YT YouTube2Text

YouTube2Text → Transcripts → EECS 373 - Fall 2026 - Lecture 15: "DACs"

EECS 373 - Fall 2026 - Lecture 15: "DACs" — Transcript

by Interactive Sensing and Computing Lab · 11,232 words · 1,793 segments · language en · Watch on YouTube

Open in transcriber Summarize with AI Download SRT/VTT

Full transcript

0:00All
0:02right.
0:12All right, we're going to get started.
0:14Let's see here.
0:17All right, so
0:19I talked to almost all of you. 30 groups
0:21is a lot. We saw some more
0:23group discussions to go through,
0:26but because we changed schedule around a
0:28little bit
0:30Project
0:31revisions are due on Friday. Please
0:34label your revised project proposal as
0:37revision so we can look at the delta
0:39between the first and the second. You're
0:40only really graded on the second and
0:42really the purpose of the project
0:44proposal is to force you to think
0:46through all the pieces of your project
0:50and kind of get your head around the
0:51scope.
0:52The thing I want you all to think about
0:54in the like the next week or so is
0:57and maybe next two weeks is really you
0:58need to
0:59You have a very vague notion of some
1:01aspects of your project and you need to
1:02start getting line of sight on them and
1:04understanding how complicated they are.
1:07How does it really work? If you can't
1:09gauge how much work is ahead of you,
1:11you're in a lot of trouble. So if maybe
1:13you have lots of questions about how
1:15your wireless module is going to work
1:16and it feels like a opaque black box and
1:18it's horrible, right? Like it's just
1:19complete unknown. You don't know
1:21anything about RF, well start doing some
1:23research online, get the parts, go talk
1:25to James, go talk to me or the IAs and
1:28get that information so it's not
1:29overwhelming so you know like how much
1:31work is it going to take to get that
1:33done.
1:34I worry when there's unknowns in your
1:36mind and then you get to like a week
1:38before the deadline and you just haven't
1:39even started it. That's usually a recipe
1:41for disaster.
1:44Okay.
1:46Oh, anyways, yeah. So the revised
1:47version put it in your project folders.
1:50Homework 7 is due on Monday. It's going
1:52to be on DAX.
1:56And then the homework solutions for
1:59homework 7 were released today and
2:00there's um
2:02uh practice exams online uh right now.
2:06And we have our fi- second fi- or second
2:08midterm uh next week, so a week from
2:11Friday in Dow. I promise I will actually
2:15check it to see if you can complete it
2:17on within the scope of the time.
2:19I'll even ask other people to check it.
2:22I mean we all uh
2:24uh not all the IAs got to look at it,
2:25but me and um
2:26James did and uh I think we just made it
2:29a little bit too long.
2:30Uh it's going to be the same kind of
2:31format. You'll get a data sheet, maybe
2:33that Wednesday beforehand. We'll have a
2:35review time in class where we'll go over
2:38the data sheet. We'll do a review of the
2:39exam. So, it shouldn't be very different
2:42from what you're already seeing um
2:46uh on your practice exams.
2:47Any questions so far?
2:53Uh and then next week after the exam,
2:55we're going to do student presentations,
2:57so there's documentation should be
2:58posted online. Um basically, these are
3:01you will come up for
3:03haven't figured exact time, but say 12
3:05to 15 minutes. Your team will talk about
3:07some piece of technology. So, this is an
3:08opportunity for you to deep dive, learn
3:11about some piece of embedded systems,
3:12then you will present to the rest of the
3:13class, so the rest of the class will
3:15learn about uh that piece of embedded
3:16system. So, an example would be how does
3:19XB work? So, a lot of people have
3:20wireless on their uh projects. Uh so,
3:23having a team describe how to interface
3:26with XB and get it working is benefit
3:28for the entire group or of entire class,
3:30so we'll probably have that team go
3:31earlier. And if it's I know there's a
3:33team that's going to use like a magnetic
3:35strip reader. Not many people are going
3:36to use that. It's still good knowledge
3:37to know, so we'll probably have that
3:39person go in the end. So, it's twofold.
3:41First, it helps you as part of your
3:43program requirements, uh present, uh you
3:45know, get feedback on presenting skills.
3:47Um it also helps teach the rest of the
3:49class about some nuanced piece of
3:52hardware.
3:53Um I typically assign topics based on
3:57your project proposals trying to load
3:58balance across um
4:01uh
4:02you know, all the teams not everybody
4:04can obviously do wireless, uh but try
4:06and load balance against the projects.
4:08Um
4:10if you're if you get assigned a topic
4:12and it seems completely weird, like
4:13that's not part of your project, just
4:15let me know.
4:16And then I and James will do practice
4:18presentations with you. We you'll come
4:19for like 15 minutes and just give it
4:21give it a practice talk and we'll give
4:23you feedback on like how to improve it,
4:25uh how to make it better for a general
4:26audience, all those sorts of things.
4:28And then while you're doing practice
4:30talks, man you know,
4:32uh attendance is required and you will
4:34be your there will be a peer grading
4:36component to this. Well, people will be
4:37voting, ranking, and those sorts of
4:39things and giving feedback. Um
4:42yeah, any questions?
4:48Oh.
4:49Okay.
4:51And so as you can see, we're getting to
4:52the end of the semester. Things are
4:54going to change, so we got our midterm
4:55coming up next week.
4:57Do a little bit of PCB design, some
4:59extra work, and then it's student
5:00presentations. And then I'm not exactly
5:03sure when the presentations are going to
5:04start stop. I haven't uh filled out the
5:06entire schedule.
5:08But uh after at least after
5:10Thanksgiving, there's no formal class
5:12anymore. This is just dedicated time for
5:14you to uh do your projects. I have
5:17milestone meetings milestone meetings
5:19are typically
5:21uh by request. Either I'm requesting of
5:23you to come and talk to us, or you're
5:25requesting to meet with one of us um
5:27outside of like just uh catch James or
5:29the IAs in the lab. So those are not
5:31inherently mandatory for everyone.
5:34Um and then we have the expo is going to
5:36take it'll be outside of class time.
5:39Um like it'll be on that Wednesday, but
5:40because there are so many
5:42uh students this semester, it's going to
5:44have to start earlier and end later. You
5:46at least need to have somebody there to
5:48man your booth. I understand someone
5:49might have class at a different time.
5:51But uh that's what we're uh we're going
5:53to have to
5:54well, it's going to have to be outside
5:55of class time. We can't just completely
5:57limit it to class time.
5:59All right, any logistics questions?
6:06I'm not that well organized. You must
6:07have questions.
6:12Okay.
6:14All right. So, this set of lectures
6:16we've been talking about
6:18analog trying to get these analog
6:19signals into the digital world and vice
6:21versa. We've talked about analog signals
6:23in general and then ADCs and now we're
6:25going to talk about DACs, which are
6:26digital to analog converters. There's
6:29several different types and then the
6:30specific ones that you have on your
6:32device.
6:33Oh.
6:36Uh there's some good references.
