hartree method. Indeed, if one starts with the assumption that the n electron wave function is a Hartree product of n one electron wave functions, then Hartree's method can be shown to be optimal. At the same time, Slater pointed out that the Hartree product wave function does not have the anti-symmetry required by the exclusion principle. What was needed was a way to extend the ideas behind Hartree's method to a wave function represented by a Slater determinant.


I'm Anne Charles. Welcome to All Things LGBTQ. It's Tuesday, May 5th, and we are tipping in Montpelier, which is unceded Indigenous land. Let's start with some headlines, beginning with Keith. Well, hello. Hi, Keith. Happy Cinco de Mayo. Ah, Rashi. I dressed as a pinata just for you. So, this week's trivia question. In the past, we've talked about Ron Squires being the first openly LGBTQ plus person elected to statewide office when he was elected to the House of Representatives in 1990. However, was there any other LGBTQ plus person who might have been serving openly in state government prior to that? And I do have an answer. So, just a little plug, the census. If you haven't done it, please do. It could mean as much as $4,300 per remontor counted. And some of the information that was just put out is that after the 2010 census, Vermont lost more in federal aid than any other state because of underreporting. And the estimate is that we lost approximately $2,500 per remontor. This is money that even though on the federal level, they're trying to ignore us. Once the money comes to Vermont, the LGBTQ plus community has a presence. We can decide or help decide how that money's get used. The other plug is vital in your health records. If you don't know what they're getting in for information, you need to talk to your provider and find that out. Can you talk a little bit about events this week? And then I'm going to talk about the legislature. They've passed several bills that are of interest to us and that we're going to want to follow. So, Linda, it's your turn. I'm up now. Well, the first thing I was going to talk about was that little snafu with pens at the hospital. Not wearing a mask.  And I'll have a little more about that. An Indian, an Indian restaurant, the fiddlehead is offering pickup during the quarantine. And they are doing so in style with full makeup and high heels. And I have a picture of them doing their food out in front of the restaurant. So I hope you enjoy that picture. Anderson Cooper becomes a dad and he said as a gay kid, he never thought it was possible. So he is really thrilled. Mrs. America and the truth about her son, John, which is a little thing about Phyllis Shafley, and a fired Georgia fire chief sues for anti-trans discrimination. Gay former ambassador Rufus Guilford was named as Biden's deputy campaign manager. Guilford, as we remember, was the gay ambassador to Denmark during the Obama administration. Queer singer Jamie Wyatt defines outlaw country as a music category. In Ohio, chairman MacGuffey, who soon sheriff Jim Nell over her fire will succeed him as sheriff if she is elected in November. She, however, walked walloped him in the primaries. So good luck to her. North Carolina police are searching for missing same sex couples. Fred Rogers advised, advised, advised officer Clemens to say closeted and to marry a woman.  So we'll have a little more about that coming up. And I have a page worth of headlines. They are as follows. And I've organized it by continent. And what I found interesting about this pattern of organization is that some countries are in part like Russia is 77% Asian and 23% European. But you know, I've rounded up to the continent that has the majority. Africa is pretty clear what continent that is. And I have my my headlines before me. Dozens of gay men are outed in Morocco as photos are spread online. And this is the story I reported on last time much more has come out about it. It's continuing. And I'm going to explore it in detail this week. Another story I mentioned last time that I'd like to clarify a bit about 19 Uganda LGBT members denied bail after public gathering arrest. I reported last time that they were arrested for people, you know, now it emerges that four people were not arrested because they were sick. I reported erroneously that they were freed, but they haven't been there. They've been in jail since they were arrested. And given no recourse, the hearing is going to be May 12. But it's clearly discriminatory. Kenyon court, this is a familiar story the fight about Rafiki, the release of the lesbian film Rafiki continues. The director appealed once again to lift the ban on the film. And the Kenyon government has denied her appeal. So it's going to stay banned in Kenya for a while. But I'm sure she'll appeal again. And Latin America actually central America. There's a Tijuana shelter protecting LGBTQ immigrants from the coronavirus. And this is a particular, it's a particular interest because it's one of the few in the country in Mexico that is moving on to Asia. And here's something to celebrate Taiwan records over 3,500 gay marriages at the end of March. The Thai Constitution, the constitutional court rejects a marriage law petition. And I have a picture now before you of the complainants to one gay male couple and one lesbian couple posing in at the courthouse