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EECS 373 - Fall 2026 - Lecture 13: "Overview: Analog Signals" — Transcript

by Interactive Sensing and Computing Lab · 10,670 words · 1,639 segments · language en · Watch on YouTube

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0:28All right, let's get started.
0:30Can you guys hear me? Okay. Y
0:33Okay. So, today we're going to be
0:35talking about uh analog signals.
0:38Quick announcement. If you haven't
0:40already put your team into that Google
0:43forms, if you could do that, I think we
0:45still have a couple teams that haven't
0:47done it. So, go ahead and get registered
0:49today. That's due today.
0:52Okay. So we're going to be talking about
0:54uh analog signals and how they uh
0:57interact with embedded systems or why we
0:59need them for embedded systems. Uh so
1:01today we're just going to do kind of an
1:03overview and then next week I don't
1:06think you guys have lecture. After that
1:07you'll learn more about the specific
1:10analog to digital converters, the
1:12different versions that we have and then
1:14digital to analog converters, all the
1:17different kinds we have for those. But
1:19today is just kind of like an overview
1:20on how all that works.
1:24So uh why is this important? So digital
1:29systems they need to kind of interact
1:31with the real real world. So the real
1:33world is analog, right? So there's a lot
1:35of things that we need to inter uh
1:37interact with like sensors and maybe
1:40some sounds that are analog. Okay. And
1:43in embedded systems, a lot of these
1:45embedded systems, you're you're
1:46interacting with them quite a lot. If I
1:49was designing maybe a server in the
1:51cloud, maybe I don't care that much
1:53about that being able to interact with
1:56analog. But for embedded systems, analog
1:59is really important. And it's important
2:00that our microcontrollers, for instance,
2:03have those analog to digital converters
2:05or those digital to analog converters.
2:10So, uh, we want to potentially measure
2:13analog signals, but there's also
2:14scenarios where maybe we want to control
2:17analog signals. Um, so maybe we want to
2:20generate sound. That would be an
2:22example.
2:23So, to to measure analog signals, we use
2:27something called an analog to digital
2:29converter. And that's basically going to
2:31take some kind of signal, usually a
2:33voltage, and it's going to convert it
2:35into a digital value. Okay. The the most
2:39go-to example is a microphone. Okay, a
2:42microphone is going to take sound waves.
2:44It's going to vibrate and it's going to
2:46create this analog voltage. If we hook
2:49that up to, for instance, a
2:50microcontroller, we would use an analog
2:52to digital converter inside the
2:54microcontroller to convert that to a
2:56digital value. And then I could, for
2:57instance, record an MP3 file. Okay.
3:01Other things that we might want to use
3:03an ADC for, um, a bunch of different
3:07sensors. Basically, any sensor out
3:08there, whether it's like a temperature
3:10sensor or a light sensor, it's going to
3:12output some kind of analog value. Okay.
3:15So, if we want to interface with those
3:17sensors, we need to use an ADC.
3:22All right. Going the other way around,
3:23let's say I have an audio file, an MP3
3:26file, and I want to listen to that,
3:28right? How am I going to do that? Well,
3:30I'll use a digital to analog converter.
3:32It'll take that MP3 file, and then
3:34convert it into a voltage, maybe like a
3:37sine wave, and then we could put that
3:39onto a speaker, and then we would hear
3:41that. Um, does does everyone know how a
3:43speaker works? I find that a lot of
3:45people don't know this. So, a speaker is
3:47like a coil wrapped around a magnet.
3:50They call it a voice coil. And then that
3:52coil is connected to a diaphragm. And
3:54when you put voltage through that coil,
3:56it'll shake back and forth. that
3:58diaphragm will move back and forth and
4:00then you'll hear that audio. Okay,
4:01that's kind of how it basically works.
4:03But we first need to start with that
4:04voltage in order for that thing to work.
4:06And so that's where a digital to analog
4:09converter comes in. Um radio
4:12transmitters that might be another
4:13scenario or another use case where we
4:15might need a DAC if we want to generate
4:18radio frequencies use those are often
4:20done with DAXs.
4:23Does that kind of make sense why these
4:24are important for embedded systems?
4:29So, you guys have already used an ADC in
4:31a DACK in lab. So, the oscilloscope,
4:34that's a good example of an ADC. It's a
4:36pretty fancy ADC. Um, it has really low
4:40noise. It can also measure a bunch of
4:42different voltage ranges. That's kind of
4:44the unique thing about an oscilloscope.
4:47Um, or function generator. That's how
4:50that works is it has a DAC inside of it
4:53and it takes some digital value. Let's
4:55say you're trying to generate a sine
4:56wave. It takes the digital
4:58representation of that and converts it
5:00into an analog signal that's outputed uh
5:03on the output jack. Okay.
5:08Okay. So sampling rate. So if we had a
5:11sine wave for instance
5:13um and we wanted to capture that there's
5:16infinite amount of points on that on
5:19that sine wave, right? So we can't store
5:22infinite data. So what we have to come
5:24up with is a way to sample that and we
5:26have to come up with a reasonable
5:27sampling rate. So how often are we
5:30actually going to measure that analog
5:32voltage? That's what we call sampling
5:34rate.
5:36Um okay an example might be a CD. Uh who
5:41knows what a CD is?
5:44Raise your hand. Okay. Who has listened
5:46to a CD?
5:48Okay. A couple. Okay. A decent amount. I
5:50thought it was going to be less. Um, I
5:52think the I the iPod came out what in
5:552001. So that that predates everyone
5:57here, right? I think um doesn't predate
6:00me obviously. Well, maybe not obviously.
6:02[laughter]
6:03Okay. Who here has listened to Spotify?
6:07Okay. I think that's everyone. I think
6:09that's a better example.
6:11So, if you were to go to Spotify's
6:14website and you looked at the audio
6:16qualities that they support, if I sp if
6:19I pay for Spotify premium
6:22um and I I put my audio quality to the
6:24max quality, they call it lossless. So,
6:27that means that um it has all of the
6:29audio data there that would be in the
6:32original file. They have these little
6:34specs here and we can see it says 24bit.
6:37That's going to be our resolution. And
6:39we'll talk about that a little bit
6:40later. And then this right here, we have
6:4344.1 kHz. Okay, that is our sampling
6:46rate. Okay, why did they pick that
6:50number? Does anyone have any idea why
6:52they picked 44.1 kHz?
6:58What can our ears hear like in air? If
7:02there's a sound sound waves coming, at
7:05what frequency can we no longer hear
7:07beyond that? Do you guys know? Yeah,
7:09>> it's 20 kHz.
7:11>> Yeah, it's 20 kHz. Yeah, it's about 20
7:13kHz. Younger people are are higher,
7:16older people are or lower. Um, okay. So,
7:20based on that, so 20 kHz, why did they
7:22kind of double that and go to 44 kHz to
7:25represent audio? Yeah.
7:27>> Um, in order to recreate a signal from
7:30sampling, you have to sample at the
7:32frequency, which is double um like sort
7:34of the maximum
7:36frequency. So, The maximum frequency is
7:3820.
7:40>> Yep. Exactly. And we'll talk about that
7:42in the next slide, but you're right.
7:44It's Nyquist and they did 44 because
7:46they wanted to go a little bit higher
7:48than 40 uh because there's you're going
7:51to have some filters in there and we
7:52kind of give want to give some headroom
7:54for those filters. We can talk about
7:55that later as well, but that's where
7:57that 44 kHz comes from.
8:00Okay, this is on the slide. I'm not
8:03really sure what medium quality sampling
8:05rate means, but there you go. 22 kHz is
8:08medium sampling. And then phone
8:11sampling. Um, who here has talked on a
8:14landline?
