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EECS 373 - Fall 2026 - Lecture 14: “ADCs” — Transcript

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0:00Let's see. Uh, you had James last week,
0:03so hopefully I don't know. You guys got
0:05through of analog sampling, I assume.
0:08Talk about analog circuits. Okay, great.
0:10So, that sets us up for this week. Um,
0:13so homework not due today. Today is not
0:15the 26th. That's scary. Next week.
0:23Next.
0:27All right.
0:29next Monday. And then homework 7's been
0:32released. It's not due for a couple
0:33weeks. Um, this week you guys need to
0:36sign up for project proposal meeting
0:38slots if you haven't already. Uh,
0:39they're going to start on Sunday or on
0:41Friday. Uh, we're not going to have
0:43class on Monday to make room for those
0:46uh, meetings. Um, and then your job
0:49generally is to complete your project
0:51perfor proposal like the night before.
0:53So me and Matt will look through them in
0:55the morning, but also bring slides that
0:57kind of outline what you're going to uh
0:59be uh um presenting to us and what your
1:03project is. Um I mean, if you really had
1:05to, you could bring up your uh project
1:07proposal uh on the the monitor, but it's
1:10just easier if you have slides. Um and
1:13then we're going to give you feedback.
1:14So the project report askked for a lot
1:17of information. If you don't know the
1:18answer to every single thing because you
1:20haven't figured out what part it is yet,
1:21that's okay. but it's to try and prompt
1:23you to start thinking through things. If
1:25there are major issues with your report
1:27or maybe you just drastically change
1:28your project, well, there's a
1:29resubmission date where you can get back
1:31the points u and and kind of really the
1:33goal is for you to have a plan by the
1:35time you leave that meeting and finish
1:38your project reports or proposals that
1:40you have a plan for what to do. Uh and
1:42then there'll be no class on Monday.
1:45Yeah.
1:48>> The night before.
1:49>> Yeah. whenever you sign up, it's just
1:51due the night before.
1:53And it's not like because it's like a
1:55variable deadline and some people go
1:56longer, get longer time, like you we're
1:58really going to grade the resubmissions.
2:00So if you get a resubmission, that's
2:02what we're going to grade. Some teams
2:03just won't need it. So don't don't feel
2:06like, oh my gosh, I'm losing out because
2:07I went first.
2:12Any other questions?
2:15If you can't find a a meeting time,
2:18please let me and James know. We'll find
2:20alternate times. We realize that we're
2:21trying to work around my schedule and
2:24James' schedule and some meetings at the
2:26NSF I have as well as all your
2:28schedules. So, just let us know.
2:31Okay.
2:34So, last week you talked about analog
2:36signals in general. And if you are EE
2:38student who's taken I think 216, is that
2:41your signals class? or 316, you've
2:44probably already done this, but uh
2:46especially we have computer scientists
2:48and people just haven't taken those
2:49classes yet. So that's kind of give you
2:50the background of analog systems. And
2:52now we're going to talk about um analog
2:55digital converters and digital to analog
2:57converter. Well, today we're only going
2:59to talk about ADCs.
3:01Uh so if you want some references, uh
3:03your reference sheet, uh chapter 20 of
3:06this book and also um analog devices has
3:09some good tutorials. There's good some
3:11good uh general stuff online.
3:14All right. And then this should be
3:16updated, but we're going to talk about
3:17sample and hold circuits and then
3:18different types of ADCs and then we'll
3:21talk about your specific ADC on your
3:23device. All right. So remember analog
3:26digital converter is basically an
3:28oscilloscope. This is just a fancy
3:29version of it. We're trying to capture
3:31some signal that exists in the world and
3:34do something with it. So here right it's
3:36these are really high speed high uh
3:39voltage tolerant range uh they can um be
3:44adjusted in in lots of different ways.
3:46Um but you your microcontroller can do
3:49almost everything. Um in fact you can
3:52buy like really really cheap analog
3:54digital converters you can buy online
3:55that are like USB ones are just
3:57microcontrollers especially if you see
3:58like the voltage range is like between
4:00zero and five volts or zero and 3.3
4:02volts. It's just a microcontroller
4:04inside. So you can get a lot of work
4:05done with an analog digital converter.
4:10So to begin with uh you need this thing
4:12called a sample and hold circuit. So if
4:14you're going to do an analog digital
4:16conversion, it takes some time to
4:18measure the signal. If that signal is
4:19moving around a lot while you're trying
4:21to measure it, it's going to be it's not
4:23going to work out so well. So um you
4:26have to use a thing called that sample
4:27and hold circuit. And again, your job is
4:30not to like, oh, how do I do my node
4:33voltage equations for this whole thing?
4:34It's to really understand why it exists,
4:37how it's used, and then deal reason
4:39like, okay, when I'm setting up my
4:41Hample and sample and hold circuit time
4:44on my microcontroller, what do I have to
4:45consider?
4:53Okay.
4:55Um, so here the goal is to take this
4:57voltage A uh input on some buffer and
5:01hold it on this capacitor and we're
5:03going to use this switch here to charge
5:05up this capacitor and we're just going
5:07to hold it for a while and then allow
5:09the output to um measure it, right? And
5:12so the nice thing here is with a analog
5:15amplifier or voltage follow or a buffer
5:17whatever you want to call it it allows
5:19it takes the voltage here and reproduces
5:21it here with no matter how much current
5:23or how much you try and low down the
5:25circuit it should not affect the input
5:26here and of course this is true for
5:28short relatively short periods of time.
5:31Um yeah so when the switch is open it's
5:34sampling and then when the switch is oh
5:36sorry when switching closed here it's
5:38sampling and then when it's open it's
5:39holding.
5:41Okay. So, we can look at a a real
5:43example or at least a circuit example of
5:45how that would work. Uh, nope, you can't
5:48see that. Okay. Hold on.
5:52Okay.
5:54Uh, but that's the wrong circuit. So,
5:56here's uh reset and run. So, all these
6:00circuits are in the slides you have. Uh,
6:02so you can play with them if you want.
6:04But here the idea is you have some
6:06sinoso signal. It doesn't really matter
6:07what the signal is, but it's um changing
6:11over time. And if it takes us a long
6:14time to uh measure the output, the
6:16problem here is that the signal would
6:17have changed. So here we can sample it,
6:20which means we're going to charge up
6:21this capacitor. And you can actually see
6:23this is over a long period of time. You
6:25can see the the voltage on the capacitor
6:26is changing as a function of time and
6:28mirroring the input. And then when I let
6:30go, it holds it there for a while.
6:33Right? And so here, this is the
6:36structure here is acting like the switch
6:37and it's keeping that current uh that
6:39voltage from discharging back out. And
6:42then we're just holding it here. That
6:44make sense?
6:49Okay. So, it's a simple circuit. There's
6:52lots of different ways to make it, but
6:54um the things that you might have to
6:56worry about is if your signal here, this
6:58is a nice voltage source, right? If it
6:59was kind of a weak signal, then maybe
7:01this capacitor could influence it. And
7:03certainly if you didn't have this um
7:05this buffer here, your analog digital
7:08converter could load down the signal and
7:10like um it wouldn't get as high as it as
7:13it would normally be. It might corrupt
7:15the signal. So that's why putting the um
7:18opamp up here is necessary to buffer the
7:20voltage.
7:23Okay.