with their representatives. So I think these petitions are going to continue. The Philippines just denied one also, but it's gonna, you know, it's going to percolate and it's going to keep going until, you know, I'm hopeful there'll be progress. Japan, a company has agreed to accept same sex partner certificates by an NGO. So that's progress. The corporate interests of Japan are moving forward with equality, even though the government is dragging its heels. This is miserable story. Paul released in Russia this week found that 32% of respondents want to isolate gay men and lesbians from society. So in better news, in Israel, the court rules against a beer sheba print shop that refused to serve an LGBT group. So University LGBT group brought their poster to this print shop and the religious owner said you're an abomination, so forth. But the court said too bad, you know, if you're performing a public service, you have to serve everybody. Israel also is going to postpone its gay pride march LGBT pride march until later in the summer, they say so that puts them in step with the rest of the world in that regard. Now let's move on to Europe. The EU is urged to act as Hungary's far right government moves to end legal recognition of trans people. And this is, you know, a repressive move couch in the coronavirus pandemic action. Anti-gay lawyer loses appeal to Europe's top court.   And the suit was upheld. But then he appealed his complaint to the high court of the EU, which said no, no, no, no, and find him again for court costs. So now he's going back to the Italian Supreme Court. But he really is standing on very fragile legal ground. The Turkish president, another deplorable supports a homophobic Muslim cleric who said that homosexuality is against Islam. He gave this as his first sermon in Ramadan. And then the Turkish president said, if you criticize him, criticize the Islamic State. So Finland better news, Finland has celebrate confirmed the first two same sex adoptions.  On to Britain with a lot of news, a transgender man in the UK loses his appeal to be listed as a father. And I have a picture of him before you now. If you saw the documentary Seahorse, he was the star. His name is Freddie McConnell. He gave birth after transitioning unsuccessfully appealed the court decision that he could be registered only as the son's mother, because he complete he stopped his transition and had this child and then resumed it and is a man now. But the court said that the word mother reflects a biological relationship, not a gender identity. So if you want to see his story, tune into Seahorse, it was at the Tribeca Film Festival last year. And there's a lot of concern in the UK. LGBT campaigners are concerned over the government plan to protect under 18 trans people from what the Equality Minister called irreversible gender decisions. So that is the Equality Minister is presiding over review of the two 2004 Gender Recognition Act. And she made this statement while saying that results are going to be released in summer. So people are worried about that. She's also inspiring with the LGBT community because she's International Trade Commissioner and has been urged to sever trade agreements with country with homophobic countries that have anti LGBT laws on the books. And so that she's engaged with the debate about that too. Three more stories from England. The M15 boss apologizes for historic homophobic persecution of the intelligent staff. He says it must have caused all kinds of hurt and it did. So he's retiring, but that's his parting statement. Although he started he enrolled in the agency while it was still going on. And it was finally ended in 1991 by Prime Minister Major. All right. More bad news. And this was last week. This was report was launched in honor and recognition of lesbian visibility week. A third of lesbian mothers have been pelted with vile homophobia at school gates from other parents. The study has found. And finally and excitingly for some of us. London Fashion Week is going gender neutral and virtual. And I'm going to talk about that in detail. But I have a picture now before you of some gender neutral and virtual models for London Fashion Week. So those are my lengthy headlines. I won't be able to talk about all of them. But that's what's going on in the world as I see it. Let's move now to Keith. Well, hello. And what I would like to talk about are a few events. And I really want to encourage people to go online and is and is about to promote Fashion Week being a virtual event. What are the virtual events that are happening here in Vermont? For which you can participate? Because as we were talking before we started taping the show, we're kind of ready to bolt for freedom and would like to talk to someone other than ourselves. And some of us are learning how to cut our own hair before war. So one of the events that's happening is being sponsored by the Pride Center in a subversual community gathering. And it happens every day. Monday through Thursday, it happens at 530pm. And on Friday, it happens at 1.30pm. And I'm told that for the 530pm events at 545, there's a Jeopardy contest using Amazon Echo. Yeah, Professor Charles could be challenged for her knowledge of trivia. So and you can access that by going on to the Pride Center site, looking at their events. I've noticed a number of