8:17Okay, most of you. Okay. [laughter]
8:20Um, so back in the days when we had
8:22landlines all over the place, those were
8:24at like 8 kilhertz. Okay. Um, nowadays
8:28if you're doing a call over 5G, it's
8:31actually sampled at like 48 kilhertz. So
8:34quite it sounds pretty good nowadays,
8:36but back in my day it didn't sound as
8:38good. If you guys have called like um a
8:42company and they put you on hold and
8:44they have that that on hold music
8:46playing and it sounds like like crap,
8:49it's because it's being sampled so low.
8:51That's what's going on there.
8:53Why when they were, you know, making
8:55these landlines, why did they decide
8:57that, okay, we're going to use 8 kHz as
9:00a sampling rate when we really need like
9:0340 kHz in order to actually represent
9:05the audio that you can hear? Why did
9:07they pick 8,000?
9:10Does anyone have an idea why they did
9:11that?
9:14So, yeah, go ahead.
9:19>> Yeah. Yeah, that's the idea behind it.
9:21So our voices, most of the the sound
9:24that our voices are making are below 8
9:27kHz or probably below 4 kHz. And so they
9:32decided, okay, 8,000 is enough to convey
9:35people's voice. And and if they went
9:37higher, that would use more data. Their
9:40the phone lines would have to be faster.
9:42So that's how they came up with 8,000
9:44kHz. Okay. So does sampling rate kind of
9:47make sense? This is all talking about
9:49audio, but we could obviously sample
9:50things that are a lot faster. Um, but
9:54yeah, so let's go on to Nyquist.
9:57Okay, so this is a theorem, Nyquis
10:00Shannon sampling theorem. And the
10:02theorem is is that if we want to
10:05replicate a signal that we have sampled,
10:08we have to sample it at twice or more
10:11than twice the maximum frequency that
10:14we're sampling. Okay, that's the only
10:16way that we can reconstruct that signal.
10:21Okay, and if we don't do that, there's
10:23something that happens called al-isting.
10:26And this is some error. And we'll kind
10:28of show some examples of what that would
10:29look like. But if if we have some
10:31signals in the signal that we're
10:34sampling that are at a higher frequency
10:36than our Nyquis rate, then we'll have
10:38alysine and it would cause issues.
10:43Okay? And it'll it'll make it look like
10:45we're actually sampling different
10:46frequencies instead of what we are
10:48actually sampling.
10:51And this theorem assumes that there's no
10:54noise and there's no clock jitter. Okay?
10:57So noise would be like if there's some
10:59high frequency noise in the background,
11:01we need to make sure we filter that out
11:03before we do our sampling. Otherwise,
11:05it's going to screw up this whole thing
11:06and we won't be able to reproduce the uh
11:09the signal that we recorded. And then
11:11clock jitter. That's how precisely we're
11:14taking these measurements. Like we need
11:16the time between each measurement to be
11:19very precise. Otherwise, it screws up
11:22Nyquis. Okay? So that's why if you were
11:25for instance uh measuring some kind of
11:27signal with an ADC, you probably want to
11:30put a timer into that ADC to basically
11:33tell it, okay, exactly at this time,
11:35this is when you're going to do that
11:36sampling. Okay.
11:42All right. So if we look at this this
11:45signal here, this has been sampled. What
11:48is the sampling rate of this signal? So
11:51why don't you guys spend like 20 seconds
11:53thinking about that and let me know.
12:10>> [clears throat]
12:13>> Does anyone have a guess?
12:17>> Yeah.
12:20>> What' you say?
12:21>> It's not 3 kHz. It's close. You're close
12:24though. Maybe you counted slightly
12:25wrong. Yeah.
12:27>> Yeah, it's 2 kHz.
12:29Um, yeah. So, we're That's how many
12:31That's how often we're taking these
12:32samples. How far apart these these
12:34points are. What is the signal? If you
12:36kind of just connect the dots,
12:39what would the What do you think the
12:40signal that we're measuring here, what
12:43frequency is that at?
12:55>> Yeah,
12:56>> I think it's 200.
12:58>> Yeah, it's 200 kHz.
13:00Okay. So, that's that's what we were
13:03that was the signal, right? that sine
13:04wave right there that was a signal. We
13:06took some samples along that point and
13:09then we can easily just reconstruct it.
13:12Okay, so if I were to output this, it
13:15would clearly be a sine wave. Okay, so
13:17this is where Nyquis works out. We did
13:19everything right. We sampled at a fast
13:21enough rate and it's really easy for us
13:24to uh reproduce this signal.
13:28Okay, what's going on here?
13:30What if I told you there was a sine wave
13:33somewhere in there? What What's going
13:35on? What's going wrong here?
13:41Is it that maybe we're not sampling
13:43quick enough? Right. So here, let's kind
13:46of look at what's going on.
13:49You can see there is a sine wave in
13:52there, but we're only we're sampling
13:53where it's at that crossover point,
13:55right? So the problem is is we are
13:58sampling at exactly
14:00twice what the frequency is. So this is
14:03a I have it here in my notes. This is a
14:072000
14:08or no are oh we're just sampling a 2000
14:10hertz signal at 2000 hertz. Okay. And so
14:14then that that's what happens there.
14:16Okay. So we can't actually reproduce
14:18that because we weren't sampling fast
14:20enough.
14:23All right. What about this? This looks
14:24very similar to the one that we looked,
14:26In fact, I think it's identical to the
14:28one we looked at uh two slides ago. But
14:31what's actually going on here? Well, we
14:33really screwed up here. We are sampling
14:36way too slow. And this 2,200
14:40hertz signal looks more like a 200Hz
14:43signal because we weren't sampling it
14:46fast enough. Okay, does that all kind of
14:48make sense? What's going on with this?
14:52All right.
14:55All right. Do we think that this we were
14:59sampling fast enough for this plot here?
15:03Yes. No. Maybe. Any guesses?
15:12So, let's look at what this actually is.
15:15So, that that's actually what the signal
15:17was. And this is a valid. This is some
15:19signal that you could have actually been
15:20sampling. In this example, what we have
15:23here is we have 100 hertz on top of 400
15:26htz on top of 1,600
15:29hertz. Okay. Um, and I believe, yeah,
15:33and this is sampled at 4,000 hertz. So,
15:36we're way above the the Nyquis rate. And
15:38we were able to accurately reproduce
15:40what was going on here. This is what
15:42like if I was recording someone's voice,
15:44this is kind of what it would look like.
15:46So we have something called a
15:48fundamental frequency and that's how
15:50fast our vocal cords vibrate. It's
15:53somewhere be between like 100 and 200
15:55hertz. But to actually like make that
15:58tone into like words that actually make
16:01sense, you have something called
16:02harmonics, which are actually higher
16:04frequencies that your mouth makes and
16:07your tongue makes. And that's how you
16:09can actually make voice, right? Or a a
16:12voice that you can understand. And so
16:14those harmonics, those are those higher
16:16frequencies in here that get overlaid on
16:18top of that fundamental frequency. Okay?
16:21So if you ever look at like a waveform
16:23of someone's voice, it's going to look
16:25really messy. It's not going to be
16:26really clear what frequencies are going
16:28on. Uh but we could use Nyquis and we
16:31could figure out exactly what those
16:32frequencies are.
16:35Okay.
16:38All right.
16:41What's wrong with my slides?
16:44Okay, this is a a theorem that I think
16:46professor sample came up with and it's
16:48called the oscilloscope sampling. His
16:51his last name is sample. So he's he came
16:53up with his own um his own theorem
16:56called the oscilloscope sampling
16:58theorem. And the idea behind this is
17:02Nyquis is like ideal like if everything
17:04is perfect, there's no noise, everything
17:06is working out well, then we can do
17:08double uh we can just we just have to
17:11double it. But in reality, if you really
17:13want something to look like what it is,
17:16five times is um what you really want to
17:20do. Okay? And that's kind of what
17:21oscilloscopes do. So let's kind of look
17:23at this spec right here. So if you look
17:27at any oscilloscope, it's probably going
17:28to have a number at the top of it. And
17:30it's and for instance, this one, it says
17:32200 megahertz. Does anyone know what
17:34that number means?