7:27Um and so you one of the challenges is
7:31you have to determine the minimum
7:32sampling time. So uh you might have a
7:36voltage source or something you're
7:37measuring and you have it's going to
7:39charge up this capacitor. Well, if you
7:42have a very strong voltage source,
7:44meaning that it can supply lots of
7:45current, no problem. It's going the RC
7:48charge time is going to be uh very
7:50short. effectively the resistor here
7:52will be very small and it doesn't really
7:55matter but sometimes you have weak
7:57signals that take a while and that's why
7:59you might want to adjust your sample and
8:01hold circuit to sample longer so then it
8:04can slowly climb up and it'll do this RC
8:08discharge curve will be or charge curve
8:10will be longer because the effective
8:12resistance would be higher and so you
8:13now you have to wait longer for it to
8:15charge all the way up so knowing
8:16something about your signal source will
8:18make a big difference um in your work.
8:21You might have to think about if you're
8:24measuring something like a voltage
8:25divider or
8:27maybe a resistive circuit and you want
8:29to go really fast. So maybe like a
8:31strain gauge for a smart glove or
8:33something. If you want to go really
8:35fast, uh you're going to have to make
8:37sure that the the charge up time is
8:40reasonable uh that you're able to charge
8:42up. So, the easiest way to do that is
8:45just do some calibration uh and see if
8:47your signal is the correct value you
8:50think it is. If it's not, then maybe you
8:51need to put an analog buffer here to
8:53hold this thing high uh to give it some
8:55more power going in or you need to
8:58adjust your charge up time. The other
9:00thing you can do is you could just do an
9:01offset. If it always charges up about
9:04the same amount of time, you could just
9:05make yourself a lookup table. That's not
9:07very reliable, but you could do that.
9:10Uh yeah, and your sample time is
9:12programmable in software because they're
9:13trying to give you this ability to trade
9:16time for accuracy.
9:20Any questions on sample and hold?
9:26I don't think you guys have ever seen a
9:27sample and hold circuit before. Correct.
9:30Okay, that's fine. You're again as
9:33embedded systems people, you're this is
9:35be like as much analog as you ever get,
9:37right? We're going to go through analog
9:39to digital converters. You're going to
9:40be like, "Okay, that's the last time
9:41I've ever studied analog to digital
9:43converters." Totally fine. But at least
9:44it'll help you decide which one should I
9:46choose if you're going to uh put one in
9:48your system.
9:50Okay. Um then, so now we're going to go
9:54on to different analog digital converter
9:56structures and there's some basic
9:58components we need to know for each one.
10:00So one of the components that's used
10:03over and over again is this thing called
10:04a voltage comparator. Basically, it's
10:06just an op amp that's not in feedback.
10:09And what it is is uh you have power,
10:11ground, and you have some output signal.
10:12And if the input is greater than the
10:15sorry, if the positive input is greater
10:16than the negative input, then the output
10:18just goes all the way high. And
10:20otherwise, it's low. So, it's basically
10:21taking two analog signals. If one's
10:23higher than the other one, the output's
10:25high. If the other one's lower, then the
10:26output's low. That's all the decision
10:28it's making. And then we're going to use
10:29this structure over and over again.
10:32The other uh structure you need to know
10:34about is a uh voltage divider. Now, I
10:38promised you at the beginning of the
10:39course that you're never really going to
10:40have to do node voltage equations
10:42because that's horrible, but you just
10:44have to have a little bit of intuition
10:45about what these circuits are trying to
10:47do. And this is uh this formula here. Uh
10:50I mean, you can drive it of course, but
10:52it should give you some of the intuition
10:53that says like, okay, you know, if I
10:55take R2 and make it zero, right? Well,
10:59then my voltage is going to get closer
11:01and closer to ground. And if I make R0
11:03really really large, like infinity, then
11:06my voltage is going to get uh closer and
11:08closer to VN.
11:10How we typically use these in um analog
11:14digital converters is we just make R1
11:15and R2 the same. And now this is why we
11:18call the voltage divider. VN is divided
11:21by two. And you're going to see later on
11:22we're going to have three, four, n
11:25different um resistors. And then it's
11:27going to be V / N. And you're going to
11:29see that there's a little uh step down
11:31for each one. And we'll we'll talk about
11:33it when we get there, but basically this
11:35is just a structure that divides a
11:37voltage from one value to another value
11:39based on a ratio.
11:42Um, now you can put those two things
11:43together
11:45and say here we have a comparator and
11:48the comparator is running at VDD and or
11:50VCC and ground and we have a voltage
11:52divider that's connected to VDD and
11:55ground. And because R equals R, we
11:57didn't say R1 and R2, we just said R and
11:59R, we know these values are the same.
12:01And so the value here is VDD over two.
12:04And now you get this simple circuit that
12:06says whatever VN is. If VN is low, then
12:10the output of the comparator is low. If
12:12it's lower than VDD over two, I always
12:14say VDD instead of VCC because I in my
12:18undergrad, I did a lot of integrated
12:19circuit design and it was always in
12:21silicon. VCC is typically for um BJTs, I
12:25think. So I don't know why why the
12:27convention is that way, but that's why I
12:28say it that way. Anyways, and if your
12:31input is above VREF, then you're going
12:33to get a high output. So, basically,
12:35this is just showing you the output. And
12:37this logical structure is just about
12:40built into every ADC.
12:43U any questions here?
12:51Great.
12:52And then it's usually just useful to
12:55look out for the the positive or
12:57negative signal. Sometimes different
12:58diagrams are not always V+ is not always
13:01on the top or uh so you just have to
13:03make sure you're looking for that to
13:04figure out what logic it is. Okay, so
13:07that should set us up for the most
13:09simple ADC
13:11that there is. Um so we call it a flash
13:14ADC.
13:16You'll see why in a minute, but it has a
13:17basically concatenation of that
13:19structure we just saw. Here we have a
13:21reference voltage coming in and we have
13:24a ladder of resistors. And here we're
13:26just going to show that we're just going
13:28to divide uh the voltage into even parts
13:32uh up on this ladder. And so now we can
13:34say that okay rewrtors.
13:41So one over seven minus RF that's the
13:44voltage here. And then you can see that
13:46each one of these is trying to make a
13:48comparison to that reference voltage
13:50from the input voltage. And we'll go
13:52through a circuit diagram or false
13:54diagram in a minute. But basically,
13:56we've got instantiated a bunch of
13:58different reference voltages. And then
14:00each comparator is trying to make a
14:02simple decision. Is the voltage input I
14:04have now higher or lower than this? And
14:07then it would have to go to a a uh a
14:10binary decoder encoder to turn this uh
14:13linear um measurement into a binary
14:16value.
14:18Oh, hey, I had great animations I didn't
14:20see.
14:22So each one of those is a uh made its
14:25own reference voltage and then it's just
14:27going to check to see which one is which
14:29which one is higher. So you know there's
14:32never going to be a case where uh R3 is
14:34high and R2 and R or sorry op amp or
14:37comparator three is high and comparator
14:402 and one are not high. um it's all
14:42going to be the same but it just says
14:44okay this is where that point is in
14:46space
14:49and then
14:51go over here we can see that in action
14:54let's see so here's the run so in fallad
14:59the the magnitude of the color indicates
15:02the voltage so you can kind of just
15:03visually see already that the voltage is
15:06uh dropping here
15:08and so here we have our reference ladder
15:10and then each one is just trying to make
15:11a decision. And you can see the input
15:13voltage is rising. And then you can see
15:15the the value here is rising as well by
15:18the colors. And then the this is just a
15:20encoder here that changes this decimal
15:22or this uh value into a binary value.
15:29What do you think?
15:34Okay.
15:36Um, so what do you think some of the
15:38advantages of this ADC is? I guess you
15:41can't compare it to anything else, but
15:43what do you think it's good at?
15:45>> Yeah.