things that are sort of in the works. There was a group in White River Junction that I think they're very optimistic, but they want to do a Pride event in July. And they've started some organizing some conversations. We may be reaching out to them to see exactly what it is they're planning, and how we might be able to participate. And along that same line, Bennington Pride, which last year held their first Pride event, paraded a weekend long series of events in June, which is when most states do celebrate Pride. They've already announced that this year they're doing it as a virtual event. So if we go on to their website, we can see how we could participate or see the activities that Queer Connect in Bennington is supporting. And then there is also Out of the Open, which does a radio hour that talks about LGBTQ issues, which is a source of information and interaction during this time of self isolation. So with that, I'm going to hand it over to Linda. Well, you know, that sounds like a lot of fun. And I was always I was wondering whether we would get to do our fourth of July again, this year, but probably not, but we'll see how things progress by then. So the first thing I wanted to talk about was the journalist who covered Vice President Pence when he visited Mayo Clinic last week says that he's now being punished for revealing that visitors were told to wear masks on the trip there and that everybody on the plane and everybody knew, despite the fact that Pence's wife apparently said on Fox News that, you know, he was unaware of it. And so that has been proven to not be true. I don't know why he would do that. But anyway, that seems to be what happened. And two women two people, two men were arrested in the killing of two transgender women in Puerto Rico. Serena Angelique Valesquez and Leila Pelees were visiting from New York City. The two men were handed over to the FBI, who are handling this case. I hope to have more on what happens to them. You know, and if they're going to trial or being convicted or anything. And if anybody's been watching Mrs. America, we haven't been able to see it because we don't have the station it's on. But it's about Phyllis Shafley and her fight against the ERA. And in it, her son is gay, his name is John. And you know, she and so the series is called Mrs. America and it's on Hulu. In the series, probably a trick or a date or something of Shafley's son George, John, I raise the doorbell and black males black males her for her silence about John. Apparently this isn't true. And it's imagined by the people who are doing this series.  He is however, and remains a big supporter of his mother. And he feels like what she's doing or what she did was right. And it seems like, if I've heard correctly, Phyllis's daughter is also taking her mother's place as another Mrs. America. Let's see, queer singer Jamie Wyatt defines outlaw country music as a category at 21. She ended up in prison after robbing her heroin dealer. And much of her experience is a chronicle in her first album called Felony Blues. Today, Wyatt says she is in a good place, is sober, not taking drugs, and is eager to connect with the queer community. So we're kind of looking forward to hearing that album. And you know, it's kind of like a little Johnny Cash, I guess there's a whole bunch of people who are considered outlaw country Western singers. And I guess Johnny Cash would be one.  But anyway, so we look forward to that. So now I think we're going to move on to Ann. And see what she has to say about what's going on in the world. Okay, I have some things to add. apropos of virtual pride, Israel's going to do that too. And so Linda is is outlaw country, progressive country? Yeah, it's progressive country. It's well country rocker. But it is definitely country in the country music genre. And she is a country music singer. Okay, and an outlaw? Yes. And, you know, there are many on I can't think of anything besides Johnny Cash, but there was quite a few that were kind of, you know, Willie Nelson might be considered an outlaw. What about Brandy Carlisle? Is she a country singer? Um, I don't know. I can't answer that. I don't think so. Okay. Well, we're out of our lead now. So let's move on. Um, I'd like to talk in detail if I may about this mess in Morocco. At least 50 to 100 gay men were outed in Morocco over the last two weeks, rights activists say, after the men were identified on location based meeting apps, while sheltering at home amid the coronavirus lockdown. And in least three cases, the men were kicked out of their houses. Many others said they had been blackmailed and threatened and thousands fear that their photos will spread on social media. One, a young man whose photos were leaked online said, I'm just waiting for my death sentence. I'm frustrated and scared.  And many keep their sexual identities under wrap.  