17:39That's basically the limit that you can
17:41use this oscilloscope. Like that's the
17:43max frequency that you can measure with
17:45this oscilloscope. But underneath that
17:48there's this other thing um called 5
17:53GASA
17:56uh over S. Can anyone guess what that
18:00stands for? Yeah.
18:03>> Yeah. Giga samples per second. So here
18:05we have five giga samples per second. Um
18:08and this is a 4 channel uh oscilloscope.
18:13Uh if for instance this oscilloscope let
18:16me measure a signal on one of the
18:19channels at 5 giga samples per second.
18:22Some of them don't. Some of them will
18:23actually spread all those samples across
18:25all of those channels. But let's assume
18:27that it could do that. In this example,
18:30this oscilloscope would be oversampling
18:33the signal like a 200 megahertz signal
18:35by like 25 times. Okay? And so the the
18:39faster you can sample it, the more
18:40accurate those signals are going to
18:42look. Does that make sense?
18:46All right.
18:48Okay. So, we talked about sampling.
18:50That's like the time between the
18:52measurements. But how do we actually uh
18:54turn those measurements into values that
18:57are digital? Um again you know we have
18:59that that problem where a a signal is
19:02has infinite values okay and we we don't
19:05have infinite bits to store that. So we
19:07have to do something called quantizing
19:10and that's where we convert those
19:11voltages to uh like basically round them
19:14to the nearest value that we can
19:16represent.
19:18Okay. And so in this example let's say
19:22we're using only three bits to represent
19:25a voltage. That means we can basically
19:28uh store eight different values uh when
19:31we're measuring something. And so if we
19:33were trying to measure the sine wave and
19:34we were taking samples, you can see that
19:37there's kind of big step. It's like
19:38there's steps there, right? And that's
19:40because we just don't have many bits to
19:42store that information. Okay? If we
19:45added more and more bits, this blue
19:48stair stair step would look more and
19:50more smooth as we uh add more of those
19:52bits. And so a potential issue with that
19:56is let's say we have this voltage right
19:59here.
20:01Well, it's going to be represented as a
20:03four. But that four could mean somewhere
20:06between 1 volt and 1.25 [snorts]
20:09volts. Okay. And so that is a limitation
20:12we have. We have to decide how many bits
20:15we want to use to to represent this
20:17data.
20:20All right. And that's that's called
20:21resolution. And the way that we can
20:23calculate that often when um when
20:27engineers talk about the resolution of
20:29an ADC, they're going to just say, "Oh,
20:32this ADC is 8 bits." Okay, but that's
20:34technically not what the resolution of
20:37the ADC is.
20:39Um
20:42this is actually the formula u that it
20:46is. Well, not quite. We we'll we'll see
20:48why that isn't quite this. uh but it
20:51kind of makes intuitive sense. You have
20:53to first take the reference voltage and
20:56that's the voltage that's the voltage
20:58range that you're measuring at. So in
21:01this example, we're measuring between 0
21:03volts and 5 volts. Okay? So that's an
21:06important input into this equation. So
21:09that this voltage reference would be 5
21:11volts here. And then we'd be dividing it
21:13by the number of steps we have which is
21:152 to the n. n is three. So this would be
21:17basically 5 over 8. And that's how wide
21:20each each of these steps is. But if we
21:23actually look at this and we count how
21:26many steps there are for this voltage
21:28range, let's just count it out. We got
21:30one here, 2, 3, 4, 5, 6, 7. We don't
21:35actually have eight. And so that's why
21:37the equation has to be 2 the n minus
21:40one. But a lot of the times if you look
21:42in data sheets, they're just going to
21:43use this equation right here. um just
21:46because once we get to bigger bit sizes
21:49it really doesn't matter and if we kind
21:52of do that math if we have a 12bit ADC
21:55for instance
21:57if we do the math there the the
21:59difference in resolution between one or
22:01the other this equation or this equation
22:04is 0.1
22:06molts which is like basically nothing um
22:10so like for instance the ADC on your XMC
22:144700 it has a 12 bit ADC and so this
22:18would be kind of the difference between
22:19these two equations. Okay, the problem
22:22with this is see this 5 volts here. The
22:25only way that we can represent
22:27one one or the only uh voltage that will
22:30actually result in this code here 111 is
22:34if we have exactly 5 volts. Okay, but
22:37all these other steps like there's a big
22:39voltage range where it would result in
22:42this value. So it's very it'd be like
22:43almost impossible that we would actually
22:45get to this this value right here 111.
22:49So that's kind of an issue. Let's kind
22:51of talk about um how we could
22:54potentially fix that. Before we do that,
22:57let's look at how we actually take um a
23:02voltage and figure out what the code
23:04would actually be. So this is the
23:06equation we can use to take a voltage
23:09value and convert it into a digital
23:11value. Okay? And I'd encourage you to
23:15not memorize these. You should be able
23:18to once you kind of understand how this
23:19all works, you should be able to just
23:21kind of infer what the equation should
23:23be. Okay? Maybe right now an equation is
23:26good to kind of understand how this
23:27works. But as we talk about it more, you
23:30should be able to just kind of come up
23:31with this equation. Like I don't have
23:33these memorized, but if someone were to
23:35ask me how do I convert uh this voltage
23:38to this value on an ADC, I'd be able to
23:41do it. So what is this equation actually
23:44talking about here? Well, we have these
23:45things called RL and RH. These are our
23:49reference voltages. In this example, our
23:52reference voltage, our low reference
23:55voltage is zero and our high is 5 volts.
23:58But we'll find out later when we talk
24:00about ADCs that you can actually change
24:04these references here. Okay? So, if I
24:07wanted to measure a smaller signal, I
24:08could potentially make this reference
24:10smaller, but you need that voltage range
24:12in order to calculate what the actual
24:14digital value is going to be because
24:15they're going to spread that digital
24:17value across the whole voltage voltage
24:20range. Does that make sense?
24:24Any questions on how that equation kind
24:26of works?
24:29Okay. So, if we kind of plug some
24:31numbers into this equation, if we have
24:352.8 volts, we can see by based on this
24:38stair step that we're probably going to
24:39get uh three here. And how does that
24:42actually work out? So, here's the math.
24:44Figure it all out. And then we have to
24:46do a floor function because we can't
24:48have a a floating point in here, right?
24:50Usually an ADC is representing the value
24:53in an integer. We have to do a floor.
24:56And you can see in this example uh
24:58that's going to be three. Okay, that's a
25:00digital value that's actually going to
25:02be stored. But this this has some issues
25:05here. We have we have a lot of error,
25:08right? The actual uh um like floating
25:12point value that we're trying to
25:13represent is 3.92. That's pretty far
25:16away from from three, right? Four would
25:19probably be a better number to represent
25:21this. So how can we do that instead?
25:24Another issue with this is this 5 volts,
25:26right? The issue that we talked about in
25:28the last slide. So what can we do
25:31instead? We can actually shift this. And
25:33this is what a lot of like ADCs will do
25:36is they will shift over that function so
25:39that our um error is not as big. Okay.
25:43So in this example, they're adding, they
25:45call it adding half a least significant
25:47bit, and that will make our ADC
25:51half a least significant bit more
25:54accurate.
25:55Does that make sense? It's kind of maybe
25:58I'll show you the math here and maybe
25:59it'll make more sense.
26:02Um, but anyways, you plug in this, you
26:05add that half of a least significant bit
26:08and then when we do a floor for that, we
26:10get a much more accurate value. we get
26:12four instead of three. Okay, which is a
26:14lot closer to 3.92. The actual like if
26:17we were to do floating point that would
26:19be the actual value that would be stored
26:21digitally.