6:38So, DACs, the equivalent mental model
6:40here is, you know, a function generator.
6:43This is going to be able to produce
6:45arbitrary waveforms. That's the goal
6:47under certain limitations. So, you want
6:49a device that is sure can do an like a
6:52digital value. Sorry, not digital value.
6:54Like a analog voltage value, but really
6:56it's more about doing time series
6:58things. So, can you make a sine wave or
7:00a square wave or a triangle wave or some
7:02arbitrary thing? And so, the function
7:04generator you have there is very um
7:07capable,
7:08but your little microcontrollers are
7:10also pretty capable in the sense that it
7:12can go up to several megahertz. This is
7:14maybe 20 megahertz is pretty standard
7:16for a cheap benchtop piece of equipment.
7:18And this one will go to like plus or
7:19minus 20 volts. Your little DAC will
7:21only go like plus or minus zero to three
7:24volts or 3.3 volts. So, different in
7:26range and you could probably adjust that
7:28if you had an amplifier on the output,
7:30but
7:31uh that is essentially what your
7:32microcontroller can do is arbitrary
7:34functions.
7:35Um and then there's lots of nuance about
7:37how to get that to work.
7:39Um the other alternative way of looking
7:40at this is just a just a speaker, right?
7:42So, when you think about
7:44uh you know, the headphone jack, all
7:46those jacks and microphone accessories
7:49on your consumer electronics are just
7:50highly optimized ADCs and DACs and
7:53usually they're optimized cuz they're
7:54trying to target specifically the audio
7:57band and how humans hear in
8:01uh sound. So, that that's slightly
8:02different than just an arbitrary
8:03function generator or arbitrary
8:06ADC.
8:08So, as you can imagine, we're
8:09essentially going to be doing the
8:10opposite of an ADC. Here, you're going
8:12to have some digital code, right? Some,
8:15uh, binary values that are going to, uh,
8:17be turned into an analog value. Now, it
8:19should be clear like this is just one
8:21point on that sine wave and you would be
8:23changing that bit value over time to
8:26approximate a sine wave. Uh, it's not
8:27that you just put one value like that
8:29binary code that yields a sine wave. Um,
8:32but that's the idea is you have some
8:34digital input it'll be turned into an
8:35analog output.
8:38Uh,
8:39yeah. Any
8:42questions?
8:44Okay. So, when we talked about, uh,
8:46ADCs, we had all these caveats about
8:49like, "Oh, we had the sample and hold
8:51circuit." We had to figure out why we
8:52wanted to have a sample and hold
8:54circuit. We talked about, "Hey, wait a
8:56second, if it's a really weak signal,
8:58right? Maybe it won't be able to charge
9:00up the input capacitor and we'd have to
9:01have special caveats for that." And then
9:04I said, "Oh, you know, maybe, uh, as I
9:06sample the thing, I'm going to have to
9:08hold it, uh, because the, um, the
9:12conversion process is going to take a
9:13while."
9:14Um, so we have those same sort of ideas
9:17related to, uh, DACs. So, one of them is
9:19loading effects.
9:21So, remember the DAC is trying to drive
9:23a signal outside of the device.
9:25And so, the way to think about loading
9:27effects here are just a simple voltage
9:29divider. Here, we have a a DAC module,
9:31has some finite resistance, and then you
9:34have a load that has some finite, uh,
9:36amount of resistance. And so, ideally,
9:38you would say that your, uh, DAC would
9:39have, uh, zero source resistance. That
9:42would be the best. And it's just not
9:43possible, but that's what you'd want.
9:45And you want your load resistance to be,
9:47you know, infinite, really, really high.
9:49And that would be nice, uh, and then
9:50whatever voltage you put out on the V
9:52desired would be the voltage output. You
9:54can you can look at the math there and
9:56figure that out. Um, but the reality is
9:58that, uh, the load is not going to be
10:01finite. It's going to be some value and
10:03it could be capacitive or inductive,
10:04which would also create, uh, challenges.
10:06So, can you guys take like 30 seconds
10:09and tell me what are some what are some
10:11things that have uh standard loads or
10:13even hard loads to drive?
10:16Take Take 30 seconds, talk amongst
10:17yourself.
10:31>> [clears throat]
10:42[clears throat]
10:55>> What do you think? What would be a load
10:57that you'd have to drive typical
10:58embedded systems with a DAC?
11:07Yeah.
11:08Speakers. What's the resistance of a
11:09speaker typically?
11:164 8 ohms. Yeah, so 8 16. Depends like
11:19home speakers for some reason I think
11:20are like 8 and like car speakers are 16
11:22or something like that. Maybe it's 4 and
11:248. Like you know, it's kind of
11:26surprising. Why are they so low? Well,
11:28they're actually inductors.
11:29Uh there's inductive mode There's an
11:30inductive element that's trying to push
11:32this uh magnet back and forth.
11:34Um what are some But that's really
11:36small, right? So, if you have 8 here and
11:38anything over there, right? You're going
11:40to get a
11:41anything even high, you're going to get
11:43something less than your desired
11:44voltage. Now, you're going to have to
11:45have some amplification. So, imagine
11:47here that our load is very a small
11:49number. Uh
11:51So, okay. So, some standard loads like
11:53just even a GPIO pin on a
11:55microcontroller is like 100k.
11:57Um which is not that bad, but if you're
12:01trying to do some exact measurement,
12:02it's fine. Uh it can be a problem. A
12:05capacitor, anything with capacitance is
12:07hard.
12:08Um so, there's a lot of different loads
12:09that could be a problem.
12:12And so, the way to get around that
12:14is
12:15um you can use a voltage buffer. So this
12:17is kind of like the same topology that
12:19you saw inside a um
12:23uh
12:24the sample and hold circuit. It's just
12:26that here we're trying to buffer the
12:27output. So whatever is there on our
12:29source is that input into V V in is very
12:32very small. So the desired
12:35the drop is going to be zero or nearly
12:37zero cuz there's no current going
12:39through R0. And then the op-amp is
12:41taking the responsibility of driving as
12:43much current as required to drive that
12:45load. So here aside from the
12:48inaccuracies in the op-amp um
12:51uh you're going to get V out is going to
12:52be the same as V in or V desired. So
12:55that's a that's the value of that.
12:58And so we can look at this in like a
12:59little circuit example here.
13:03Let's see.
13:06All right. So here I'm going to vary
13:08these little sliders, vary the value of
13:10these resistors. Is that true?
13:13No. Wait. No, for some reason I'm
13:15varying RS. I don't like that.
13:18Mhm. Well, that gives you example here.
13:20Let's try and do this.
13:23Uh slider.
13:30All right.
13:33It did not work. Oh, there we go. Okay.
13:36R load for both of them. So here as I
13:38change the resistance you can see that
13:39this voltage no matter what this
13:40resistance is is always five and that is
13:43going to be some other value. So here is
13:44this you can see here's the challenge
13:46and it gets much worse if you're trying
13:47to do like an AC signal into a DAC or
13:51into a capacitor. You get some weird
13:53effects or an inductor.