15:47>> Yeah, it's fast. And well, it was in the
15:49name, but uh, so it's a flash ADC only
15:52because not because flash has anything
15:53to do with it as a technology or for any
15:56other reason except for the fact it can
15:58go very quickly. In fact, it can do this
16:01uh within one clock cycle almost
16:03guaranteed because you're just looking
16:04at the propagation delay through this uh
16:07comparator and then through this logic.
16:10So almost guaranteed you're going to get
16:11this done in less than a clock cycle. So
16:13it's very very fast.
16:17Uh let's see.
16:21So, one of the challenges here though um
16:24is that it can be kind of hard to be
16:26accurate because now on a on a piece of
16:28silicon you have to have all these
16:30resistors having exactly the same value.
16:32Here we put the we did it offset by two
16:35uh or by half on here. So, this is um
16:38fifth 500 and this is 500. But basically
16:40all those resistors have to be
16:42approximately or have to be the same
16:44size. And if one was point Let's see if
16:48I can can I do it? Yeah, sure. So, if I
16:51made one accidentally, it was
16:53mismanufactured, let's say, and now it's
16:550.980.
16:58Okay. Right now, this voltage is going
17:00to be under reportported. Right? So,
17:02it's going to trip higher than normal.
17:05And so, uh you can't tell from the
17:07inputs that that's what's happening. Uh
17:10but because of this manufacturing error,
17:13the step size between one ADC value to
17:15the next ADC value isn't linear anymore.
17:18And that's a challenge. Why this would
17:20happen? Well, you're making a piece of
17:22silicon and they do have lots of tricks
17:24to make the resistors all the same size
17:26and how you did the layout, but there's
17:28lots of little reasons, manufacturing
17:29errors or how it's polished where that
17:32may not be true. In fact, we have to use
17:35all of those have to be exactly the same
17:37throughout the chip for you to get a
17:39good uh linear ADC. So, that is one of
17:42the challenges. Uh, another challenge is
17:45that resistors may not be obvious, but
17:47resistors take up a lot of space on
17:49silicon. Um, they like a transistor is
17:52super small, but resistors uh depending
17:55on how they're made, there's different
17:56types, uh, can be, you know, hundreds to
17:59thousands of times larger than uh than
18:02that comparator there uh just in terms
18:05of space on your die. So now this thing,
18:08it's not obvious, but this thing is
18:10actually takes up space and is going to
18:11be more expensive from a die area point
18:13of view. And so now you have something
18:15that's very fast, but also very
18:16expensive.
18:18And the last thing to think about is if
18:20this is a a simple threebit solution,
18:23but say you wanted to get up to 24 bits
18:25or something some high value, think
18:27about how many resistors you have to
18:28make. how to scale this thing up is
18:30going to be a challenge because now you
18:32have to get all those resistors the same
18:33size and they have to all fit on um this
18:37piece of silicon. So both of those limit
18:40typically uh flash ADCs to be relatively
18:43low number of bits. I mean you can still
18:45get 12 bits. It's not inherently a
18:48problem. Um but you're not going to get
18:51the highest bit range out of these sorts
18:53of ADCs because it's usually not cost
18:54effective. 10 bits, 8 bits is pretty
18:57reasonable.
19:02Okay,
19:04[snorts]
19:05so let's see if I if I remembered all
19:07these correctly. So yes, it's very fast
19:09by definition. Uh is only the
19:11propagation delay through a few gates
19:13and that comparator. So it is very fast.
19:16I guess you still going to have to have
19:17a sample and hold circuit, right? So
19:19you're going to have to pay some penalty
19:20there. Um but all the devices that we've
19:23talked about are going to have to pay
19:24that penalty.
19:26uh resolution. Now you're limited to
19:29that ladder stack up. That's the
19:31challenge. You can't get very high
19:32resolution. And then the complexity just
19:35of how many devices you have to have. So
19:37it's not it's reasonably complex for
19:40uh the number of comparators and
19:42resistors you have to have.
19:45And then here we're on the power
19:46consumption. The power consumption of
19:48these is typically higher just because
19:50you have this big resistor ladder, lots
19:51of comparators uh compared to some of
19:53the other techniques we'll show in a
19:55minute.
19:56So any questions about flash ADCs?
20:02Okay.
20:04Um different types of ADCs here. So a
20:07slope integrator. This is a different
20:09style that's trying to accomplish the
20:10same task. And the idea here is we're
20:13going to use time rather than So the
20:16other one was using we're going to use
20:17reference voltages here. We're going to
20:18try and use time to measure uh um
20:22voltage. And remember, microcontrollers
20:24in any digital system is only really
20:26good at measuring time. So that's we're
20:29on the the good side of the piece of
20:31silicon.
20:33Um, so here we're going to use like a
20:34analog ramp function. We'll talk about
20:36how to make that in a second. And then
20:37we're going to see how long it takes to
20:39to hit the input voltage. So here we
20:41have time. We have some input voltage.
20:44We're going to say it's held uh constant
20:45with that sample and hold circuit. And
20:47then we're going to cause a little ramp
20:48function to come up. And when these two
20:51um cross each other, we're going to say,
20:53"Aha, that is when uh then we know when
20:56that voltage occurs." And then we're
20:57going to take a measurement of time. So,
20:59we're going to count how many clock
21:00cycles go by. And so, if that input
21:02voltage was lower and we use the same
21:05ramp function, then that time would be
21:07smaller. And if we went longer,
21:09obviously the time would be longer. So
21:11now it's about as long as that ramp
21:13function is nice and even and and
21:15reliable then we can just uh use time to
21:18measure uh your ADC value. So that's
21:22again the you have good clocks in u
21:25because you have those good watch
21:26crystals on your devices.
21:28[clears throat]
21:29So the question is how do you make this
21:31slope generator? Uh that is uh we'll
21:33leave that to the analog engineers but
21:35the the big the quick idea here is we
21:38know how RC charge works. So here you
21:40could have a a circuit you you uh close
21:43it and then the resistor and capacitor
21:46rise at a known rate. Um it's a little
21:49less obvious is that if you had a
21:51current source going into a capacitor um
21:53this rises at a constant rate. So here's
21:56this exponential and this is a constant
21:58of uh rise time. And so, um, it turns
22:03out that making current sources on, uh,
22:06silicon is actually relatively easy, uh,
22:09compared to if you're trying to make it
22:11on a breadboard. So, because of that,
22:14uh, it's fairly easy to have these
22:15constant ring up times. So, we'll show a
22:17quick example of how that works in
22:19practice.
22:22All right, so this is a super
22:24complicated circuit now that I think
22:25about it, but it's not too bad. Let's
22:27start off. Um, so here we have our
22:31analog voltage and we have a comparator
22:34and then bunch of control logic. Don't
22:36worry how that works. Nobody cares how
22:37that works. It just all it's going to do
22:39is some sequencing. It's going to switch
22:40between it's going to switch uh the ramp
22:42on and off. And then we have um some
22:46display technology here. Right. So this
22:48is just a display. This is a binary
22:50counter. So this is doing the timing for
22:52us and this is going to make it readable
22:53for us. All right. So we'll start and
22:56then I'm going to start the whole
22:57process. Oh, wait. It started on its
22:59own. That's cool.
23:02Oh, that's because this new uh control
23:04logic's handling that. Okay. So, what's
23:05happening is every so often this thing
23:09is going to fire. It restarts the
23:11sampling here and then um it restarts.