26:24Does that make sense?
26:28Okay.
26:32All right. So, we kind of talked about
26:34what resolution is. That's kind of just
26:36like the distance between each step.
26:38Like what's the voltage range for each
26:40step? That's our resolution. If we have
26:43larger steps, that means we have less
26:45information and a worse resolution. So
26:48if we need really good resolution, we
26:50need to decrease that step size or
26:52increase the number of bits that we're
26:55using. Quantization error. This is this
26:59is that error we were talking about. Um
27:02and we can change it. So if if in this
27:04example the quantization error is one
27:08significant bit or least significant bit
27:10one least significant bit. Okay so we
27:12could be off by a whole least
27:14significant bit. But if we shift this
27:16over the max error that we can have so
27:19at these corners that's where we're
27:21going to have the most error. That's
27:23going to be half the least significant
27:25bit. And so this this plot here kind of
27:27shows at these points that's where we're
27:30seeing the most error. If we get really
27:32lucky, maybe we'll be right on the dot.
27:34Uh, but this is what our max error is
27:36going to be. Does that make sense?
27:39Because it So, make sure that you
27:41understand these two terms because
27:43that's going to be the next question
27:45here.
27:48So, look at them just a little bit
27:50longer.
27:51All right. So for this question, why
27:55don't you work for 90 seconds with your
27:56neighbor and tell me what the
27:59quantization error is for a 12bit ADC
28:03with a voltage range of 0 to 3 volts.
28:06Okay,
28:08so we gave you that equation a couple
28:09slides back. Think about it a little bit
28:11and what would the quantization error
28:13be? So go ahead and work with your
28:14partner.
29:07>> [clears throat]
29:12>> power.
29:18You're like angels.
29:37It's like I
29:39really like
30:03All right. Does anyone want more time?
30:07Does anyone have an answer? Like an
30:10actual value
30:12like they plugged into a calculator.
30:13Does anyone have a number?
30:17No one has it. Yeah.
30:2136.
30:22>> Yeah, you got it right. U so it's really
30:25small. It's in the millolt range because
30:27our ADC is so it has so many bits. It
30:30has 12 bits. The quantization error is
30:33quite low. Okay. [snorts] And this is
30:34going to be way below whatever noise
30:36you'll typically experience. So, um,
30:39once we get to these these size ADCs,
30:42unless you have a really, u
30:45analog circuit on the front end of this,
30:49um, you're most likely these lower bits
30:51are just going to be kind of blown away
30:53by noise.
30:56Okay, is anyone confused how this
30:58equation kind of works? And is anyone
30:59kind of confused
31:01uh why this equation should be
31:04intuitive? Is it intuitive to everyone
31:06now? how how you would kind of take a
31:09voltage range and then divide it by
31:13uh the number of steps we have.
31:19Everyone's good on this.
31:21Okay.
31:25All right. So, let's talk about that
31:26voltage range a little bit more. Okay.
31:28Let's say we have this signal. If we put
31:31our our lower range and our higher range
31:35inside of that, well, we're going to
31:36have we're going to have clipping. Okay,
31:39that's what that's called clipping. And
31:41so, we're not actually getting our whole
31:42signal there. So, we have to be careful
31:44with those those reference voltages in
31:46order to make sure that our signal
31:48actually fits between them. But we also
31:51don't want to make them too big. The
31:54reason why is we're kind of we're kind
31:55of throwing away a lot of resolution of
31:57our ADC, for instance. So, let's say I'm
32:00trying to measure uh brain waves. Brain
32:03waves are like in the millolt scale. If
32:06I were to just hook up my ADC on my XMC
32:084700, which has a reference voltage of
32:113.3 volts, so 0 to 3.3 volts, and we're
32:15trying to measure brain waves, which are
32:16like millolts. We're going to have this
32:18issue here where the signal is just so
32:21small that it's only going to be a
32:23couple values. It's only going to vary
32:25by a couple digital values. Okay? And so
32:28what we could do is we could actually
32:30shrink that range to kind of get our
32:32signal. What's another another way that
32:34we could modify the signal to like if we
32:39had an ADC that was between zero and 3.3
32:41volts? Uh what could we do to the signal
32:44in order to actually read it with that
32:46ADC? Yeah.
32:49>> Yeah. Amplify it. So that's often what
32:52you would do if you wanted to read brain
32:54signals. probably want some analog
32:56circuit before your ADC, some kind of op
32:59amp that's going to amplify that signal
33:01for our ADC.
33:05And so, ideally, this is what we want to
33:07see. We want to see that signal just
33:09barely below the top reference voltage
33:12and just barely above the bottom
33:14reference voltage, but not outside of
33:16it. Does that make sense for everyone?
33:20Cool.
33:24All right. So, we talked about going, I
33:28think, from a voltage to a binary code.
33:30Oh, wait. No, this is different. All
33:32right. What are we talking about here?
33:33This is just talking about um what the
33:36the different uh digital values could be
33:39for different reference voltages. So,
33:41for here, we have a reference a lower
33:43reference of zero and an upper reference
33:45of 4 volts. And so, if we have a voltage
33:48of 3.25, 25 that would result in a code
33:52of 110.
33:55And if we change those reference
33:56voltages to one and 5 volts
34:01and we have that 3.25, that same thing,
34:04well, you can see that that's a
34:05completely different digital value that
34:07we're going to record because those
34:08reference voltages are different. Make
34:11sense?
34:18Okay. Um
34:21what is this talking about? Okay, using
34:23anti-aliasing filters. Okay, so we can
34:26actually use uh analog filters to make
34:29sure that those higher frequencies are
34:31not getting into our our sampled signal.
34:35Okay, a simple way to do that is with a
34:38simple RC filter. Um
34:42and we would call that an anti-alysis
34:44filter. Do we actually need to do this?
34:48Yes.
34:49uh longer answer, yes, but sometimes
34:52it's already done for you. So, a lot of
34:54ADCs are already going to have that
34:56filter built into it, but but you need
34:58to read the data sheet in order to
34:59understand if it's actually doing that
35:01and to understand what that filter is
35:03actually filtering out. Um, it's going
35:07to be designed to filter out. It's
35:09basically be right at that Nyquis limit,
35:11right? So you need to be uh filtering or
35:14sorry you need to be sampling at your
35:16maximum rate in order for that filter to
35:18actually do its job. If you're sampling
35:20at a much much uh smaller rate, let's
35:23say I'm sampling audio, right? My a the
35:26ADCs on our microcontrollers can go way
35:29faster, like in mega samples per second.
35:33But if I'm doing audio, I'm sampling way
35:35lower. So, I'm going to have to actually
35:36put an external circuit out there in
35:38order to filter out all of those
35:41frequencies outside of my Nyquis rate.
35:44Okay? Okay. So, if I'm sampling at uh 48
35:47kHz, then that's that's where my filter
35:50needs to live more in that range than in
35:52the like mega megahertz range.
35:58And this is a little bit more detail on
36:00how you would actually create an RC
36:02filter. Where do they teach this in 215,
36:06right?
36:07>> 216. Okay. So, if you took 216, this
36:10should be familiar. If you ever need to
36:13need to look back at these slides
36:14because you need to do some filtering,
36:16you can look back at this. But one
36:18important thing is this is uh it's it's
36:20kind of there's a rolloff here, right?
36:22It's not like these filters are magic in
36:25that they immediately just uh filter any
36:29frequency above what it's designed for.
36:32There's kind of a rolloff there. And
36:34that kind of goes back to why um they
36:37sample audio at 44 kHz because they're
36:40kind of accounting for this that some of
36:42those higher frequencies are actually
36:43going to kind of sneak through uh
36:46because this thing rolls off. All right,
36:50but yeah, you can take a look at this
36:51equation if you ever need to build one
36:53of these circuits.