In a rage, she released a profanity laced video, encouraging women to download the location based meeting apps like Grindr and Planet Romeo, which are usually used by gay men. I gave you a garbled version of this story last time, but these are the details. In subsequent videos, she said her aim was to reveal the hypocrisy of Moroccan society by showing her attackers how many gay men were living in their vicinity, perhaps even in their own homes. Many people followed her lead and created fake accounts on the apps to gather photos of gay men, which they then posted on private and public Facebook pages, setting off homophobic attacks. Adam Eli, the founder of the New York based activist group Voices 4, worked in coordination with Moroccan LGBTQ rights activists to get the Instagram account deleted. A spokesperson for Facebook, which owns Instagram confirmed, we don't allow people to out members of the LGBTQ community because it puts them at risk. We've disabled Nafual Musa's Facebook and Instagram accounts, and we're taking proactive steps to find and remove other content like this. What seems to have set Ms. Musa off was a late night conversation with a little known Instagram user who in an interview asked to be identified only as Yacine for fear for his safety. She has become famous as an Instagram personality, using her platform to talk crudely about sex and to entertain followers in a confrontational and insolent manner in Vulgar Moroccan Arabic. This has made her an object of fascination and horror for more than her half million followers.  Yacine, the 22 year old, said he was initially delighted to be picked up on her Instagram. But what felt like an honor rapidly turned into embarrassment and shock as she compelled him to acknowledge that he was gay, threatening to post revealing photos showing him with another gay man. It's unclear how she obtained the photos. I was shocked and very scared. He has since been forced to move out of the house of a family member and to use his savings to rent a small apartment and change year. Everybody is sending the video and saying bad things about me, he said. My mom also, she's very sad. She's not talking to me anymore. My friends at the gym, friends I went to school with, they all blocked me. Many who saw the outing of Yacine were outraged and attacked Ms. Musa, flagging her account to Instagram.  So that's a creepy terrible story that's still having repercussions. I have two more quick points unless you want me to move on. All right, I'll move on. Since no one's silencing me. I'd like to go to Latin America now to this Tijuana shelter. And I'd like to show you a picture now of three people from left is the Organization for Refuge, Asylum and Migration Executive Director Steven Roth. With Jaime Marin Roca, and his mother, Yolanda Roca, of Jardín de las Mariposas, and that's the name of the shelter. And this is significant, because Yolanda Roca is the founding member, and her son Jaime is the Executive Director. There are local media reports that there are more than 400, I'm sorry, 500 Coronavirus cases in the border city. Mexico responded very late. The city is now under lockdown. And the US is terrible down there. The US has temporarily stopped asylum seekers, as we know, from entering the US. The Mexico US border is only open for essential traffic. Jardín de las Mariposas is a nonprofit organization founded by Yolanda Roca, the person pictured above before you. She's the current director, and he holds another another post in support of the organization. It's always, it always receives anyone who seeks to help with addiction or emotional problems, because of their sexual orientation, with love, respect, and without cost. It's the only center in Tijuana that openly welcomes the LGBTQ community. The organization has lately focused on providing help to asylum seekers and refugees, because of the increased immigration to the US. One Jaime Marie Roca is the Shelter's Legal Representative, and his mother's the director. And the other person, Steve Roth, is an ally who has helped raise money for them. Unfortunately, there are only 20 people, and they've had to close their doors, because a lot of the residents are HIV positive, have cancer, they're at risk. But anyway, that's a bastion of hope in Tijuana. I have one more, one more picture I'd like to show you. The Gender Recognition Act Supervisor, whose name is Liz Truss. This is her picture. And she's the one who has caused a lot of concern by announcing, or saying that she's concerned about trans youth doing irreversible damage to themselves if they're under 18. So those are my stories for this segment. I have much more to talk about, but I think it's time for me to reluctantly yield the floor, or happily, we yield the floor to Keith. Hello. And I want to talk a little bit about our legislature and some political process here in Vermont. And I want to start with, if you haven't heard, and you haven't gotten an appeal yet, that openly lesbian Chintin County Senator Debbie Ingram has officially announced she is running for Lieutenant Governor. Along those same lines, there was a Zoom community meeting with two other candidates running also running on the Democratic Party for Lieutenant Governor. And they were Zoom bombs.  