23:15So, here I can change the voltage. So,
23:17if I lower the voltage here, you can see
23:20it takes less time to get here. And we
23:22see it's five. And I raise the voltage
23:25and it's going to take longer. and then
23:27the the binary values here. So here is
23:29this this ramp function here which is
23:31occurring at this point here is just
23:35ramping up until these two things are
23:36equal and the logic just traps it holds
23:38it on that uh display value and you can
23:40see it counting up.
23:48Now I want you to take 30 seconds to say
23:50well how could you increase the
23:52resolution of this timer? So why don't
23:54you take 60 seconds talks with each
23:56other and figure out what is the easiest
23:59way to make uh this a higher resolution
24:02um uh EDC so we can get more bits for
24:06every uh sample.
24:12[snorts]
24:18[groaning]
24:49I think you can All
25:02right. What do you think? How could we
25:03change the resolution of this timer?
25:08>> Does that question even make sense?
25:15>> We were thinking if you could increase
25:16the clock cycle, you have more
25:19operations at the same time.
25:20>> Yeah.
25:22>> Yeah. So here it just happens to be I
25:25can do that right now. So here we're
25:26going to do I'm going to increase the
25:27clock frequency of this clock that's
25:29running this counter. And so now I can
25:32count up and now let's see for this
25:36particular input voltage which is 3.8 uh
25:38we are going to get let me can pause it
25:40here.
25:42So
25:44so there we're at 31 which is the the
25:47count. And if I slowed it way down,
25:51right now we're going to do another
25:52cycle, right? Where got the analog
25:54voltage is at the same point. We're
25:55ramping up, but we're going slower. So
25:58now it's at six. So the same hardware,
26:02but now I was able to make a trade-off
26:04versus time versus resolution. Just by
26:07running my counter faster allowed me to
26:09get better resolution out of my ADC.
26:11That seems like a nice trick. What did
26:13we what what cost us? What did we uh
26:16have to give up to get that trade-off?
26:31All right, talk amongst yourselves for
26:3230 seconds. Figure out is there anything
26:34by running the clock faster do we do we
26:36give up? Do we lose? Why not just always
26:39run this thing as fast as possible?
26:53>> [clears throat]
27:10>> All right. What do we give up?
27:16Yeah.
27:22>> And like a bigger value for whatever you
27:25have, which means you can't store.
27:34>> You mean my Vmax, the maximum voltage I
27:36can measure is going to be smaller? I
27:38don't think so.
27:40Um
27:43I think Vmax is really defined by the
27:45slope function. So if I go and take
27:48uh let's run this again. So I put my
27:51voltage my input voltage here is what
27:53like 5 volts.
27:55As long as this ramping function that's
27:57made by this current source going into
27:59this capacitor, right? This is we're
28:00comparing this value to this value. And
28:03when this value equals this value, then
28:05we stop. As long as I can get up there,
28:08that's my limiting factor. It's it's not
28:10necessarily a time thing.
28:13What else? What would we give up? Why
28:15not just run this ADC as fast as
28:16possible all the time?
28:21>> Yeah,
28:23>> register.
28:27>> That's true. Maybe that's what you were
28:29saying. um you so let's just assume that
28:32our counter value is large enough that
28:37that's not a problem that would be a
28:39that would be a constraint but we can
28:41fix that at design time.
28:44>> Yeah. So we're going to run a clock the
28:46counter faster where that means that
28:50that digital logic is going to be
28:51clicking over faster and faster and
28:53faster. It's going to increase your
28:54power consumption. Now, maybe compared
28:56to the power consumption of your devkit,
29:00uh, running at full blast, it's not that
29:03big a deal. But if it was a really low
29:04power application, maybe you'd want to
29:06make a trade-off between, hey, I got to
29:08run this thing faster. I get higher
29:09resolution, but do I really want to
29:11spend that extra extra power?
29:14But that's for me, I I always like this
29:16one because I get to make a trade-off
29:18and I get uh between using time to
29:20measure uh some voltage, which is kind
29:23of interesting idea.
29:26Okay. Now, what we find, oh, let's go
29:30back here.
29:32Okay. So, we talked about Oh, I I did
29:36gave away the power question in the
29:37terms of voltage trade-offs, but what
29:40could be one particular issue with this
29:42sort of scenario? Like remember, we're
29:44making integrated circuits. We're trying
29:46to make hundreds of them, thousands of
29:48them at a time, and I can't tune each
29:50one. So what would be the challenge with
29:53creating with using a single slope
29:54integrator uh with when when it comes to
29:58um or what potential issues when will
30:01happen to the current and capacitor
30:04measurements because of um how I use
30:07these circuits or how these circuits are
30:09manufactured. So uh take 60 seconds
30:11think about that. If you have some
30:12workarounds that would be great too.
30:32Let me know [snorts] why.
30:41[clears throat]
30:50Yeah.
31:12How about that?
31:21All right. What do you think? What are
31:22some potential issues with relying on
31:25current and capacitance to measure uh
31:28voltage or to to have those be constant
31:32as a function of time?
31:43Yeah,
31:44>> one sort of issue that we brought up is
31:46that um you're not measuring the voltage
31:48directly. So for instance if your
31:51capacitors and capacity push up um the
31:54way
31:56vice versal
32:08>> Yep. What are some things that influence
32:12uh your capacitance or your current?
32:15>> Yeah. Parasitic.
32:18>> Oh, yeah. Parasitic capacitance on your
32:20device. Uh, so and then what's one way
32:23around that?
32:27>> Yeah. So, a manufacturer time they could
32:29measure that. What are some other uh
32:33factors?
32:34Maybe something you can't Okay. Yeah.
32:37>> Heat. Yes. So, uh that you can't take
32:40care of at manufacturer time, right? So,
32:42they do calibrate a lot of your things
32:44through testing. So if there was a
32:46little offset in your ADC because of you
32:49know wire resistance or something they
32:51could account for that but temperature
32:52changing as a function of time they
32:54can't really account for and so uh your
32:57capacitance right if you have a
32:58capacitor we often use capacitors as
33:01sensors and we'll put some dialectric in
33:03between to say changes its uh size as a
33:07function of temperature
33:09or humidity. So this is how you make
33:11humidity sensors. Well that's that's how
33:13you make a nice sensor. Now they're
33:14trying to mitigate those quantities when
33:16they're making onchip capacitors. But
33:17still there's a little bit of change
33:19just at the silicon level. It gets a
33:21little warmer that capacitance moves a
33:23little bit. Uh your current source you
33:25get a little bit warmer and then
33:26electrons flow a little bit uh
33:31less good. Yeah, a little bit higher
33:34resistance through your uh gates. So now
33:37you have a slope that's dependent on
33:39temperature and now your ADC
33:41measurements depends on the temperature.
33:43So now you're correlating, you have
33:45these confounding factors. Um, how would
33:48you get around that issue?