13:56Okay.
13:57Any questions on why you would need a
13:58voltage buffer for an output?
14:02Is this you people you guys remember
14:03this from 215?
14:05Does this seem like intuitive knowledge?
14:09>> [snorts]
14:10>> No? You guys Yeah.
14:12Go ahead.
14:12>> Yes, sir.
14:14What's the reason that we just don't
14:15make the
14:16uh load very high
14:20>> You don't have that option. You're
14:22trying to drive some load. So, if it's a
14:23speaker, right? Um it could be 8 ohms.
14:26You don't have a choice.
14:28Um if you were trying to drive like uh
14:31you don't really drive motors this way,
14:32but I mean technically you could.
14:34There's a lot of weird
14:35um
14:36things. I don't know why I can't think
14:37of any, but like a piezoelectric speaker
14:39is like is a high impedance thing, but
14:41slightly capacitive. And then you get
14:42some a loading conditions.
14:45Um
14:47You could even think of like an LED if
14:48you're trying to do dimming an LED with
14:50voltage, which is probably the wrong way
14:51to do it. You would still have some load
14:53on that that would uh change the output
14:55voltage.
14:59Yeah.
15:06Correct.
15:08Right. That's true. I forgot to tell you
15:09why we care. I just started I I just
15:12knew I cared. I forgot to tell you why.
15:14We're going to spend the rest of lecture
15:15trying to make our desired or the output
15:18of this
15:19uh thing right here. We're going to
15:20figure out all these fancy ways to make
15:22this analog voltage, but then I don't
15:24want to get corrupted by my load. So,
15:26that's why we're putting this buffer in
15:27between.
15:30It's a good question.
15:32Okay.
15:36All right, there's loading effects. So,
15:37let's talk about like the simplest
15:40uh possible analog output. In fact, you
15:42don't even need a full DAC for this. And
15:44this is a great way if you just need to
15:46like add a buzzer to your to your final
15:49project. You're like, "I just need a few
15:51extra points. I don't want to put time
15:52and effort into this. I just want to get
15:54points as fast as possible." This is a
15:55way to do it.
15:57You don't even need a DAC.
15:59Uh like the full DAC on your device, but
16:01it still is a version of getting an
16:02analog output.
16:05So, imagine you have a GPIO pin and
16:06you're just going to put PWM signals
16:08through. You can see here this is like
16:10an RC filter. And so, the idea here is
16:12that you're going to smooth out the um
16:16the high frequency components, leaving
16:18only the low frequency components. And
16:20then you will get over time, you will
16:22get an analog output on average. And so,
16:26um, it would turn into something like
16:27this. This would be a better example
16:29where I have a bit stream going out and
16:31then this is the filtered version. And
16:33you still get some distortion because
16:35basically there's an RC discharge going
16:37on here. And so you're charging up and
16:38discharging. But by varying the duty
16:41cycle, uh, you will be able to uh,
16:44create a very high value or a low value.
16:48So let's see an example of that.
16:52Uh, here.
16:56All right. So here is this something
16:57that makes a square wave or a uh, that
16:59we can change the duty cycle on. And
17:01then this is just an output buffer just
17:02to show that that exists. I didn't put a
17:04load resistor on there. And here's the
17:06filter.
17:07And so if I change Oh, and then down
17:09here we can see the red lines are the
17:12output of the the PWM pin.
17:15Let's say. And then this is Let's see
17:17what's over here. And this is the blue
17:19line down there is the analog output
17:21voltage. As I changed my duty cycle,
17:25you can see that on average that value
17:27raises and lowers.
17:29So here, now I have a higher value. And
17:32this is all I did was change the duty
17:33cycle of something and now I have a
17:34different analog value. And the reason
17:37we have the buffer on there is because I
17:38put any load on the output, right? It
17:40would that resistor that 5K resistor is
17:42very large. So I get a big voltage drop.
17:45And so this is like a very cheap way to
17:46make an analog signal.
17:50And so, that some of the challenges with
17:51this version here is that
17:54um, it's actually fairly slow in a sense
17:56compared to your clock. It makes it have
17:58to have multiple clock wave signals to
18:01change this. So compared to something
18:02that would maybe in one clock cycle be
18:05able to produce an analog output, this
18:07is particularly slow way of doing it.
18:09Um, and there's a lot of there's ripple
18:11on it. And it's hard to reduce that
18:13ripple under all conditions. Maybe
18:14certain certain frequencies,
18:17uh, you could do it well, but certainly
18:18not all possible scenarios Can you get
18:21rid of that signal?
18:26Any questions here?
18:33So
18:34a piezoelectric buzzer would be a great
18:35example here and you'll you won't get
18:37high fidelity sound but you'll certainly
18:39get buzzers and tones if you needed to
18:41indicate something.
18:42Uh
18:44yeah.
18:46Okay.
18:48All right, so that's like the simplest
18:49way and then we can go to some of the
18:51more classic ways of making um
18:55uh resistors. Uh I mean
18:58DACs. So oops, let's go this way. So the
19:03resistor um resistor voltage divider is
19:06kind of like the flash ADC. It's kind of
19:08the inverse. So here we'll have a
19:11voltage ladder and this produces all the
19:14possible voltages. Now if you remember
19:16back to the ADC version this voltage
19:18ladder was the references, right? This
19:20was
19:21if you had a voltage of this particular
19:23value you would compare and see if you
19:26were higher and lower and that would
19:27produce the output. Here you have a
19:29voltage ladder and then you're selecting
19:31which one of those voltages voltage do
19:33you want to have on the output.
19:35So we can take a a look at that.
19:39Oops.
19:47Uh so here we're just going to
19:49have a binary selection. This is
19:51the last version I showed you before it
19:53was there's no decoder but this
19:55structure essentially makes
19:56encoder let's say that we can use to
19:59change my take the binary value into
20:01like
20:03um
20:04one hot encoding space.
20:06And so here I can change like if I have
20:08all the switches are low then I'm
20:11connecting the bottom thing and you see
20:13it's like negative nano volts. That's
20:14just be as kind of maybe the error and
20:16false start but should be effectively
20:19zero and nano volts is zero and then
20:21here I can add in let's do the lowest
20:23bit. I don't know this is the lowest
20:24bit. And then I can add in particular
20:27things in here. Multiple things are
20:28being switched in at once, but then
20:29these outputs are actually uh deciding
20:31what goes in. And so now I can hit my
20:33binary value to hit any one of these
20:36three-bit values here.
20:38And basically all you're just doing is
20:39having a switching network that selects
20:42the voltage is already here.
20:47What questions you have?
20:53Why don't you take a a couple minutes or
20:55a minute to talk amongst yourselves
20:56about the pros and cons and reflect upon
20:59the pros and cons of a flash ADC and see
21:01if those kind of cuz this is like the
21:03mirror image of a flash ADC. So like
21:05what are the pros and cons of this
21:06particular topology?
21:15>> [clears throat]
21:38[snorts]
21:56>> You guys are quiet.