And the person who bombed their meeting, used profanities and put swastikas up on their site. Brenda said this was very unnerving in this current time. And as an aside, the Southern Poverty Law Project has stated there has been a dramatic increase and bias and hate motivated crimes during the COVID-19 stay at home orders. That all of that activity has become much more active. So some pieces of legislation here in Vermont that will be of interest to us. The Senate passed S 346. This is a bill that would provide additional payment to people who are identified as being essential workers. And if someone works more than 108 hours per month, they would get an additional $1,000. And if someone worked at least 34 hours a month, they would get an additional $600. Now, the 34 hours per month was of interest to me. That could be someone who is identified as an essential healthcare worker for somebody with disabilities who needs some daily assistance, but not necessarily a full shift. So they're looking at the type of interaction and ensuring everybody is covered in this. The other piece of legislation that's actually passed both chambers is S 333, which would impose a statewide moratorium on rent evictions and foreclosures. This is something that people have talked about. There's also some landlords who have released information saying I'm giving my tenants a rent holiday, knowing that these are financially stressed time for them. So this bill is on its way to the governor's desk. There's every indication that he is indeed going to sign it. Some other pieces of information that will be of interest to us is that Department of Health Commissioner Levine has announced that they're going to do contact tracing. And they are going to do more of it. And as opposed to how the federal regime may have approached this, what Commissioner Levine has done is reached within his own department. And specifically to the epidemiology division, where they have expertise doing this relative to HIV infections and STVs. They know how to take a history. They know how to develop a contact list. And they are well trained at how to do sensitive and informative outreach. This is one of those cases where indeed Vermont got it right. So and the other thing that Commissioner Levine share during a recent press conference is they're going to start doing some random trace of random sampling. So if you get a strange phone call that says this from the Department of Health or a letter in the mail saying we want to advise you to come and have a COVID-19 antibody test, it's actually legitimate. It's not the same as some of the pop up bogus clinics that had happened in the South where they said they were doing a random sampling. And all they were doing was taking your money. What this will provide to Vermont. And I haven't seen where they've established the number of Vermonters they're looking for. But it's a random sampling statewide. And what it will hopefully provide is an indication of virus prevalence in the state of Vermont. Because there is an epidemiological formula that can be employed where you have x number of positives out of x number of samples taken. And that gives you an indication of community spread or the likelihood of community spread. So that's what I had. So I'm going to turn it over to Linda. Well, you know, that's really good news. I was reading or I saw someplace that they're using sewers to sort of test whether an area has the coronavirus or not to. Because I guess if there's depending on how much there is in the sewer system tells you somewhat about how much is in the community, which was kind of interesting, I thought. But that's good news. And I'm glad we're moving in that direction. So I have a little story about Mr. Rogers and his neighborhood. And for anybody who has watched Mr. Rogers or has watched with children, there was a policeman on there called Officer Clemens. He was African American. And he was advised by Fred Rogers to be closeted and to marry a woman because it would be better for him. But he didn't. And for 25 years, Rogers was one of the most watched shows by children. And these children have known Officer Clemens on Mr. Rogers neighborhood. You know, for 25 years. And so that's the story about Mr. Rogers neighborhood. Anyway, and I watched this show on Netflix called Circus of Books. I don't know if anybody has seen it. But it's a documentary about the history of LGBTQ media and censorship. The store was owned by Karen and Barry Mason. And they distributed primarily gay men erotica in their store. And so it centered on this store that was in West Hollywood, where apparently, there were a lot of gay people in the in years past. And it's called Circus of Books. And it's really interesting. They, and their son comes out as gay, you know, at the end of the film, or is at the end of the documentary. But it was really interesting. They were both Jewish. And she was really religious, he wasn't. And when her son came out, even though they were people who were doing this, you know, giving LGBTQ people places to go and get, you know, erotica into, you know, tapes and films and magazines, when her son came out, she had a really hard time with it. And so it was it was kind of interesting. I enjoyed it. So I would suggest if you have Netflix, you might want to watch that. So that's all that I have, I believe, I'm having to do with national news at the moment. I hope everybody is safe and has a lot of good films and documentaries out there. So keep yourselves busy. And I think I will now move on. We heard the sewer story on Rachel Maddow. Okay. I'd like to focus for a minute, if I may, on London Fashion Week. And I'd like to show you the picture again of the non binary models. For the next 12 months, all London Fashion Weeks will fuse women wear and men wear to create a single gender neutral platform. As the fashion world scrambles to adapt to the consequences of the Coronavirus