34:03Guys are very tired. I can I can that
34:05must be it. Either I'm boring or you're
34:07tired. So I'm going with you're tired
34:08and I'm super interested. Um so the way
34:13around one way around this is that if
34:15you are temperature dependent you could
34:16have a temperature sensor that tells you
34:18what the relative temperature the
34:20temperature is now and then you could
34:21have a offset table and it it's not
34:24obvious but uh almost every piece of
34:26silicon can have a free temperature
34:28sensor. uh the the trick is you have two
34:30diodes of they're manufactured almost
34:32you know as precisely as possible and
34:34you put two dissimilar currents uh
34:36between them and the resulting voltage
34:38is proportional to absolute zero uh just
34:41a trick of physics and on silicon you
34:43can bet about half a degree accur deg C
34:46accuracy with that um anyway so now you
34:50could have a lookup table to try and
34:52compensate for the temperature var
34:54variations not the ideal method uh so
34:57there is a way around that um
35:01uh oh and here's the answer um yeah so
35:05basically these are inaccurate because
35:06of uh temperature but you can get around
35:08it through factory factory calibration
35:10and temperature compensation. So the way
35:13around this is what they call a dual
35:15slope integrator. We're not uh the the
35:17exact operation of all the analog
35:18circuits not important but the intuition
35:20of how the slope integrator should works
35:23which is this you're you have a constant
35:24rise time and you're seeing when the
35:25voltage equals and this one which is uh
35:29we'll talk about in a second which is
35:31rise and fall time. Understanding though
35:33that trick is what's important and when
35:36to apply it. So a dual slope integrator
35:39is kind of the industry standard and uh
35:41what it does is it's uh uh samples has a
35:45sample phase and then it has a uh or
35:48integration phase and then it has a um
35:51measurement phase. So the trick here is
35:54that in phase one you have uh some
35:57current or some voltage uh like you have
36:00a trans impedance amplifier. So you have
36:01your input voltage and that's being
36:02turned into a current through the magic
36:04of analog circuits. And basically that's
36:06charging up your capacitor. So you'd
36:08have um some value like that. And then
36:12at some point in time you reverse that
36:14and you have a known current pulling u
36:17charge out of that capacitor. And then
36:20if you that's phase two and then if you
36:22do the math you can remove the R and C
36:25from the equation allowing you to have a
36:28value that's just proportional to uh
36:31your voltage reference and your input
36:32voltage and time. So this way you can by
36:35charging up the uh capacitor and then
36:37discharging capacitor you pay the
36:39inaccurate penalty of your capacitor was
36:42too big or too small uh once on the way
36:45up and then you subtract that off on the
36:47way down. So the the trick is that uh
36:50you just um you those R and C's both
36:54cancel out of your circuit.
36:57And so that's why it's a very popular
36:58circuit, this dual slope integrator. We
37:01can see a quick example of that here.
37:05Again, another super complicated
37:06circuit, but this is just supposed to be
37:09a trans impedance or transconductance
37:11amplifier. Sorry, this is just an op
37:13amp. Doesn't matter how it works. And
37:15you're going to charge up this
37:16capacitor. And then you're gonna have an
37:19op amp here, uh, which is doing the
37:22comparison. And then you're going to
37:24discharge this capacitor through here.
37:26Um, and so we're going to push this
37:28button. And then we're going to that's
37:30all going to trigger this thing to start
37:32counting. So let's try it.
37:35Let's see.
37:37Start. Oh, I have a simulation going
37:39very slow. So here we uh Oh, I'll start
37:43again. I went too fast.
37:50And here we go. We'll start it.
37:54And we're we're basically we connected
37:56this input through this uh
37:58transconductance amplifier and it's
38:00charging up this capacitor.
38:04And then after some period of time just
38:06defined by this circuit here, it
38:07switches to this current source here and
38:09it's pulling this thing down. So now
38:12we're not dependent on the Rs and C's in
38:14here. and the Rs are implicit. We're
38:16just dependent on uh the value of this
38:18current source here. Um and now we can
38:21measure this value and we get that over
38:23here. I didn't I didn't put the
38:25frequency part on here. Uh but you still
38:28get the same benefit here of you could
38:30have a clock that's going faster
38:33uh to do a higher sample rate or that to
38:37increase your ADC resolution. Uh the the
38:40downside of all these devices is that it
38:42takes a lot of time to get there, right?
38:44So you think about trying to do
38:46operations within as minimum number of
38:48clock cycles as possible. And now you
38:50say I I want to have this high
38:51resolution ADC that's going to count up
38:53to you know uh you tens of thousands of
38:56uh units. Well, it's going to take that
38:59many clock cycles. So now this is very
39:01slow compared to your uh
39:04microcontroller, but it has high
39:06accuracy compared to other ones and it's
39:08relatively uh cheap and small.
39:14Uh
39:19yeah. So it's slow u but it uses time to
39:22measure. The resolution is the highest.
39:24Uh typically these are used in like
39:26multimemeters or even benchtop
39:28multimeters where you want to get like
39:30um you know five five digits of
39:33accuracy. Um the complexity is
39:36relatively high. Uh but it has good
39:38noise performance, good interference
39:39performance, those sorts of things.
39:43U power consumption is relatively low.
39:46You don't have a lot of comparators. You
39:47did have some digital logic in there,
39:48but that's pretty cheap. Uh in the
39:50current source seems like it would be
39:52bad, but actually in reality it's not
39:54that big compared to say all the
39:58comparators we saw in the flash ADC or
40:00all those resistors that needed to be
40:02biased.
40:04All right. So, any questions about slope
40:06ADCs?
40:12Remember that the conceptual trick is
40:13here we're charging up capacitor. Uh
40:16maybe we're discharging the capacitor,
40:17but that charging up we can measure with
40:19time. That's that's the trick you want
40:21to take away from this thing.
40:23Okay.
40:25And then so um the pop more popular
40:27version here is a SAR ADC. This is
40:29what's on your uh microcontroller. So a
40:32successive approximation register ADC
40:35and uh this device has uh a unit we
40:39haven't in there I haven't told you
40:40about yet which is a digital analog
40:42converter. So just even though we
40:44haven't taught you what that is just
40:46assume you put some digital values in
40:48and it's going to produce an analog uh
40:49value out basically you know just what a
40:53um speaker would do.
40:56And so now we're going to take we have
40:57some sample and hold circuit. We didn't
40:59show that in the other circuits. All
41:00circuits would have a sample and hold
41:01circuit but basically we have some input
41:02value. We're going to hold it here and
41:04then we're just going to make a
41:06comparison. Okay, is it you know this
41:08value? Is it higher or lower than this
41:10value? And then you're going to uh use
41:12this control loop here to say okay if it
41:15was higher or lower then I have this
41:16successive approximation. Basically it's
41:18doing binary searching to try and find
41:21where the value is. So it's going to be
41:24uh searching back and forth. I think I
41:26have an animation of that. Yeah. So we
41:27have two inputs and a comparator. Uh and
41:29then the binary searches you start off
41:31at say half half half your binary value
41:34size and then you're just going to try
41:36and look is this value greater or less
41:37than my deck output. And whatever it is
41:40then you're just going to do your binary
41:41search and keep trying to look for that
41:43particular value.
41:47And of course if it's above then you you
41:49choose back up. So this is just a kind
41:51of analog way to or digital way to
41:54search for an analog value. So the nice
41:56thing is here it doesn't take as long to
41:59converge as your slope integrator slope
42:01integrator was like I have to count
42:03every single um uh uh point right every
42:07single clock cycle I have to count
42:09something all the way up to my value
42:11here I can just basically do power by
42:13two so it's much faster at converging
42:16but it is more complex
42:21and so if you this would be another
42:23another way to show this um So here's
42:25kind of that search process. Here we
42:27have time and then some analog voltage
42:30here. So here we have our sample and
42:32hold circuit. So sis for whatever
42:34reason, let's say it started at zero.
42:35We're not going to pay attention to
42:36anything that happened in the past. And
42:38you have some sample time. Well, that's
42:39going to charge up this capacitor. And
42:41then we're going to hold it. Then we're
42:42going to start doing an analog
42:44conversion. Start at say 1 0 0. We're
42:46going to say, are we higher or lower
42:48than that? Well, we're higher. So we'll
42:50go up to half between, you know, 0.5
42:53volts and 1vt. uh whatever that is
42:55binary and then we're going to guess and
42:57that is 1 one zero 0 and we're higher
42:59than it was. Now you can see that we're
43:00kind of converging and searching for
43:03that analog value. Uh and now you
43:05remember we still have quantization
43:07error. We talked about that before or
43:09last week. So we didn't exactly get to
43:11the value but this is the closest binary
43:13value that will represent that analog
43:15voltage.