36:57Okay, so going from analog to digital.
37:01So, we have a physical phenomena and we
37:03put it into a magic black box and then
37:05we get engineering units. That's what we
37:07want. How do we get there? We take that
37:11thing. Maybe it's light. We have a
37:13sensor. That sensor also is known as a
37:17transducer
37:18that converts that light into, let's
37:20say, a voltage or maybe a current. We
37:23then plug that into our ADC
37:26analog to digital converter. that's
37:29going to make some digital value and
37:32then we're going to use our software to
37:33convert that into
37:36maybe we're measuring light. So we're
37:38going to convert that into lux which is
37:40a way to measure light. Okay. So this is
37:42the way that we would take light and
37:44convert it all the way to lux.
37:48So here's an example where
37:50we have a temperature sensor. Um, and
37:55this you'll often find this with
37:56temperature sensors where uh they'll
37:59take um
38:02like a temperature for instance and
38:03they'll output a voltage. Okay, you
38:05actually need to power this thing. Some
38:06of these pins are your power and then
38:09usually the middle pin is a voltage
38:11that's going to be outputed. Okay, and
38:13the great thing about this is we can use
38:15an ADC to measure that voltage and then
38:18we can figure out what the actual
38:19temperature is. Okay, but we have to do
38:22a lot of math in order to get that to
38:23work. Um, so we call it, so taken from
38:26Wikipedia, a transducer is a device that
38:29converts one type of energy to another.
38:31So here we're converting temperature
38:33into a voltage. And this is this would
38:36be something that would be get pulled
38:38out of a data sheet. So you would buy
38:40this temperature sensor here and you
38:42would look at the data sheet and they
38:43would have this graph here. And then you
38:46would have to use this graph in order to
38:48figure out what your code is actually
38:50going to do with this voltage value
38:52because we have to convert that voltage
38:53into a temperature. Temperature is what
38:55we're trying to get here. So that's
38:57what's actually useful. But we would
38:58need to convert it first. Okay? And so
39:01you would go into the data sheet, you
39:02would see something like this. Hopefully
39:05they give you an equation and then you
39:07can put that into your software for it's
39:10really important you guys know how to do
39:12this because it's going to be on the
39:14midterm. So definitely something like
39:15Oh, everyone. That was crazy. I said
39:17midterm and everyone's head just like
39:19went up. That was crazy.
39:23Okay. [laughter]
39:28Um Okay. So, I'm going to have you do a
39:30worksheet, okay? And I want you to
39:32answer these four questions
39:35um using the information that you have
39:36on this slide.
39:41Go.
39:43Go.
39:45>> [snorts]
39:45>> Yep.
40:00>> Thank you.
40:01>> Yeah.
40:06>> Here you go.
40:09>> Here you go.
40:21I mean this is the first
40:38you
40:56Pass those down.
41:15Thank you.
41:15>> Yep. No problem.
41:25>> Yep.
41:31Here you go. Here you go, guys.
41:41terrorist.
41:45>> Mhm.
42:08I'll pass this down.
42:21>> Yep.
42:22Those are good.
42:26Yep.
42:36>> [sighs]
42:46>> Yep.
42:55>> [clears throat]
42:59>> Yeah,
43:05>> there's three. I think
43:09>> you're not in this class.
43:13>> I heard you were giving. [laughter]
43:16>> There you go.
43:20I think you can just count.
43:24>> That should be three. If not, let me
43:26know. There you go.
43:34>> Yep.
43:42>> Very good at this.
43:58I might have given you too many.
44:02>> Good.
44:06Right.
44:12I miss anyone?
44:31He's
44:58a one status.
45:0712 something.
45:39Yeah.
45:48[snorts]
45:56Whatever.
46:05Good morning.
46:31>> [clears throat]
46:44>> I think
46:46I
46:58The only thing
47:12I like.
47:38Oh yeah.
47:41>> Yeah.
47:56Sorry guys.
48:28>> [clears throat]
48:33>> Yeah,
48:35there you go. Yeah.
48:48I should have
48:52second
49:07and Like I was
49:18thinking,
49:36you know, I
49:38teasing me.
49:59Let's do that.
50:05[clears throat]
50:07Does anyone need help and want me to
50:08come by?
50:10>> Anyone? [clears throat]
50:33>> Yes.
50:36>> [clears throat]
50:39>> As far as like the step size, that part
50:41I think made sense. It's just the same
50:43process of doing like 3.3 over.
50:49>> Yeah.
50:50>> And then actually going from like the
50:51transfer function part are is that
50:54should we be like then using this
50:57>> or I'm kind of confused.
50:59>> But you also have to use this, right?
51:01>> Is that to get
51:05So what what your alult your ultimate
51:07goal is to take think about the software
51:09that you're going to write, right? So
51:11the software is going to output an ADC
51:13value and this is an integer between 0
51:17and 2 to the n minus one.
51:19>> Yeah.
51:20>> Uh so that's what my ADC is going to
51:21output. I want to take that value and I
51:25want to convert it into a temperature.
51:26Let's say this is a lab, right? And we
51:29want to put temperature out on the
51:31terminal. Okay. Yeah.
51:33>> So, we have an So, we have this equation
51:36is how we take um an ADC value. Well,
51:41you'd have to flip it. This is how you
51:42take an ADC value and turn it into a
51:45voltage or the other way around. You
51:47take a voltage and turn it into an ADC
51:49value.
51:50>> Okay.
51:50>> Okay. And this is an equation that takes
51:53a voltage and turns it into a
51:56temperature. So if you can combine those
51:58together,
52:01I can take an ADC value, convert it into
52:04a voltage, and then convert it into a
52:06temperature.
52:07>> Okay.
52:08>> Okay. So I Okay. So I originally I was
52:12kind of on that track, but I guess I
52:13then I missed this aspect of actually
52:15getting the
52:24>> Yeah. Keep thinking about it. You're
52:25good. All right.
52:28Yeah.
52:31[clears throat]
52:35>> Yeah.
52:38>> Almost like reverse engineering it like
52:40we're giving we're given an ADC value
52:42and we kind of go backwards and see okay
52:44what's the temp that gave this
52:45>> and then what would the temp be that
52:47gave that.
52:48>> Yep.
52:48>> Okay. And then for four for the same
52:50thing frequency like I'm obviously
52:51thinking of like Nyquist. Um, but like I
52:54guess I don't know how we get a
52:55frequency out of just like
52:59>> you don't you have to think about the
53:00application.
53:02Think about why you would want to use
53:04this temperature sensor and what
53:06sampling frequency you would want to do
53:08based on what I'm using it for. And we
53:11didn't really give you that much
53:12information.
53:12>> So is it possible that people get
53:14different answers?
53:15>> Oh yeah.
53:15>> Okay.
53:15>> Yeah.
53:16>> So it's kind of just like
53:17>> Yeah.
53:19>> Yeah. Think of a use case where you
53:20would use a temperature sensor and then
53:22tell me what you think that sampling
53:24frequency is.
53:31>> Yep.
53:40>> How we doing?
53:46>> I think we're figuring it out. Okay.
53:58>> How do you already get How did you
53:59Where's your work?
54:01>> You did this all in your head.
54:03>> Oh, well, I used a calculator.
54:05[laughter]
54:07>> Dang. Okay, man. These calculators must
54:10be advanced now, huh?
54:12>> So, I guess we can use like
54:13>> I mean, is this looking correct? Because
54:16this is just
54:17>> I mean,
54:20Oh, no. That's not right.
54:22>> Okay. [laughter]
54:25>> Well, maybe it is.
54:27>> I don't know.
54:29>> Um, what are you trying to do here? So,
54:31you're trying to get a temperature X.
54:33What is X here?
54:34>> Oh, that is
54:36the ADC value. Sorry.