21:58Normally if I give you a chance to talk
21:59like you you can't stop. You're excited
22:01to talk to each other.
22:03Like no.
22:07All right, what's what's the one
22:08advantage of this uh style compared to
22:12uh well I have you haven't seen any
22:14other ones. You saw one other one. So
22:15what's the advantage compared to the
22:16other ADC that or DAC that you saw?
22:26Yeah.
22:28Very fast. You call it a flash
22:30DAC if you want, nobody calls it that,
22:31but it's called a R RC ladder. Um
22:35Uh but yes, it's very flat fast. So this
22:37because, you know, all the values here
22:40are instantly available and all you have
22:42to do is switch between them. There's
22:44not even um
22:45uh just switching delay. There's no
22:47other um there's no comparators even
22:50involved. So it's actually pretty um
22:54power or you don't have the power
22:55consumption of the comparators, just of
22:57the uh resistor ladder.
22:59What else? What are some other uh what's
23:01the disadvantage?
23:04Yeah.
23:09Yeah, so um it's it's it's typically
23:12more like it wasn't manufactured
23:14correctly, that's typically what it is.
23:16And it it still remains hard to get all
23:18those uh voltage steps to be perfectly
23:20accurate. Maybe only with eight
23:22resistors it's not that big a deal, but
23:23you know, if you had um you know, 32 or
23:26128 resistors, okay, it's going to get a
23:28little bit harder. And so you imagine
23:30that if one of them was 99, that means
23:32that little step or you you know, even
23:34smaller, that little step is going to be
23:35slightly different, right? That little
23:37uh step from one binary value to another
23:40binary value, that that voltage step
23:42would be smaller than you would expect
23:43or could be larger. So that's that's the
23:45challenge. Any other advantages or
23:47disadvantages?
23:52Yeah.
23:55That's probably higher power
23:56consumption. I guess we didn't really
23:57talk about we don't have much to give it
23:59an example to, but yeah, you do have to
24:01have um this voltage ladder going, which
24:03may be not that bad um because there's
24:06no other switches or anything. I mean,
24:07the switches are pretty minimal, but
24:09they aren't like comparators and stuff,
24:10but it's not the cheapest. Uh it's
24:12probably also pretty large on silicon.
24:15Uh a non-obvious problem and probably a
24:18problem most embedded people wouldn't
24:19consider because either it's already in
24:21your microcontroller and you don't care
24:22how much how big it is or uh you're
24:25buying an external module and the size
24:26doesn't matter. But I think that would
24:27proportionally say that this topology
24:29could be expensive in this in a sense
24:31that
24:32uh it takes up more area and the area of
24:34your silicon is the the forcing function
24:36for cost.
24:39I don't know. What else is there?
24:40Complexity is relatively simple. There's
24:42not much going on here. So, that's nice.
24:48Okay.
24:49Uh
24:50let's see.
24:53Okay. So, one of the challenge here the
24:55the challenges of this one is now we
24:57have to have um
24:59a switch for every particular value,
25:01right? So, what happens if you wanted to
25:03reduce the number of switches?
25:05Um so, we can think about some
25:08structures.
25:09Um you know, it would be more effective
25:11if we didn't have to do that binary
25:13encoding with those switches if we could
25:14just actually switch the voltage in. And
25:16so, we're going to use an analog
25:17structure to help us and that's the
25:19summing amplifier. Did you guys see
25:21summing amplifiers in 215? Those that
25:23took 215?
25:26Yeah. Okay.
25:28Um really remember this class you don't
25:30have to know anything about analog. I
25:31promise. You just have to have like
25:33basic intuitive knowledge. It sums some
25:35voltages. That's all this thing does.
25:37So, we'll see an example of how does a
25:38summing volt you know, amplifier sums
25:40some voltages? There's an equation here.
25:42It's a gain factor. And then uh the
25:45trick with this topology is that it
25:47gives a negative voltage output. We can
25:49assume that on your devices uh that the
25:52analog engineers have done a good job of
25:54actually producing a positive voltage
25:56output and all the inputs are going to
25:57be negative voltages. It's not that hard
25:59to do all that. It's just the extra
26:01circuitry to demonstrate that to you
26:02would be kind of hard. So, I won't do
26:04that. But, uh you can conceptually see
26:06how it would work.
26:07And so, here
26:09Uh wait a second. Where Oh, you're off
26:11to side. Why? Why?
26:17Come on. Pinch.
26:22Okay.
26:24Um okay. So, anyways, here
26:27Is there a
26:28view fit?
26:32I don't remember.
26:35I don't know. All right.
26:36Well, anyways, uh so here we have some
26:38two voltages and we have the output
26:40voltage and it's just a simply All
26:42right, so I change these two voltages.
26:44Um they happen to be negative in this
26:45example, so we get a positive output,
26:47but you can just see that they're
26:48summing them and here really the trick,
26:50the conceptual trick, is that the
26:52current being driven through this node
26:54here, we can add currents together
26:56easier than you can add voltages
26:58together. So, here we're going to sum
27:00these volt- these currents together. I
27:01have a current that's being defined
27:03going through uh resistor one and
27:05another current being defined going
27:07through resistor two. This node is
27:09always uh uh
27:12uh equal to zero. It's being trying to
27:13be driven to zero. And now this voltage
27:16uh divide or so this resistance divided
27:18by the voltage drop across here defines
27:20the current. So, as I increase my uh
27:23voltage, let's say
27:25or decrease my voltage
27:27uh in this particular case, but increase
27:28the voltage drop across this thing, more
27:32Oh, god, the whole time it was I was
27:34doing so good. I was just in there and
27:37it Oh,
27:38Jesus.
27:41Oh, man, I'm not going to be able to do
27:43that that good again.
27:45Oh, man.
27:48All right, thank you for letting me
27:49know. All right.
27:53One nice guy, the rest of you were like,
27:54let's see how far he can go.
27:57All right. Uh what I want to show you, I
27:59don't know. You guys have to imagine
28:00what I was talking about. Um
28:03Anyways, I changed this voltage in here
28:06and uh you can see the voltage out here
28:08is proportionally changing. Yes, it's
28:10negative, but we're going to ignore that
28:11fact for a second.
28:13And so it's doing the summing action and
28:15the trick, the conceptual trick, is that
28:17it's the current through here is the
28:19summation of the current going through
28:21here and here. And you could have n
28:23number of branches and so the voltage
28:25drop uh the voltage drop across this
28:27thing creates the current and now I can
28:30create different voltage drops because I
28:31can change these voltages.
28:34Let's see like that. And now we see that
28:36it's pulling more current as I increase
28:38this current as I increase this voltage
28:40here or increase the voltage drop, I'm
28:42pulling more current. Yeah, you can see
28:44that there. And so now that value is
28:47larger. So we're going to sum the
28:49currents together. That's the the trick.
28:50That's all you have to remember. This
28:52allows you to have voltage that sums the
28:54current.
28:56All right.
28:58What questions you have?
29:03Okay.