43:20And we can see this circuit in action.
43:24Uh, all right. So, let's see. So, this
43:26one, uh, a lot of little control
43:29elements here, unfortunately, but
43:31there's a timer and a controller block.
43:33That's this is the thing that's doing
43:34the binary searching. Uh, and then you
43:37have your DACK. So, basically, it's this
43:39loop right here. You have your analog
43:41voltage coming in. We're going to
43:43compare it to the DAC output. This thing
43:45is going to go high or low. And then we
43:46just have this controller that's going
43:48to search back and forth and and see if
43:50we can find it. So, let's start it.
43:53And what do I have to do? Oh, it already
43:56started. Okay, good.
43:58So, here's the analog voltage. And we
44:00can see that binary search. It goes up a
44:02little bit higher, then it came back
44:03down. And then, uh, you have to know
44:06when to to look. It doesn't have a like
44:08a hold when it's done. Like the
44:10simulation doesn't stop when it's done.
44:12Um, but we can change the analog value.
44:16Let's see. So, what this does, it's
44:17going to put out four pulses. So, it's a
44:19four bits. and we'll start on this next
44:21one here.
44:23So there's four values here. And now you
44:26can see it's doing the analog searching
44:28or digital searching for that analog
44:30value. And then so I should have said
44:33this before, this little counter here
44:36pulse uh puts out four pulses as four
44:40clock cycles because it's a fourbit uh
44:42ADC. And then the value is is uh uh
44:46accurate here. And if I change the
44:48voltage up here, hit reset and run, we
44:53can see that the analog voltage is
44:56higher. And now we can see that the uh
44:59ADC, the DAC is kind of searching for
45:01that value.
45:13>> Zero question. Oh, good. I'm Thank Thank
45:15goodness you're here. Sure.
45:26>> How do we know if we're like within like
45:28half basically?
45:30>> You don't
45:32um basically you're going to keep going
45:34uh until you um I mean there's a little
45:37state machine that says we're not going
45:38to go back, right? We're always going to
45:40go that one bit over,
45:42>> right? So basically say this was a 8bit
45:45thing and but now you know that um
45:50uh you came very close to it at the very
45:52beginning. Well then it's going to say
45:53well I can't go any higher. So it might
45:55go up and might go back down but it
45:57can't uh it's just going to converge on
45:59that because it can't get any closer to
46:00that that value.
46:08All right.
46:13Oh, that's the old version. Okay.
46:18And so, uh, this, so now we in the
46:20trade-offs of speed. Uh, so this is an
46:22analog binary search. So, it's a nice
46:25compromise between speed and resolution.
46:28Um, I should have said this before. One
46:30trick you can do with SAR ADCs is if you
46:32want to go faster, you don't have to
46:34convert all the all those bits. Say you
46:36have a 16- bit uh SAR ADC, but it just
46:40your clock speed is limited. Uh or say
46:43um you want to go faster, but your
46:46propagation delay through your uh device
46:48won't let you go fast enough. So you
46:50want to go say a megahertz, but uh your
46:52full 16- bit conversion takes longer
46:54than that. Well, what they do is they'll
46:56just not convert the last few bits. So
46:58you could do like a 8 bit or two bit or
47:00four bit. Two bit wouldn't make sense,
47:02but four bit or 8 bit or six bit,
47:04whatever it is. And that would allow you
47:06to have less time uh to get to a
47:09conversion and then you could sample
47:10faster. So this is another way of uh uh
47:14optimizing speed versus um
47:17uh accuracy which is nice. Um I would
47:21say that the the complexity is maybe
47:24medium or so. Um because you do need
47:26this DAC and we talk in a control unit
47:28but we don't need in one uh comparator
47:32um but we don't need uh you know voltage
47:34or current sources or those dividers
47:38and power consumption is um pretty uh
47:41reasonable considering the costs of most
47:44microcontrollers. So, it's less than a
47:46flash ADC,
47:48probably not as much as a uh uh uh
47:52sorry, it's much less than a flash ADC
47:54and probably more than a slope
47:56integrator.
47:58Okay, so the goals uh for you guys is
48:01not to necessarily know every ADC and
48:04work through every single topology and
48:05be able to recreate those circuits on an
48:07exam because that would be horrible.
48:09Your goal is to say, "Oh, these devices
48:12have different trade-offs, right? I
48:14would want to choose one of them to uh
48:17have to accomplish certain goals. And so
48:19the reason I show you those uh circuit
48:21trade-offs is just so you can figure it
48:23out. Uh you can play with the circuits
48:25on your own. Oh, you need more. Sorry.
48:30Set those up. Uh and just kind of learn
48:33about those trade-offs as well. You can
48:36just take those and hand them up that
48:38way. Go that way. And so for this thing,
48:40you're just trying to rate
48:43um
48:46you know them from one to three. I think
48:48it's three is the fastest or the best
48:50and one is the worst. And you can kind
48:52of figure out like comparatively which
48:54one would you choose for different use
48:56cases.
48:57[snorts]
49:16here. I can help some along.
49:19There you go.
49:22There you go.
49:25That way.
49:31Pass those out that way.
49:53It says this one is this one is easy for
49:55speed. If they're right in the name,
49:57it's giving you points.
50:12>> [groaning]
50:15>> That was great.
50:34about
50:51[clears throat]
51:27might
51:44reservation.
52:05You must
52:08Glory.
52:31[groaning]
52:35Yeah.
53:05Open.
53:22Heat. Heat.
54:01Happy
54:19glory.
54:22Oh,
54:34please.
54:53What is
55:17>> Yeah.
55:18>> [clears throat]
55:22>> Are you
55:24watching?
55:44All
55:48right.
56:15Facebook.
56:28Yeah.
56:56>> Okay.
56:59All right.
57:05[clears throat]
57:26Perhaps
57:37>> [clears throat]
57:53>> What do you want?
57:56That's your
58:39Okay, now
58:42these are not supposed to be like
58:43absolute like not every category can you
58:46come up with absolute value for because
58:48some of them are like like die like area
58:51You'd have to do the layout to figure
58:52that out. We can just kind of guess,
58:54right? This exercise is more about
58:56trying to compare them. What do you
58:57think the trade-off?
58:59So, uh, resolution. I didn't even really
59:02define what I meant by resolution. Who
59:04who had a definition for resolution?
59:07What do you think that means?
59:15>> What does that mean?
59:17>> Like step [clears throat] size.
59:18>> Yeah.
59:19>> Yeah. Yeah. So I was thinking of like uh
59:21step size like what's the smallest
59:24measurement you can make right? So
59:25higher resolution low resolution would
59:27be really coarse steps and higher
59:29resolution would be um small steps. So
59:32which which device could give you you
59:36know in theory higher resolution than
59:38the other ones. What do we think?
59:44I see I know you guys had things on your
59:46papers. Saw them.
59:49Yeah, I would say that's probably right.
59:51And now it's of course you could also
59:53say like I'm going to make a really big
59:56class A and then it could have higher
59:58than an instance. But it's trying to
1:00:00just argue like what is this technology
1:00:02good at or bad at? So I said and somehow
1:00:05my columns are off. I don't know. But I
1:00:07said here like um look the dual slope is
1:00:10going to give us this opportunity to use
1:00:12time to measure things. Right? So now I
1:00:16can I can have a really slow ramp up
1:00:19time and I can count really really fast.