54:45size
54:46>> it might be right
54:48>> but
54:50>> I don't know
54:51>> I don't have it memorized so
55:28>> Yeah.
55:38>> Hey, how you guys doing?
55:41>> Little confused.
55:42>> Yeah.
55:43>> Okay.
55:43>> For the first part, is it is the right
55:46do like 3.3 / 2 to 10us for the first
55:49part. Okay, for the second part we were
55:53just talking about would we rearrange
55:55this?
55:56[sighs]
55:59>> Um,
56:01yeah, that that could be a Yeah,
56:04>> basically what we're trying to do is
56:05we're trying to take
56:07um
56:10>> we're trying to take a a temperature and
56:13figure out what the resulting Well,
56:15actually the other way around. We're
56:16trying to take an ADC value. We're
56:18trying to figure out get an equation
56:21that would actually tell us the
56:22resulting temperature.
56:25>> Oh, I see.
56:27>> So, if we rearrange this so you can
56:42>> Yeah. So if you go uh one slide back,
56:47these equations here, that's a way to
56:49get an ADC value with a voltage, right?
56:52And this equation right here gives us a
56:54voltage. So we could plug that into
56:57there. But this one is taking it the
57:00other way around. It's taking a voltage,
57:02converting it to an ADC value. We need
57:03to take an ADC value and convert it into
57:06a voltage and then convert it into a
57:08temperature.
57:39The sample your You're asking what the
57:41answer would be for four.
57:43>> I'm guessing like are we like do we just
57:45base it off the output frequency of the
57:47temperature sensor?
57:48>> We don't know the output frequency of
57:50the temperature.
57:50>> So I have to figure that out without
57:52knowing.
57:52>> It could be could be infinite kind of. I
57:58guess you have to think about your use
57:59case. What would you use a temperature
58:01sensor for?
58:03>> Maybe like I don't know if you like
58:06temperature maybe. How often would you
58:08need to sample if you were doing room?
58:10>> Barely. Maybe once every like half an
58:12hour or something.
58:13>> Yeah. Well, probably every minute. I
58:16mean, a thermostat will probably do it
58:18once a second.
58:19>> Oh, really? It's pretty fast.
58:21>> Yeah. Yeah.
58:22>> Okay. So, like a use case.
58:23>> Yeah. Yeah. I think about a use case.
58:25Yeah.
58:25>> Can I ask you a prelab question?
58:26>> Yeah.
58:27>> I was working on the prelab
58:29>> for seven
58:31>> or six.
58:32>> For six.
58:33>> Okay.
58:36I was going to say I just posted seven.
58:37Yeah, you you're on it.
58:54>> Um, not whether or not you need to pay.
58:56Well, I don't I have no idea if ST paid
59:00for these addresses,
59:01>> but they basically have two addresses.
59:03Yeah.
59:04>> And they use a pin on the micro or on
59:07the accelerometer to choose between
59:09those two addresses.
59:12>> Okay. So, they decided that because I
59:15might want to put two of these on a PCB
59:17for some reason, I'm going to give the
59:20user the option to have two addresses.
59:23And the way that they can choose between
59:25those two is they can use this extra pin
59:28that we added to the device that you can
59:30set either high or low. And that will
59:31change the address of the device.
59:34>> So we we would write to the like GPIO
59:37pin connected to, right? Not to the SA.
59:40>> Uh do we
59:42>> Well, you you don't even have to connect
59:43that to a Are you asking if you connect
59:46SA to a GPI open?
59:48>> Yeah. Is that how
59:49>> you could, but or you could just connect
59:51it to ground or VCC? You don't even have
59:53to connect it to your microcontroller.
59:55>> I you probably are just going to keep it
59:57at one value, right? So just connect it
59:59to either ground or VCC.
1:00:01>> Oh, then wait what would drive the data
1:00:03line then?
1:00:04>> The data line is your other those are
1:00:06different uh wires. Those are your SCCL
1:00:09which is your clock and your SDA.
1:00:11>> So those two wires are where what the
1:00:13data is actually going to be. This is
1:00:15just like an input into the chip to to
1:00:17tell the chip which address it should
1:00:19have.
1:00:21Like I could get rid of that completely,
1:00:23that pin, and just design the chip to
1:00:27not have it, and just have a fixed
1:00:28address, one address, and then I
1:00:31wouldn't even need a pin like that. But
1:00:32they decided they want two addresses.
1:00:35>> And so they gave you a pin to select
1:00:37which address you actually want.
1:00:41>> But
1:00:43to actually like address the registry,
1:00:45we use the sub address. So why do we
1:00:48need this address? No, no. There's the I
1:00:51squared C address and then there's the
1:00:53sub addresses. The I squared C addresses
1:00:55if I have multiple sensors on I squared
1:00:57C bus. They all have different
1:00:59addresses. Okay, so I need to first send
1:01:02that address to let the bus know who am
1:01:04I actually talking to. Maybe I have 10
1:01:06different sensors on this bus. They all
1:01:08have different addresses. I first need
1:01:10to send that address to be like, hey, I
1:01:11want to talk to the accelerometer. Then
1:01:13once I'm actually talking to the
1:01:15accelerometer, that's where I start
1:01:16sending the sub address, which is the
1:01:19address of the registers inside of the
1:01:21accelerometer.
1:01:23>> Okay.
1:01:24>> So it's two separate addresses.
1:01:27>> Oh, so I send the
1:01:30like S0 connected ground.
1:01:37>> Yeah, makes sense.
1:01:40>> I might have to
1:01:41>> Oh, yeah. We we can talk after lecture
1:01:43here. Okay.
1:01:56>> All right, let's go through these
1:01:59answers.
1:02:02Um, I got to find the slide.
1:02:13Okay, let's start with the first one.
1:02:15What is the minimum step size of this
1:02:17ADC? Who's got the answer? Yeah.
1:02:29>> Is [clears throat] that what you got?
1:02:31>> Okay. So, it should be pretty intuitive.
1:02:33I have a voltage range. We told you that
1:02:36the voltage range is between 0 and 3.3.
1:02:40We need to divi to to divide it by the
1:02:42number of like steps we have in our ADC.
1:02:45So it would be 3.3 divided by 2 to the
1:02:4910. That's how each how big each step
1:02:52is.
1:02:53Okay, this is one of those things that
1:02:56you should just you should just be able
1:02:57to intuitively know without knowing the
1:03:00equation. Technically, we should have
1:03:02put that minus one there, but we didn't.
1:03:06All right.
1:03:08Oh, before I go through that answer. All
1:03:10right. What is the answer to this one?
1:03:12Well, I guess was that the answer?
1:03:15I think that No, no, that was not the
1:03:17answer. What's the answer to this one?
1:03:20There should be an equation that's going
1:03:21to take basically a ADC value. So, a
1:03:25value between 0 and 4,95.
1:03:30It's going to take that value and
1:03:32convert it into a temperature. Yeah.
1:03:43>> USUS 0.96
1:03:48>> maybe. [laughter]
1:03:51Let's go through it and you can tell me
1:03:52after we go through the whole thing if
1:03:54this is what you had. All right. So,
1:03:56let's kind of do it step by step.
1:03:58Um,
1:04:00I don't have the answer in front of me.
1:04:01That's why I can't tell you whether that
1:04:03was I don't even know why I asked you
1:04:04because I can't even verify it. But
1:04:06we'll find out if that you were right.
1:04:08You already told everyone what it is. So
1:04:10hopefully you were right. Okay. So first
1:04:12we have this equation here. This is what
1:04:15we were just given right here. This is
1:04:18what that is. So we have a temperature
1:04:20and then we plug it into this equation
1:04:22and we get a temperature or sorry we
1:04:23have a temperature. We plug in this
1:04:25equation. We get a voltage. Okay? That's
1:04:27what's being outputed by our sensor.