29:06Yeah, ch-ch-ch. So now we can take
29:08advantage of that. So here this is the
29:10R2R ladder. Basically, the idea is we
29:13want to have a voltage ladder that idea
29:17but instead of having lots of switches
29:20or instead of having lots of switches,
29:22we want to minimize the number of
29:23switches. Um and there's good reasons
29:26for that as well. And so here what we're
29:28going to do is we're going to use these
29:30to create different currents of
29:32different proportions. And so uh by
29:35sizing them correctly so we have the
29:36first ladder, all those are R uh value R
29:40and it could be any value R per se, but
29:43say it's like, you know, a kiloohm. And
29:44then all the resistors in this part are
29:472R. And so making resistors that are
29:51uh matched is easier than making
29:53infinite number of values. And then
29:55things that are double are easy because
29:57in layout you would just double the
29:59resistance or double the stack that you
30:00would come up and come down. And so now
30:03you basically have two resistors of R
30:05size just linked together. And so now
30:07these are still structures that are
30:08pretty good at being the same size,
30:10which is nice when you're manufacturing.
30:12The the the errors are a little bit more
30:14tolerable. And so now they're going to
30:16produce different currents through here
30:18and then we're going to
30:19uh sum those switches together. So for
30:21example, you're going to see here this
30:22would be half the current, quarter the
30:24current, eighth, and a 16th. And then
30:26you can walk through this math to kind
30:28of figure out, okay, I can switch those
30:30in. So here's the switching factor say
30:31they're one or zero. And then that's
30:33going going added into my summing
30:35amplifier, which will pull current in
30:37through here.
30:39Okay?
30:42Now, I won't make the same mistake.
30:44Okay.
30:49So, here is that voltage ladder. Uh here
30:52is 50k and 100k, doesn't really matter.
30:54And as you can see, there's actually no
30:56current going through here cuz
30:57everything's disconnected. And if I go
30:59to one of the smaller bits here, I get a
31:02small amount of current coming through.
31:04And you could do it binary style. You
31:06could go one at one at a time.
31:08But then you can also do um
31:11do them together. So, here this is like
31:13a full one, I get -8, and then I can do
31:15a next one, get 12. And so, now this
31:18summation of this current coming through
31:20here
31:21is what's happening. So, it's really
31:23each one of these paths, I don't know if
31:25you can see it. Yeah, I can see these
31:26current kind of creeping through. So,
31:28that's uh the flow you see is
31:30proportional to how much current there
31:32is.
31:33And um
31:35you can see this one is
31:36approximately twice as much as this, and
31:38onward and upward. And so, this is the
31:40way that I can eliminate the number of
31:42switches and have slightly less
31:44resistors to get a analog uh voltage
31:47output.
31:52Yeah.
31:54Sure.
32:03Yeah, you just put some voltage up here,
32:05you mean?
32:06Yeah, you just put some voltage.
32:13Sorry. This This one?
32:21Yeah, I think that is saying Wait,
32:23that's a good question. So, where So, IR
32:26is
32:29How does IR get in here? So, this is the
32:31quarter, half,
32:32uh eighth.
32:36I think IR is this value Oh, no, this is
32:38just a constant, I think, that is in
32:40that formula. I'd have to look through
32:41that.
32:42Did that answer your question? Not
32:43really.
32:46Yeah, I mean, it's just the voltage that
32:48would be coming through
32:51So, what IR So, how do you How is IR
32:53defined in this equation? I I can't
32:54really see.
33:00Yeah, but there's like this constant
33:01offset. I'm just trying to figure out
33:03IRS. This is a good point. Let me Maybe
33:06this diagram doesn't match this math.
33:08Maybe that's the problem. Maybe in this
33:09particular diagram there is this that is
33:12not here. You could have a line that
33:14comes directly to a switch and it's not
33:16divided.
33:18Um
33:19So, yeah, maybe that's wrong. Okay, I'll
33:21look at that. That's good good question.
33:23Yep.
33:24Oh.
33:27All right, so why don't you take a
33:28minute and talk amongst yourselves.
33:30What's the advantage or disadvantage of
33:32this one compared to the other op amps
33:34or sorry, DACs that you've seen?
34:43>> Mr. Harris
35:07>> All right, what do you think? What are
35:08some advantages or disadvantages of this
35:11particular topology?
35:18Yeah.
35:27Uh
35:28so, it's expensive to do this because of
35:29the size of the resistors, you said?
35:34Yeah. Yeah.
35:35Yeah.
35:36Um is it worse in terms of resistors
35:39than it than the for the number of bits
35:41than the ladder that we saw last time?
35:46I think it's slightly better. It's not a
35:48magically better. Slightly better.
35:52Okay.
35:54What are some
35:55um advantages or disadvantages? Anything
35:58else?
36:00Yeah.
36:07Yeah.
36:11Yeah, and it's always in comparison to
36:13other things. So, like all of them you
36:15need to add more resistors, right? So,
36:16like but there is uh inherent issues
36:19with uh some topologies, right? That you
36:21to get to higher and higher DACs is
36:22going to take uh be challenging.
36:25Um and it's also the same for um higher
36:28bits for ADCs.
36:29What's some What's an advantage of this
36:31one?
36:36Yeah.
36:37>> We were saying that the growth is kind
36:39of exponential, though.
36:41For every stage of the ladder that you
36:43add, like you double the number of bits
36:46that you can represent. Like with one
36:49more switch, that's one more bit, which
36:51means that you can
36:52double the information.
36:55So, I think that, you know, in
36:57comparison to just the
36:58resistive ladders I talked about before,
37:00this is a lot
37:02clearer. We're going to have a much
37:03higher performance.
37:04>> Right. So, that is the advantage. The
37:06the penalty is that there's some
37:08issues here with you might have less
37:11linearity because now you have to have
37:13resistors of different sizes.
37:15Um
37:16one of the advantages here is still
37:18pretty fast.
37:20Um we didn't There All the topologies
37:22are actually going to be uh relatively
37:24fast, but there's not it's not like the
37:26you need a lot of acquisition time like
37:28you needed with the SAR ADC where you
37:30had to like search for something. That's
37:32not usually how DACs work.
37:35Okay.
37:39Uh
37:40okay. And then uh the next one is the
37:42binary weight uh uh resistor D uh DAC.
37:47So, this is very similar to the one we
37:48just saw. So, I think the topologies are
37:51kind of confusing.
37:52Um so, here, let's see here. So, the
37:55voltage was here and then you went
37:56through a resistor network and then you
37:58had switches. Not drawn exactly the
38:00same. Here, you have switches, then a
38:02resistor network, and then you have your
38:04output stage. So, slightly switched
38:06things around. Here, the trick though is
38:09I have resistors of different values.
38:11Every resistor is a different value.