1:00:21I can get a really high uh number of
1:00:23step sizes that I can differentiate. And
1:00:26so that's pretty universally going to be
1:00:28the the highest resolution.
1:00:31[clears throat]
1:00:31Flash on the other side is bound. You
1:00:34can't make them too big just because
1:00:36then you have to get all these resistors
1:00:37perfectly aligned and there's just
1:00:39limitations on how practical you can
1:00:41make a flash. I'm seeing usually that
1:00:42has the smallest uh resolution out
1:00:45[clears throat] of these categories and
1:00:47SAR is somewhere in between.
1:00:50Anybody want to argue I like arguing
1:00:52like no it's something different. Okay.
1:00:57Flash is in the name. All right. So
1:00:59flash is going to be the fastest. There
1:01:01is no clock involved in any of those
1:01:04circuit diagrams I show uh because the
1:01:07propagation is just uh through one um
1:01:11comparator and those are going to be
1:01:13really fast. So these are the things
1:01:15that will go up to the gigahertz uh and
1:01:20beyond. So these are really what the the
1:01:21workhorse for fast things are. But you
1:01:23have to give up resolution as you see
1:01:24above because you can't get a lot of
1:01:26different steps.
1:01:28The slowest right is going to be dual
1:01:30slope or even just slope integration
1:01:32because here every measurement you make
1:01:36you have to have a clock cycle for while
1:01:38SAR is at least it's uh uh 2 to the n
1:01:42right so here you're doing binary search
1:01:44this one is your linear linear search
1:01:47looking for the value so uh you know
1:01:50it's it's this is kind of on average of
1:01:52course if the input voltage happens to
1:01:54be zero you're going to find it
1:01:55immediately with uh slope integrator
1:01:58It's going to take you longer to find
1:01:59that value with your SAR ABC. But on
1:02:02average, the slope integrator uh is
1:02:04going to be slower than the SAR.
1:02:09Uh what about accuracy? What do you guys
1:02:11think? It's going to be the most
1:02:13accurate one. And here I meant didn't
1:02:16tell you accuracy means uh for a given
1:02:19step size, whether it's big or small,
1:02:21how constant is that step size? or if
1:02:24you take one measurement one day and
1:02:26take another measurement another day,
1:02:27how likely is it that they're going to
1:02:28be the exact same value? What do you
1:02:30think the most accurate
1:02:33uh device is?
1:02:43>> I would say it's a dual slope. I'd say
1:02:47um it depends on the least number of
1:02:50analogy parts, right? So the flash ADC
1:02:53has always resistors that have to be
1:02:56perfectly negative and if there's a
1:02:58little deviation one resistor then your
1:03:00step size a little bit worse and sorry
1:03:03you see um it's not bad it's just that
1:03:08uh you have a deck and there will learn
1:03:09about decks and they have their own
1:03:10inherent problem here we figure out way
1:03:13to get rid of the RNC constant inside
1:03:16that thing by charging up the capacitor
1:03:17and then subtracting off the RNC as you
1:03:20charge down. So this one while still has
1:03:23errors in measurements and and other
1:03:25issues, it's just less prone than the
1:03:27other devices. So it has higher
1:03:29accuracy.
1:03:32Uh what about complexity? We didn't
1:03:33really talk about even what that means.
1:03:35Generally was thinking about the number
1:03:37of components you have to put into these
1:03:39things. Not the digital logic. We'll say
1:03:41the digital logic's free, but like the
1:03:43number of comparators, number of
1:03:45resistors, like how much of those extra
1:03:47pieces you have to put in.
1:03:55Who wants to dispense a guess? Doesn't
1:03:57have to be correct.
1:03:59>> Yeah. What do you think?
1:04:00>> I guess the simplest one is the dual
1:04:02slope per
1:04:04simplest one. Dual slope. What did I Who
1:04:06knows? I forgot what I even said. Let's
1:04:08find out. Uh I said the dual slope was
1:04:11the most complex. Why did I say that?
1:04:14>> No. No. I said the dual Well, it depends
1:04:17if I want complexity to be up or down.
1:04:19Simple
1:04:20>> least. So what did you mean to say? You
1:04:22want you can redefine it.
1:04:24>> Simplest
1:04:25complexity.
1:04:26>> Okay. So simplest is a slope.
1:04:29>> Yeah.
1:04:29>> Okay. I don't even I made these slides
1:04:32like two weeks ago. I don't even know
1:04:33what I meant by complexity. But uh so
1:04:36let's see. Let's try and interpret what
1:04:38that means. Um complexity in the sense
1:04:40that um there's a lot of analog
1:04:43trickiness. Okay, that's in the uh slope
1:04:46integrator. But there's less parts to
1:04:49get wrong.
1:04:51Okay. And over in the Flash, I'd say the
1:04:53Flash says the structure is pretty in uh
1:04:56[snorts] easy to understand, but there's
1:04:58lots of components to get right. So
1:04:59maybe I would look at uh flash as being
1:05:02the most complex in the sense of trying
1:05:04to get it wrong. And dual slope is maybe
1:05:07the easier one to get right. Maybe I
1:05:10need to pre-label that one. Okay. How
1:05:13about power?
1:05:18Which one's going to be the most power
1:05:20consuming of all these devices?
1:05:23Yeah.
1:05:28>> Yeah, I'd say I'd say so. So I I said
1:05:30that as well. Flash in a sense here we
1:05:33have a comparator for every step size.
1:05:36For every step you have to have a
1:05:37comparator. Those are always on. Um, and
1:05:41then you have to have that resistor
1:05:43ladder as well before you have any of
1:05:44the decode logic. So, taking the digital
1:05:46logic out, I'd say that's the most power
1:05:49consumption. And the dual slope
1:05:51integrator only has one compared
1:05:56circuits, but those are relatively
1:05:58[clears throat] minor compared uh to all
1:06:00the other ones on the left. And you're
1:06:03seeing a trend here. Somehow SAR keeps
1:06:05falling in between both of these two
1:06:08extras.
1:06:09Now here's the the the one that's the
1:06:11hardest and most arbitrary of all the
1:06:13other arbitrary ones that are up there.
1:06:16uh we can think about uh cost is most
1:06:18arbitrary because the cost that you will
1:06:21see as designers as a meta system
1:06:23designer is like uh probably more about
1:06:26IP than it is about intellectual
1:06:28property than it is about like the
1:06:30actual die area right uh it's like
1:06:32you're trying to get a package thing a
1:06:35component you can buy off somewhere and
1:06:38die area is not a direct function but
1:06:40let's just assume that size is closely
1:06:43related to cost. Uh what do we think
1:06:46would be the [clears throat] most
1:06:47costly?
1:06:49Probably flash. I I think so too. Let's
1:06:51see if I if I agree with myself. Okay.
1:06:54This time. So flash uh because it has
1:06:57these large resistors uh takes up a lot
1:07:00more area. So that's what it means in
1:07:02terms of cost. Um
1:07:05and then dual slope only has you know
1:07:08one capacitor on it relatively small and
1:07:10sorry somewhere.
1:07:12Okay. Is there anyone here you're like,
1:07:14"No, I disagree with
1:07:17could disagree with me." It's fine.
1:07:23>> I guess
1:07:28[clears throat]
1:07:34that's a good point. Yeah, that's a good
1:07:36point. So, some of these are flexible,
1:07:38right? So, of course, you could run your
1:07:40dual slope um with a really coarse um
1:07:44timer, right? A really slow clock and
1:07:46then it resolution really fast. So,
1:07:49that's that's a fair point. Um somehow
1:07:52in my mind, maybe the mind of the
1:07:54internet as well, these are like if
1:07:56there's somehow equivalent, right, that
1:07:59these are what the curiosity these are
1:08:00all 12 minutes.