1:04:30Okay. And then here is the equation to
1:04:33figure out what that what a voltage
1:04:36would be converted into as an ADC. So
1:04:39these are two separate equations. Okay,
1:04:42does this kind of make sense? This is
1:04:46the voltage that we're measuring and
1:04:48then the range that we're measuring
1:04:51over. So we're measuring between 0 and
1:04:533.3 volts. If we we're getting basically
1:04:57a ratio there, right? If I have a low
1:04:59number here, I'm going to get a low ADC
1:05:02value. If I have a high voltage, I'm
1:05:04going to get a high ADC value. So, we're
1:05:06going to take that ratio and then we're
1:05:08going to multiply it by 2 to the n.
1:05:10That's how many steps we actually have.
1:05:11And so, then that will give us that
1:05:13integer value that we that our ADC will
1:05:17will output.
1:05:19Okay. So, we have those two equations.
1:05:21We basically just need to combine those
1:05:22together. So, we'll take this voltage
1:05:25that we're actually getting from the
1:05:27temperature sensor and plug it into this
1:05:29equation right here. And so, then we got
1:05:31this.
1:05:33And then because we don't actually want
1:05:38um temperature or we actually don't want
1:05:40ADC counts. We want the temperature
1:05:43based on the number of ADC counts we
1:05:45have because that's what our software is
1:05:47actually going to have access to. Our
1:05:49software is going to see the number of
1:05:51ADC counts and it's going to convert
1:05:54that into a temperature. That's the goal
1:05:56of what we're doing here. And so this is
1:05:58the equation that we actually need. And
1:06:00if we plug in more numbers into here, so
1:06:03VREF, that's going to be 3.3, right?
1:06:06That's our range of voltages that our
1:06:09ADC is set up to measure. And then 2 to
1:06:12the N, that's how many steps we have.
1:06:15Okay? And then you do some algebra here
1:06:17to figure this all out.
1:06:20I'm glad it's already done for me
1:06:21because I would struggle. And this is
1:06:24the final equation.
1:06:26If we do this division stuff here, this
1:06:28is what we actually get. So this is the
1:06:30actual answer here. We take these ADC
1:06:33counts, we multiply it by this number,
1:06:35and then subtract this number, and that
1:06:36will give us the actual temperature that
1:06:38we're trying to measure. Did anyone
1:06:40actually get that? Did you get it? No.
1:06:42[laughter]
1:06:43Okay. Does it make sense how we got
1:06:45there though? Do you think you could do
1:06:47this on an exam where we could give you
1:06:49a temperature sensor? We often do that.
1:06:51We always pick temperature sensors for
1:06:53some reason. We could give you that
1:06:54temperature sensor and then you'd have
1:06:56to write CC code that would take that
1:06:58ADC value and convert it into a
1:07:01temperature
1:07:03think so is it do all of these steps
1:07:05kind of make intuitive sense why we did
1:07:08it? Yeah.
1:07:18Yeah, it's like the measured voltage.
1:07:20It's the voltage of the sensor. Voltage
1:07:23T is for the temperature sensor.
1:07:29>> Say again.
1:07:34>> Well, no. It's just like we're we're
1:07:36going to take a measurement. It's going
1:07:38to be one just measurement. It could be
1:07:39anything between
1:07:41Well, it could be anything between this
1:07:44range right here. So, 8 volts to 1.3
1:07:48volts.
1:07:49Anywhere in between that. If we plug
1:07:52that into our equation, the resulting
1:07:55uh after plugging in this equation, we
1:07:58should get the temperature down here.
1:08:00Does that make sense?
1:08:03>> Yeah.
1:08:08Um
1:08:09technically yeah but we are um
1:08:16I don't think it really matters in this
1:08:17scenario. Do we actually have to do
1:08:19that? Do we need to floor it anywhere?
1:08:23Because we're dealing with such a high
1:08:25resolution. I don't really think it
1:08:26matters. Okay. the the error that you're
1:08:29going to get between flooring it and not
1:08:30flooring it is like point something 01
1:08:35temperature or whatever something like
1:08:36that. Okay,
1:08:39any other questions?
1:08:44Okay, let's go on to the third question.
1:08:48Okay, so what is the ADC value for
1:08:51temperature of 50° Celsius?
1:08:55Did anyone get it?
1:08:58Yeah,
1:08:59>> I got 361.
1:09:00>> 361. Let's see if you're right.
1:09:04I'm just going to skip ahead. Let's see.
1:09:06361. You got it right. All right, cool.
1:09:09All right, let's think about how this
1:09:11works. And I already kind of forgot, so
1:09:13I got to think about it more. All right,
1:09:15so here's our equation that gives us the
1:09:19uh voltage and temperature, right? Okay,
1:09:22that's this equation here. And then we
1:09:24divide it by the reference. So for our
1:09:26our reference is 0 to 3.3 volts. So we
1:09:29would have 3.3 here. That's giving us
1:09:31that ratio again. Okay. Then we multiply
1:09:34it by the number of steps. And then
1:09:37that's our ADC. So we got 3.3. We got
1:09:4050. That's our temperature.
1:09:43361 is the value that our ADC is going
1:09:47to output. Okay. Does that make sense?
1:09:50Let's kind of think about it.
1:09:52Um, so if we plug
1:09:56uh that temperature into here, we're
1:09:58going to get a voltage of 16.
1:10:02And if we look at the graph, yep, that
1:10:05makes sense. Okay, so that's always a
1:10:08good way to kind of check things like
1:10:10plug in all plug it just pick some
1:10:11random numbers, plug them in there, look
1:10:13at the graph, does it actually work?
1:10:16Okay, yeah, we're probably doing
1:10:17something right here. Okay. And then the
1:10:19last question, what sampling frequency
1:10:22should we use
1:10:24for this? Does anyone have an what would
1:10:27you use? There's really no correct
1:10:29answer.
1:10:31>> Does anyone have have a guess? You can't
1:10:34be wrong. Well, maybe. I guess you could
1:10:36be a little bit wrong.
1:10:38>> Yeah.
1:10:44>> Yeah.
1:10:47>> Yeah. That really depends on your
1:10:48application. If I have a thermostat,
1:10:51maybe I want to just sample it at one
1:10:53hertz, so once a second. Okay, we might
1:10:56want to be careful about our filtering,
1:10:58right? We're really we're sampling
1:11:01really slow. So maybe we want to take
1:11:04multiple samples and average them
1:11:05together. Maybe we want to put some kind
1:11:07of filter in there. Although a filter at
1:11:10one hertz is pretty crazy. Um, so yeah,
1:11:13it could really be anything. What if I
1:11:14had a temperature sensor though inside a
1:11:18GPU die? Right? You they actually have
1:11:21temperature sensors in there. I don't
1:11:22know if you've ever looked at if you've
1:11:24ever done some gaming and you're looking
1:11:26at your GPU and what temperature it's
1:11:28at. It'll tell you what it is, right?
1:11:30And it's got a bunch of fans on there.
1:11:32Well, that thing has to be sampled
1:11:34really quickly because that thing that
1:11:36temperature sensor is making sure that
1:11:38your GPU isn't going to catch fire and
1:11:41um and just melt, right? So it's going
1:11:44to actually throttle down the frequency
1:11:46of the GPU in order to not go above a
1:11:49certain temperature. So that might be an
1:11:51example where we need to sample at a
1:11:53much higher rate. Okay, with a
1:11:55temperature sensor.
1:11:58All right, so one last thing I kind of
1:12:00added this slide because I think it's
1:12:02kind of important and it's about
1:12:04measuring resistance and measuring
1:12:06current.
1:12:08So my question to you is how could So
1:12:11we've been talking about ADCs and it
1:12:14seems like the only thing that they can
1:12:15actually measure is voltage and that's
1:12:17true. Just by themselves they can only
1:12:20measure voltage the way that they're
1:12:21designed.