38:13Now, it's nice that they're uh you know,
38:15multiples of two of each other. That
38:17makes the layout easier and you can
38:19imagine for for reasons of binary that
38:21that's good. Um but, that does mean that
38:25um
38:26a small error may not be
38:29uh
38:30will be passed on to multiple things,
38:32right? So, let's say the R over 2
38:34resistor is slightly smaller,
38:36disproportionate
38:37uh than the rest of them. That means
38:39that and we're going to reuse that for
38:41every one of the smallest bits. So, you
38:42now you're going to get more error as
38:44you um in every one of your codes or
38:47every fourth code I guess because that
38:50thing is going to be maybe slightly
38:51different slightly weird.
38:53So that that is one of the challenges.
38:54It's more less tolerant to manufacturing
38:57defects, but it's much smaller which is
39:00the benefit.
39:01So let's see.
39:06And you can imagine this not too
39:08surprising again. This is just
39:10making different ways to pull current
39:12through this node and we just generated
39:14different ways of making current come
39:16through these resistors. And so here I
39:19have my switch. Hey, why are you doing
39:20that?
39:22And I'm just basically switching on and
39:23off these resistors, but because they're
39:25all a different proportion of current
39:27coming through them.
39:29I get the benefit here of being able to
39:31create binary values and or use turn
39:34them on simultaneously so I can put a
39:36binary code in here to turn these things
39:38off and on.
39:40>> [clears throat]
39:41>> Okay.
39:44What questions do you have?
39:53And here we just
39:54it doesn't matter if this is inverted or
39:57this is positive like there's lots of
39:58ways to make the chip in this particular
39:59one I just said the input was a negative
40:01reference voltage which it produces a
40:03negative or positive output voltage. So
40:05take 30 seconds and kind of talk about
40:08what's the advantages and disadvantages
40:09of this one.
40:35>> [snorts]
40:50>> Today is the
41:06>> [clears throat]
41:14>> All right, so we already know this one's
41:15going to be fast. They're all fast. More
41:18or less. I mean, we'll talk about in
41:19real world ones their settling time and
41:22your back on your device has speed
41:25limitations. So, as we go to the extreme
41:27of speed
41:28different issues come up. Um but not
41:31from the first order. So, this is just
41:33as fast as the rest of them cuz you take
41:35a switch in one time second or one
41:38clock cycle and then you get the value.
41:40But, what are some advantages or
41:42disadvantages?
41:53Yeah.
41:54>> One thing that we're talking about is
41:55that it might be easier to order a lot
41:57of resistors in bulk, which would occur
41:59in the UGB that we saw
42:01>> Mhm.
42:02>> like, you know, for each stage you have
42:04like a different resistor value. With
42:07each stage you just buy one of the same
42:08resistor.
42:10That was one of the ideas.
42:12>> That's a That's a interesting point of
42:14view. Um and we just to be clear, you
42:16should never build one of these by hand.
42:18That would be an insane process.
42:20Um
42:22And maybe there's I could maybe that if
42:24you want to make a really simple one,
42:25there could be a value in making one on
42:26a PCB. But, these should all be done in
42:28silicon. Um but, your idea of like, I'm
42:32going to buy in bulk still applies in
42:33the sense that it's much easier to make
42:35one resistor value over and over and
42:37over again to make n resistor values.
42:40Um but, as a side note, when you are
42:43buying components one day out there and
42:44you're buying for your board,
42:46uh
42:47your manufacturer's going to specify a
42:49tolerance range and you'll find that
42:52within one batch the tolerance range is
42:54usually smaller than across batches. So,
42:58if you're trying to make sure that you
42:59have matched resistors from you have n n
43:02instances of your product and you want
43:03to make sure that they're as close to
43:04the same getting the same batch
43:06resistors actually usually does help.
43:08All right, but that's a side note.
43:11All right, any uh so let's see a maybe
43:14disadvantage?
43:16Um what's the advantage?
43:19Yeah.
43:20>> The
43:21op amp is charging a lot more like the
43:23analog resistor.
43:28>> Hmm, that's a good question.
43:30Uh I would say it's probably more than
43:34uh the resistors, yeah.
43:36There's uh inside there's depends on the
43:39op amp topology, but there's a lot more
43:40paths to the ground. They can be made
43:42very low power. You trade off speed and
43:45the resistance you don't have to go like
43:47full volts across these things. You
43:49could do a smaller value, but maybe I'd
43:50say I don't know for any one resistor
43:52I'd say that the op amp consumes more
43:54power.
43:57But that's also like
43:58just a ballpark number, right? I can't
44:00There's no hard rule of thumb. You'd
44:02have to actually do the layout analysis.
44:06All right, I don't think I think we said
44:08it in different ways, but um
44:10linearity and manufacturability of this
44:13is hard, but you need less resistors.
44:14This is the one where you need the least
44:16amount of resistors of any of them.
44:18So, that's the advantage here. This can
44:19be small. This is one that's typically
44:21used in silicon
44:22um like on a a microcontroller. They're
44:24trying to optimize for size. You're not
44:27buying uh the DAC a microcontroller just
44:30for how good and linear the DAC is
44:32typically, right? You're going you want
44:35the flexibility. You want to have a
44:37design that could have a DAC or not have
44:38a DAC. Um
44:41if you really cared about really precise
44:43audio output or
44:45analog output, you might buy a dedicated
44:47chip just for that and you can buy
44:49uh you know, analog codecs that will
44:52some of you have talked about them.
44:53They're like a protocol called I2S,
44:56which is equivalent to I2C, in which you
45:00will stream digital values to your DAC,
45:03and it will do all the generation of
45:05analog for you. And you don't have to
45:09mess with a lot of that stuff. So,
45:10there's dedicated chips that will do a
45:12better job than your
45:13device.
45:15In fact, there's a whole hobby market
45:16about like where are the really good
45:17DACs to get for your audio amplifiers
45:20for your headphones.
45:22Okay.
45:26So, there's trade-offs there.
45:30And then, of course, we have all sorts
45:33of quantization error, just like we had
45:34with ADCs and analog in general. These
45:38all have obey the same quantization
45:41limitations, right? So, you're always
45:43going to have a half-bit LSB. You wanted
45:46a particular output analog voltage, but
45:48you can only get discrete steps.
45:51Often times, that would mean
45:54um
45:55you're going to do a lot of steps, so
45:56you don't really care. But if you wanted
45:57really pure sine waves, you might have
45:59to put an output filter on that. And
46:01that output filter will remove those
46:03high-frequency steps, but you're then
46:07limited to you can't have a frequency
46:08that's higher than the output filter.
46:10So, if your application is allows for
46:14fixed output frequency or limited range
46:18of output frequencies, then putting a
46:19filter on the output is nice. You can
46:20smooth out that stair step. Um but if
46:23not, then, you know, you're just going
46:25to have to deal with that noise and and
46:27think about like how does that affect
46:28your design. Um
46:32You could imagine that there are
46:34RF transmitters that actually go at
46:36gigahertz that are trying to do direct
46:38digital synthesis. Maybe megahertz is
46:40more of an accurate statement, but
46:41you're trying to do direct digital
46:42synthesis. So, those edges would also be
46:46spurious noise that goes out on the RF
46:48channel. You don't want that.