pandemic. The British Fashion Council has announced that for the next 12 months, all London Fashion Weeks will fuse women wear, women's wear and men's wear to create a single gender neutral platform according to an April 21 press release. Beyond opting for a less rigidly gendered format. The British Fashion Council also stated that the June edition of the London Fashion Week will now occur through an online portal featuring interviews, podcasts, designer diaries, webinars and digital showrooms. The current pandemic is leading us all to reflect more poignantly on the society we live in. And how we want to live our lives and build businesses. When we get through this said Carolyn Rush, the chief executive of the British Fashion Council. The other side of this crisis, we hope will be about sustainability, creativity, and product that you value, respect and cherish. By creating a cultural fashion week platform, we are adapting digital innovation to best fit our needs today and something to build on as a global showcase for the future. The BFC's decision to make London Fashion Week gender neutral marks the first instance in the biannual events 37 year history, the shows would not be separated along binary lines of menswear and women's wear. Mi Leggett, designer of the gender free label official rebrand, designer of impact. I'm sorry, the main positive impact of BFC's decision, according to be Mi Leggett promises to be the setting of a simple, though fundamental precedent by not saying women's buyers, women's press, you go here, and men's buyers men's press you go there. BFC is breaking down the binary. Deeply entrenched in these business structures, they they tell them, which is the them is publication. As British folk reports, the BFC's decision to move London Fashion Week online reflects the broader fashion industry's increasing willingness to employ nontraditional modes of interacting with fans and potential customers. So this is a very interesting development. It'll be interesting. I hope it lasts longer than 12 months, but we'll see. Alright, so on to Keith. I've given all that I had to share this week. What about the trivia question? Okay. If we're done with the stories. Yes, indeed. I have the answer to the trivia question. I believe we're finished. Okay. So, Ron Squires was elected to the House of Representatives in 1990. And is generally acknowledged as being the first openly LGBTQ plus person elected to a statewide office. However, it wasn't necessarily the first openly LGBTQ plus person to serve in state governments.  David Curtis would go on to form the Curtis Hough Law Practice with former Governor Bill Hough. And as sort of a background piece, Defender General is the state agency that is comparable to the Office of Attorney General. Only what the Defender General does is has oversight and provides guidance to public defenders. They're looking out for the interest of the people who are the defendants who have been charged with a crime by the State of Vermont, as opposed to the Office of States Attorney and Attorney General, who is the prosecutor in those cases. And in one of my conversations with David Curtis, he acknowledged that Governor Keunan when she appointed him was aware that he was an openly gay man. And her only concern was, can you do the job? And Anne has something she would like to add. I know if you, since we have time, one story, national story that we haven't covered, when it is the victory of activism in New York City, in the form of Franklin Graham's Oh, that's Samaritan's Purse finally agreeing to leave Central Park. Can you tell us a little more about that, Linda? Well, actually, no, I didn't, I didn't get to that story for some. But if you know anything more about it, you can, if you would mind freely sharing it with us, that would be great. I know they're gone. I've been following it closely. And first of all, St. John the Divine, they were supposed to coordinate with St. John the Divine. And they said, no, no, you don't reflect our values.  And, you know, of course, they had the statement of faith that they required their volunteers to sign. We did kind of cover a little of that last time. Well, I won't go back into that. But Reckling Pride and other New York activists have been demonstrating there. And they confronted Mayor one of, I believe one of our mentors, Andy Hum, participated in confronting Mayor de Blasio about this. And de Blasio's wife is bisexual. And he was like, Oh, so finally. And this is exciting, because it's a victory of activism. Samaritan's Purse has agreed to leave Central Park within two weeks. And they're fumigating and everything. Because there were, you know, there was another deal that was going to happen with that Israel involving Samaritan Purse's infiltration of that hospital system. But it's all been called off. And it just shows that activism works. I don't know how this deal with the devil happened to begin with. But now it's been cut short. And I have to commend our activist friends in New York for making it happen. Yes, and it shows that we can even do we can even we can even win during these times of being by being activists. Okay, I think we have to sign off now, don't we? Yes, we do. So Linda, take us home. Okay, be safe, be healthy. We'll see you in two weeks. And in the meantime, like they did in New York, resist.