1:12:23What could we do to measure resistance?
1:12:25A lot of sensors out there and a lot of
1:12:27transducers,
1:12:29they actually output a resistance
1:12:32instead of a voltage. Okay? Like
1:12:34temperature sensors, a lot of them,
1:12:35that's how they work. It's basically a
1:12:37resistor. As it gets hotter, the
1:12:39resistance goes up. Or if it gets
1:12:41colder, the resistance goes down. How
1:12:44could we measure resistance with an ADC?
1:12:47Yeah.
1:12:57like that.
1:13:00You have the right idea. Yeah.
1:13:08>> Yeah. But draw the circuit out for me.
1:13:11How do I How does the vol where am I
1:13:13actually putting volt? You're not in
1:13:14this class, but I'll let you answer.
1:13:24>> Yeah. Does everyone know what a voltage
1:13:26divider is? Yeah, you're going to
1:13:28definitely need it for next lecture.
1:13:30Okay, it's really important that you
1:13:32understand what a voltage divider is.
1:13:34There's a very simple equation for a
1:13:36voltage divider. That's what it is. And
1:13:38basically what it is, you take two
1:13:39resistors and you have a voltage at the
1:13:42top, you have a voltage at the bottom.
1:13:44Usually, it's ground. And then there's a
1:13:46voltage in the middle and you can plug
1:13:48in your resistance values. Actually, I
1:13:51think it's this one right here. You can
1:13:52plug in those resistance values,
1:13:55multiply it by the voltage that you're
1:13:57supplying to this whole circuit, and it
1:14:00will output a voltage here. Okay? And so
1:14:02this, if I know the resistance of one of
1:14:06these, then I can just use this equation
1:14:08to solve the resistance of this if I
1:14:12know what this voltage is. Does that
1:14:14make sense? You're going to be doing
1:14:16this in lab, but it's really important
1:14:17that you understand that for ADCs
1:14:20because there's a lot of voltage uh
1:14:22dividers in ADCs and DAXs.
1:14:27All right, one more question. How can we
1:14:29measure current? It's kind of a similar
1:14:31idea. How do we typically measure
1:14:33current in circuits? Does anyone know
1:14:35like what the go-to method is? Yeah.
1:14:45Yeah. Why do we want it to be really
1:14:46small?
1:14:51>> Exactly. Yeah. We want it to be really
1:14:52small because uh we don't want to
1:14:55basically dissipate a bunch of heat out
1:14:56of this resistor and we don't want to
1:14:58impact whatever else is using that
1:15:00current. And so what we could use is
1:15:02something called a shunt resistor.
1:15:04And um
1:15:07how that works is you take a really
1:15:09small it's actually physically big
1:15:11because it's usually putting a lot of
1:15:13current through it but it's a small
1:15:15value and if we know that value it's
1:15:18usually very precise we can measure the
1:15:20voltage drop across it as the current
1:15:23flows through it and then we can measure
1:15:24that voltage drop plug it into our ADC
1:15:27and that's how we measure current.
1:15:30Cool.
1:15:31All right. One thing, I didn't do this.
1:15:33This is all professor sample. I'm going
1:15:35to kind of ex try to explain what he was
1:15:37doing. It was kind of cool, actually.
1:15:39Um, I hadn't watched this lecture
1:15:41before, so this is all new to me. But
1:15:43what he did is at Disney, he created
1:15:46this this watch that could detect what
1:15:49you were touching, which was kind of
1:15:51crazy. It's kind of magical. Um,
1:15:55so how does it work? So, we kind of have
1:15:58to understand what EMI is. So every
1:16:00electro mechanical device has something
1:16:02called EMI. Electroch or electromagnetic
1:16:07interference that it outputs. Okay? So
1:16:10your phone has some EMI. Um anything
1:16:13that's really electronic is going to
1:16:15have some kind of EMI that it outputs.
1:16:17Okay? And when you're designing a phone
1:16:20for instance, you have to make sure that
1:16:21the EMI that this thing outputs is not
1:16:24out of spec. there's something called
1:16:26the FCC and they really don't want
1:16:29random uh radio frequencies getting
1:16:32outputed out into the air. So, they have
1:16:34requirements on what this thing can
1:16:36actually output as far as EMI. And so,
1:16:39in order to uh make sure that your
1:16:41device isn't outputting those
1:16:43frequencies, you would take it to one of
1:16:44these chambers. It's kind of similar to
1:16:46those chambers for audio where you do
1:16:48audio recording. This is for radio uh
1:16:51frequency stuff. And those walls will
1:16:54actually absorb reflections,
1:16:56uh, radio frequency reflections, and
1:16:58they have this really fancy yaggy
1:17:00antenna, and you point it at your
1:17:02device, and you get the plot that looks
1:17:04like this. And you need to make sure
1:17:06that all of those frequencies are below
1:17:08the required uh uh requirement from the
1:17:11FCC.
1:17:14Okay. And so this is what the watch that
1:17:16they kind of made, this wristband. And
1:17:18so you would wear this thing, and it
1:17:20basically has an ADC on there. So, we
1:17:22got a Cortex M4 just like what you guys
1:17:24are using. Has an ADC on the the thing
1:17:28and as I touch something, that EMI is
1:17:31going to travel through my body and then
1:17:32go to this watch and this watch is going
1:17:35to actually measure that EMI. Okay? And
1:17:38what they found is that every device has
1:17:41its own kind of unique EMI signature.
1:17:44Okay? So, if I'm touching my my laptop
1:17:47and touching my phone, they have
1:17:48different signatures. Okay? Okay. And
1:17:51this is what they kind of found. They
1:17:52found all of these different devices.
1:17:54They actually classified all of these
1:17:56and they looked at, okay, well, this is
1:17:58like for for that ADC, this is what a
1:18:01power drill looks like. This is what a
1:18:02motorcycle look looks like. You see the
1:18:04motorcycle is really noisy. Probably the
1:18:07spark plugs or something.
1:18:09Um, and so how it works is a bunch of
1:18:14filtering that I don't really
1:18:16understand. They take some
1:18:18environmental. So they take b like
1:18:20basically a base reading and then once
1:18:24you start touching something they kind
1:18:26of subtract all that environmental EMI
1:18:29from the signal just that's kind of like
1:18:31the background noise. We need to get rid
1:18:33of that first and then they plug it into
1:18:36all kinds of crazy stuff and then they
1:18:37do some machine learning where they
1:18:39actually take that that signature and
1:18:42they figure out what it actually is. And
1:18:45so here's a video of them demoing this.
1:18:48So, he did this with some students
1:18:51and you can see it's really it's pretty
1:18:53quick. Like the second you touch
1:18:55something, it just immediately knows
1:18:56what you're touching. And I think the
1:18:58use case was I don't know like let's say
1:19:01you lost your phone. Maybe it would be
1:19:02useful to know when was the last time I
1:19:05was touching my phone.
1:19:07And so we got a sander, a 3D printer,
1:19:13drill,
1:19:15and then the the one unique story he
1:19:17told is um so at the end of this they
1:19:21touched a ladder. Why would a ladder
1:19:24have EMI? Does anyone have a guess?
1:19:27Yeah,
1:19:29>> because it's an antenna. So, it the
1:19:31ladder actually had some kind of uh some
1:19:34country station radio signals on it, and
1:19:37that's what they were actually picking
1:19:38up because it's this ginormous piece of
1:19:39metal picking up as an antenna.
1:19:44All right, I'm going to just skip
1:19:46through that, but you can look through
1:19:47that if you're curious. Maybe ask him
1:19:48some questions. But just to summarize,
1:19:51we did some we talked about sampling
1:19:53today. We talked about quantization.
1:19:55That's where we're converting digital or
1:19:58analog into digital.

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