1:08:04That's a fair point. Any other any other
1:08:07caveats or questions or things you want
1:08:10to argue about?
1:08:13Okay.
1:08:16Uh let's see.
1:08:20All right. So, we went through those.
1:08:21There are a few other ones you might
1:08:23see. This is just enough to know like
1:08:25that they exist. So, uh, sigma delta or
1:08:29delta sigma ADC's um, is kind of like
1:08:32sorry to see except there's this one bit
1:08:34ADC and and there basically just
1:08:37accumulating these samples over time.
1:08:39It's an interesting uh, device to look
1:08:42at and then there's also pipeline ADCs
1:08:45where each stage is doing a small bit of
1:08:48the calculation of the voltage. So now
1:08:50you can do um, all these processes in
1:08:53parallel. It's kind of like multiple um
1:08:57SAR ECs all stacked together and now you
1:09:00have a a voltage uh distribution
1:09:03function that gives each one a separate
1:09:04little piece of that voltage to look at
1:09:06but not not part of the exam or
1:09:08anything. You just have to know that or
1:09:10just it's good to know that there are
1:09:11other types of ADCs that exist.
1:09:15Okay. So for your particular device uh
1:09:18you will be using it in lab. Uh so it's
1:09:21a you have four ADCs. They're all 12
1:09:23bits. They're all SAR ADCs. And then you
1:09:26get to make the tradeoff here between uh
1:09:29sampling speed like how fast you want to
1:09:31go. Three mega samples per second, two
1:09:33mega samples per second. And you have a
1:09:34bit tradeoff whether it's this 8 bit or
1:09:3712 bit. And so really usually it's
1:09:40trying to figure out what's the fastest
1:09:42sampling speed I need for my signal. So
1:09:44my signal is coming in. I want to do
1:09:46overnight twist, but you probably want
1:09:47to be like maybe five [clears throat]
1:09:48times faster depending on what your
1:09:50signal is just so you can get uh rid of
1:09:53the noise and everything and really
1:09:54understand what signal it is. So, it's
1:09:56probably good to over sample, but uh
1:09:58then you can see like well do I really
1:09:59need I want to go faster, but do I
1:10:01really need the the higher resolution?
1:10:03And [clears throat] sometimes there's
1:10:04other signal processing tricks you can
1:10:05do say um using opamp to get it full
1:10:09range. Right? So before we saw last week
1:10:11you probably saw examples where if it
1:10:13was really narrow range well then you
1:10:16don't have very many bits to measure. So
1:10:18if you use the op amp you can increase
1:10:21the the range of your signal. So there's
1:10:24kind of choice as to where you're trying
1:10:25to go faster or how many bits you need
1:10:27to represent something.
1:10:29Uh so you have uh eight channels per ADC
1:10:33which means you have one ADC but you can
1:10:35channel them in from different sources.
1:10:37So you can basically use them
1:10:38pipelining. So it won't work if you're
1:10:40trying to go for the fastest for every
1:10:42channel, but you imagine you have eight
1:10:44different values you're trying to
1:10:46measure
1:10:48and uh rather than and basically it's
1:10:51going to act like a muck. So maybe you
1:10:52have a a glove smart plug you're trying
1:10:55to make with a bunch of resistors on
1:10:57there to measure finger angle and now
1:10:59you can send all those signals to
1:11:01different pins and those get routed and
1:11:03then the ADC is going to select between
1:11:06which one it's going to cue. So he's
1:11:08going to do time domain multiplexing
1:11:10sample one then next one next one next
1:11:12one that allows you to set this thing up
1:11:15uh to do ADC conversions and it'll just
1:11:17cycle through each one and then set put
1:11:20the results in a register set of
1:11:22registers for you.
1:11:25Um you can do 14 bit oversampling. I had
1:11:27to figure out like what do they mean by
1:11:29that? How do they take a 12- bit
1:11:30[clears throat] ADC and turn it into a
1:11:3214-bit ADC? Didn't make sense to me. Had
1:11:35to look in the data sheet kind of
1:11:36remember what they were talking about.
1:11:37So basically they're going to over
1:11:38sample. They're going to sample
1:11:42um the input multiple times and then
1:11:44they're just going to sum them all
1:11:46together and shift over to do averaging.
1:11:50So basically on devices it's going to
1:11:52over sample the thing and then do
1:11:54averaging and then put that result back
1:11:56to you. And if you know if you're slow,
1:11:58if you're working in a world that's
1:12:00relatively slow, it doesn't really
1:12:01matter. If you're trying to go at, you
1:12:03know, uh, 2 megabit samples per second,
1:12:06that's not going to work. Now you have
1:12:07to do all these extra conversions. But
1:12:09it is a way to get extra uh, bits out of
1:12:12this by basically doing hardware
1:12:14sampling. So, um, hardware oversampling.
1:12:17So, that's a a feature that they give
1:12:19you that's not on all microcontrollers.
1:12:22Uh, and then of course you can generate
1:12:24all sorts of interrupts. You can
1:12:26generate interrupts when your device is
1:12:28done, right? So when you've done an ADC
1:12:29conversion, you there's a small plot
1:12:31prime here. So you can uh take you know
1:12:35so all eight of those samples and when
1:12:36all eight samples are done then it'll
1:12:38throw an interrupt where you can pull
1:12:39data out of that spot. You can also do
1:12:41things like monitor a pin and if the
1:12:44analog voltage is above a certain value
1:12:46or below a certain value then it'll
1:12:47throw an interrupt. So maybe you're just
1:12:49trying to see if some signal goes high
1:12:51or low and it's in some range. It's not
1:12:53binary. It's not [snorts] one or zero.
1:12:55So, you just want to see if I don't know
1:12:57what it would be. Maybe it's a light
1:12:59sensor. You want to see if the thing uh
1:13:00dips below a certain value. Well, keep
1:13:02your mic controller asleep until
1:13:04[clears throat] that happens where you
1:13:06turn on your ADC module, have that
1:13:08going, and then throw an interrupt when
1:13:10uh the signal is outside of that range.
1:13:14And then, uh we kind of showed the slide
1:13:16before, but here you're just going to go
1:13:18through and you want to figure out what
1:13:20your calculation time is. You got to
1:13:22figure out what your sampling time is.
1:13:23you're going to get some sampling whole
1:13:24time and then your conversion time and
1:13:26that's just the number of n bits that
1:13:29you have times the clock time and then
1:13:32um uh yeah your here your here's sample
1:13:35time as software configur
1:13:37um so so just an example um for a
1:13:41particular ADC configuration you know
1:13:43you have a clock of uh 16 MHz can sample
1:13:47with four bits
1:13:49or sorry four clock cycles and uh four
1:13:52cycles for a sample and hold, you can go
1:13:54calculate what your conversion time is
1:13:57to actually uh convert that value and
1:14:00that would tell you what your highest uh
1:14:02sampling frequency could possibly be.
1:14:06Okay, we're almost at time. So to recap,
1:14:09uh it's good to know uh it says single
1:14:12slope, but you can just think about um
1:14:14slope integrators in general and be able
1:14:17to reason about the trade-offs. Why
1:14:18would you choose one over the other? And
1:14:20then the slide still says the wrong
1:14:22thing, but on your uh SAR on your
1:14:25microcontroller, you have a SAR ADC that
1:14:27does give you the speed versus
1:14:28resolution grade. All right. Thanks.
1:14:35If anybody has questions about projects,
1:14:37now's a good time to chat.

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