This is the one-two finger pattern exercise. We're going to start on the G string and play four strokes per finger, four quarter notes per finger, then three, then two, then one. Again, this is the one-two finger pattern exercise. First kind of fine third position. We're there, ready to go. Here we go. Back to the G string, three quarter notes per finger. Back to the G string, two quarter notes per finger. Back to the G string, one quarter per finger.


Hi, this is evil rabbit. I'm drifting with Nate and there's Chris somewhere on the track. Oh I'm saving that Hello, and welcome back to the channel. I'm evil rabbit staring down the start finish line of formula drift, Texas 2020 layout in a a new Z a new 370 Z Working on some pro one style cars got my buddy Nate and Chris here Chris is rocking in the a 90 Nate's in the m235 these are about 820 horsepower pro cars So we're gonna be seeing if we can tackle fd 2020 layout because watch that definitely an amazing event So make sure you guys follow me on all social media all over your phone in description box below Fd 2020 layout. I guess you're leading first Nate. All right sure Chris is back there.  Arrow for actually the download link for this track I'll leave his video in the description box below if you guys want to check it out and download this track yourself Unfortunately, the cars are still private so you can't have those But you guys can check out mr. Arrow's Uh link for this track layout I know a lot of people when I was doing the random tandems of the old Fd taxes people like oh, you should get the new one. Well, we're here. We got it new cars new track See what we can do Click flick in Don't drop tires Run that out as far as we can Oh deep in that hour zone. Can I hold it? Yes I'll I'll take that as a very solid run with the Nate right behind me Chris was Chris was there too I couldn't see him through the smoke Huh Hey now you get to lead Throw him right to the fishes in these in these uh high powered You know pro style cars So I am working on the big body car pack that will be coming out very shortly Those cars will also have more power than my original cars. So Chris you gotta get on the other side of me.  It's it's done It's done over. You are saying goodbye Have a nice day So just a bit of a a practice session here for shakedowning of some new cars And you know, well a new track thing Your car's getting dirty. I kind of love the damage model on that m235 Dirt all over your car too.  I was making sure I was at full boost out invisible wall Watch that The invisible wall is definitely very You know Shocking when you hit it because it's like, oh gosh So the fan attack if you guys know it's actually working very well And uh, it's has not had given me any other issues since I fixed it I have been in contact with fan attack going back and forth with them to figure some things out so Luckily the wheel is good. We got our safety screw in. I don't think it's gonna break See if we can't get up Good start. I need to learn how to use a clutch apparently That's the left foot one Oh, okay And that was super close. Oh Just a just a just a tap And all right ready ready Slip the clutch a little bit. We're good Oh god. Oh god I lost it Inside line This is not an easy track And then Chris back there just like la la la. What are you guys doing? I'm like, oh I just see in my mirror this a 90s go bloop Let's see if I can actually get a launch and not uh And not what's the word I'm looking for Get left behind that's a better. That's a better run.  Let's see who wins I'll let you roll off first Go figure when I say it's lead and chase time is when I actually do good Well, we were past the line That was pretty good pretty close I tucked into you there at the end We may have to go we may have to go uh review the actual replays of it so we can actually see And assess the replays of these final two runs Well, I think you got it there Although the hit didn't really mess you up too bad All right, we're gonna go take a look at those replays so We'll catch you guys back once we get to the replay. Sorry What fd they have fd camera. Okay, we'll go with the fd camera. All right So My lead Good on there. You're kind of a little why but you're there At least you got out to the zone a little tire drop a little bit back but not too