46:50So, but there's all these other ways to
46:52mitigate trying to get rid of those uh
46:55Some
46:56uh sensors or some control loops are
46:59done in analog, so maybe you have some
47:00analog components and then your digital
47:03uh world is trying to inject into the
47:05analog control loop. Well, then you
47:06might have to worry about those uh stair
47:08steps as well.
47:11All right. So, why don't we think
47:12through a little bit? I think we did
47:14most of these things already. I don't
47:16have a worksheet for you. I'm sure
47:17you're tired of them by now.
47:19Um but we can just mentally think
47:21through uh resolution. Uh just think
47:24through, talk to yourselves, what do you
47:25think uh for the top one, the low-pass
47:28filter PWM, voltage divider, uh R-2R
47:31ladder, or the binary one? Which What is
47:33the um
47:34given the same area, which ones have the
47:37best resolution? Uh so, take a second
47:39and uh we'll we'll come back.
48:34What do you think? Which one's the has
48:35the highest resolution of the group?
48:43Should we vote?
48:47How about this? Uh this will be one.
48:49This is two. This is three. This is
48:52four.
48:53So, raise your hand and indicate with
48:55your fingers which one you think is
48:56which. Which one has the highest
48:58resolution given the same area.
49:01Okay, I got one.
49:04Four.
49:05Yeah, I can't see that far. I'm getting
49:07old. I got lots of fours. I got a few
49:09ones, maybe a three. Okay. Let's see
49:11what I Let's see what I thought last
49:12year when I made this slide.
49:14Um
49:16I said that I think for the voltage
49:17dividers, this makes sense because uh
49:20sorry, for the this the last three, the
49:22binary weight one, that one is trading
49:25uh
49:26re- you're making resistors of different
49:28sizes to encode currents.
49:30And uh that one has the least number of
49:34resistors for the end number of bits.
49:36So, like the binary weight is the best
49:39in terms of resolution per area. This
49:41one I said this one's kind of like out
49:43there. It's kind of hard to say uh
49:45because also it's very noisy. Uh so, it
49:47has like a this trade-off between those
49:49other ones. These ones will actually
49:50keep that voltage stable, while this one
49:52will inherently wiggle. And then maybe
49:54this one isn't really that applicable
49:56for silicon, although certainly you can
49:58make it. So, um
50:00I don't know. May I don't know why
50:01exactly I said maybe, but I don't think
50:03it's a fair comparison cuz they have
50:04these other trade-offs.
50:06Um
50:08And then yeah, because I think that
50:09these, given the same voltage range and
50:11a reasonable bit size, you can get much
50:13finer, like little little step sizes.
50:15Well, this will always have this RC
50:17charge time. So,
50:18uh on average it might be low, but I
50:20think in general like you just can't
50:22rely on it that much. Does anybody have
50:24a different opinion?
50:26Does anybody understand why I'm saying
50:27like this has so much variance ba-
50:29baited into it that it's like you could
50:31imagine this one for the same voltage
50:33range could have like
50:35uh you know, the last four sniffing
50:37least significant bits could just be
50:39last four bits could just be the rise
50:40and fall time of this one. So, it kind
50:42of not fair.
50:44All right, let's do Well, we already
50:46talked about speed.
50:47So, I'll just give that one away.
50:50But um my argument for speed is that
50:53these are all high. They're all less
50:55than a clock cycle over there, except
50:56for this one. This one's like extremely
50:58slow. So, if this one is
51:01uh you know, whatever your clock is X,
51:03right? Uh you know, 100 MHz, well,
51:05that's too high, but let's say MHz for
51:07those. Those are all going to be
51:09be done in the one clock cycle. Well,
51:10this one for that same clock cycle, now
51:13you have to run a timer, and then you
51:14have to break that into a PWM, and then
51:17you have to go and slowly change that
51:19duty cycle. So, this is, you know,
51:21hundreds, if not thousands of times
51:23slower than these guys, but you're
51:26probably not choosing this one for
51:28speed, you're choosing this one because
51:30you're like, oh, I just need some analog
51:32output, and I only have a digital pins,
51:34right? That's why you're choosing this
51:36one. Uh so, it's kind of in a different
51:37class.
51:39What about linearity?
51:41Why don't you take, and this means like
51:43that has consistent bit sizes uh across
51:46different error types. Um so, why don't
51:49you take, you know, 30 seconds and
51:51discuss what do you think the linearity
51:53uh is, and then we'll do the voting
51:54again of which one is the has the best
51:57linearity.
52:08>> [snorts]
52:41>> All right, what do we think? We're going
52:42to vote. This will be one, uh two,
52:44three, and four over there. Uh who
52:47thinks, uh I don't know. What do you
52:49think? Which one is the most linear of
52:51all these?
52:53Two, two.
52:55Two, I got a
52:56four, maybe. All right, these people,
52:58they're not voting. One person over here
52:59they have no have no idea. They over
53:01here, we have a couple people voting.
53:02Okay, two. Why? Why two? Anybody want to
53:05I see your fingers were up. Why two?
53:19Yeah, I think the the voltage divider
53:21one
53:22um if any one resistor is bad, it only
53:24affects one bit. So, that's right. And
53:26they're all exactly the same size. So,
53:28the the likelihood of getting them all
53:30to be very similar is is good. The other
53:33ones uh they're different sizes and if
53:35any one of them is wrong it it hit
53:38affects uh all those uh bits that are
53:41associated with that uh resistance. So,
53:43uh yeah, that's that's essentially the
53:45reason why. So, let's see what did I
53:47put? I said low. Well, linearity of this
53:49one is horrible
53:51in the sense that it's just time varying
53:53on its own.
53:54Um and then these are you know, the
53:56proportionality here ratios of linear to
53:59non-linear.
54:00Okay?
54:02How about I guess power? I'll just do
54:04power. It's kind of hard to say because
54:06you
54:07power is based on so many other factors.
54:09So, I would just say here uh the
54:13low-pass filter is just a digital IO
54:15pin, right? It can't like its power is
54:18uh uh
54:19you know, an output gate. Uh so, that's
54:21really low. Uh the other other of them
54:24have to have an op amp and some number
54:25of resistors and we could argue that
54:27some of those resistors are like uh
54:29maybe they're slightly different because
54:31there's less uh loss between some of
54:33those resistors especially with like the
54:34binary weight. It's more efficient. Uh
54:37and it's not some of those um resistors
54:40aren't even turned on where all the
54:41resistors here are dissipating power in
54:43the voltage divider. But then it really
54:45comes down to like topology and you have
54:47to do a detailed analysis. So, we can at
54:48least say they're all like medium or at
54:50least all the same in this one and um
54:53is uh relatively low uh
54:56on the side.
54:58Okay.
54:59And then um
55:01I guess I shouldn't have combined these
55:02but this is kind of a uh number of um Um
55:05number of resistors per switch. Um and
55:08so uh uh this is kind of getting at
55:10complexity. So, why don't you take uh 30
55:13seconds and say which one is going to
55:15have the What did I What How do I say
55:17this? Which one has the least number of
55:20resistor and switches uh in it?