terrible You kind of managed to cut the angle and catch up towards the end so Overall not a not a terrible chase There's a little bit of a gap So let's see what my chase looked like So as much closer through that section, I didn't get all the way out to that section then I hit you in transition so Ah, I think I think that probably would have ended up going one more time because the hitting you didn't actually cause you to Mess up and we both made mistakes lead and chase So I don't know I'm gonna let you guys judge it down in the comments Let me know what you guys think who do you think won that battle between Nate and I and that lead and chase that you guys just watched Let me know it on the comments and we'll see what you guys think So make sure you guys follow me on all social media big thanks to chris and Nate for coming out testing out the Track and the cars as always as I thank you guys for coming back and watching. I'm evil rabbit I'll see you guys on the track


Look at that We got these chairs They're very ergonomic They can be rented at a price of five dollars a month five dollars a month. You can rent these chairs We got a table. This table can also be rented at four dollars a month. I said, what's this material called? I don't know, but it's made by the Amish Yeah Yeah, yeah, that's what I said. That's why I bought it. Amish chairs. Yeah, they said it's Amish made It's lux craft. So chat today. We are going to make We have this quick classic pancakes makes 14 pancakes. How many pancakes do you want to make? I'm gonna keep it a buck with you. I've never been a waffle person I've never actually made either so this is where I can get a couple of big cans like oh, yeah Well, they're both Chef is just so oh Wild so two cups original bisquit baking mix this quick really sounds like it'd be a Pokemon if it wasn't a pancake eggs Yeah, a big ol yikes from me No, no, they're good. No, it's a fresh yet. I Thinks first put the egg back down. Yeah, what we do is we grab some this quick mix Okay, two cups of original this is a family recipe Not mine, but somebody's going to take two scoops of this and put it in each And then yeah, that's one one. Yeah space boy, I want you to take these two eggs to scoop chef And I want you to put that in there Okay, get a big spoon and I want you to mash the shells the eggs into The extra nutrition hush up. It's actually yeah, do we need that copper do we get a glass cup? Cuz all cuts are cups right? Yes, so we're going to take one cup of egg milk and then we are going to or listen to here Chef with all due respect chef. Why do you measure with a glass cup?  This is like cake batter Well, chef, I don't know if you know egg is actually really makes things a little bit more thick chef It's only one egg was added to this mixture chef Scientifically biologically speaking so how does this work?  Well, so what happens you just fill it Do you fill it to the perfect like you're filling concrete on foundation? Yeah, basically all chef. Yes chef Please I think this is I don't know if this is usable.  That's quite a healthy I'm a bit of a scientist myself back to formula back to formula No, no, you can't do this to me. Okay. I didn't even need a magazine. All right, chef I Squeeze her in there Okay, so here's what we're gonna do We couldn't actually that So now we're gonna make a waffle There you go film the crack chef Fill in the crack Coming So that plan was proper procedure that plan was terrible. So we're going to quickly change plans And we're going to See that's just that's I mean it's the same thing. It's the holes just bigger The cup is basically just a big syringe so I'll be guard chef. Yeah, well, you know, that's what I do I can garden From the planet of obvious a lot of people don't know this heat rises and It also expands Send me a big thing of angioma in my p.o. Box whenever they got rid of it like It's weird You put that paper plate there chef I see I told you Well, we can get scissors. Oh look at that.   Where did you learn that word? The older kids at church? Enjoy your dinner. Enjoy your dinner. Don't yell You're getting the family apart daddy was staying at work extra late with that girl Sally what girl?  I need you to get my lighter out of the building Oh, yeah, I need to put my cigarettes in the microwave Here's I put