55:23Uh aside from this one. How about you
55:25just look at those ones?
55:26Um
55:27cuz this has no no switches.
55:30So, take 30 seconds, try and figure out,
55:31then we'll vote of these three
55:33uh which one has the small lowest number
55:35of resistors and uh switches.
56:00>> [snorts]
56:24>> All right, so we'll vote. This will
56:26still be one just out of convention and
56:27two and three and four over here, but
56:30we're only going to really consider two
56:31and through uh four. So, which one has
56:34the least number of uh resistors and
56:37switches?
56:39Four.
56:41Four. Yep, it's four. And you can go
56:43through and calculate for n n bits how
56:46many resistors and switches are. And
56:48really uh this is proportional to area.
56:51Switches aren't
56:53a large area, I think of, compared to uh
56:56the resistors, but it still leads to
56:58complexity. And so, here's really the
57:00trade-off is trying to reduce uh the
57:02resistor count.
57:03Um
57:04but again, this one doesn't quite follow
57:06this trend. It's a different topology.
57:09Okay.
57:10Any
57:11questions on the pros and cons of
57:13different DACs?
57:16Yeah.
57:17>> What's the problem with audio playback?
57:19Like if you want to like a super
57:20accurate one, you would like not use
57:22these.
57:22Separate like structures.
57:25>> Um you would probably not want to use if
57:28you're really an audio file and you have
57:30better ears than me.
57:32Right? And you just could hear all the
57:34notes in these this music, you're
57:35probably not going to use the DAC that's
57:37on the XMC.
57:39Right? You're not going to use the one
57:40on your microcontroller. They have made
57:42special modules that will be audio DACs
57:45for audio and they haven't been
57:47optimized for like your DAC goes goes up
57:50to 5 MHz. Well, you don't need that for
57:52audio. You only need it to go up like 40
57:54kHz, right? Um and some uh and then
57:57they'll be like 24-bit. Now, I can't
58:00hear the difference between 16-bit audio
58:02and 24-bit audio and most of us are
58:04listening to audio that's been
58:05compressed anyways. So,
58:07those bits aren't even available for us
58:09anymore. Um but there's special
58:11hardware. And then they also will add
58:13in, you know, uh special smoothing
58:15functions like uh our like um
58:18LC filters and all these other things to
58:20make it just right. So, if you're going
58:22to do audio, you want to do it just
58:23right, buy the correct module.
58:27Any other questions?
58:29All right. So, I think the real takeaway
58:31is from the ADCs and DACs is not that I
58:34expect you to be able to calculate your
58:36way through any of those voltage
58:38dividers and switches. It's much more if
58:41you're in industry and somebody's
58:42saying, I need to go and buy I need a
58:45fast high-speed ADC, which one should I
58:48buy? That at least you can come back and
58:50remember, oh, that's probably going to
58:51be a flash and I hope they don't ask for
58:53too many bits or else we're in trouble.
58:55Right? That's like that's the sort of
58:56tradeoff I'm looking for.
58:58Um or if you're doing um you know, a
59:00DAC, why why are the what if I'm looking
59:04at a a really low-cost thing, why is it
59:06that I might have to worry about
59:07linearity? If I'm especially if I'm
59:09doing controls and analog controls,
59:11mixed digital analog controls,
59:13maybe you really don't want to use that
59:14binary weight or you're just like it's
59:16free and I'll have to find some way to
59:18compensate for some of those errors.
59:22Okay.
59:24Let's see.
59:25And then so on I don't know why it's all
59:29out of order
59:30but on your particular devices you
59:34I think most of you had lab this week
59:36but um
59:37it's a audio
59:39like DAC
59:41and so you'll have you have two DACs on
59:44your device.
59:46It's interesting you can go to full
59:47resolution at
59:492 MHz but then
59:51there's reasons here while if you want
59:52to go to faster 5 MHz you have to reduce
59:54your resolution. So there's this speed
59:56trade-off
59:58that happened. Now the SAR has that
1:00:00built in fundamentally built into it.
1:00:02This is much more about the secondary
1:00:04effects of like
1:00:06how the settling time works and how the
1:00:08analog outputs of these things work
1:00:10rather than a fundamental of the flash
1:00:12or the sorry the DAC type but there is a
1:00:15resolution speed trade-off here as well.
1:00:17This DAC
1:00:19well as most DACs that you would
1:00:22ever use does have an output buffer and
1:00:24they specifically say it's rated for 5
1:00:26kiloohms
1:00:2725 picofarads
1:00:29and that's just like a pretty reasonable
1:00:31thing right? They're saying okay we can
1:00:33drive a power source that's more for
1:00:35signal level and the capacitance is
1:00:37always is important that they mention
1:00:40that because
1:00:41capacitance lives parasitically
1:00:43everywhere and
1:00:4550 picofarads is actually kind of a lot
1:00:48of
1:00:48capacitance so they've kind of optimized
1:00:50for most analog signals that you would
1:00:52come up against
1:00:53but if you make control circuits things
1:00:57can become unstable if you have too much
1:00:59capacitance or at least at the minimum
1:01:01it's going to take too long to drive
1:01:03that thing and this will start slowing
1:01:05you down. Now this is only 5 kilohertz
1:01:08or kiloohms so you can't go and drive
1:01:10reasonably drive that 8 ohm speaker Um,
1:01:13why you need to have something in
1:01:15between So, uh, if you're going to if
1:01:17that's part of your lab or your final
1:01:19project, you're going to drive a speaker
1:01:20and you're going to do it with a DAC,
1:01:21that's cool. Um,
1:01:24that gives you lots of flexibility in
1:01:25how you control sound, but you're going
1:01:27to need an output stage that's really
1:01:29designed to drive speakers. And because
1:01:32speakers are so low voltage and need
1:01:34high current, um, or so so low
1:01:37resistance and need high current,
1:01:38there's usually output devices
1:01:40specifically made to drive speakers. So,
1:01:42you want something that's a speaker
1:01:43driver. Uh, cuz it's such a common thing
1:01:45and it's a kind of a unique operating
1:01:47point. So, for this, you drive this
1:01:49into, uh, you know, an audio speaker
1:01:52driver, some module that does that. You
1:01:54plug it is powered externally and then
1:01:56that plugs it you plug your speaker
1:01:58directly into that module and then you
1:01:59can have uh, nice sounding audio.
1:02:02And I think we talked about this most
1:02:03project groups. Just reminder that the,
1:02:06uh, expo's going to be loud. So, if you
1:02:08have something that you want us to hear,
1:02:12and you remember I can't hear anything.
1:02:14So, now you're going to have to have
1:02:15that extra loud for the, uh, expo if you
1:02:17want us to do it. Um, an easy way to do
1:02:19that is just put PC speakers. Bring some
1:02:21PC speakers, turn them up. We'll be able
1:02:23to hear it.
1:02:24Um, okay.
1:02:28Um, we'll do quickly talk about some
1:02:30error types in DACs and ADCs. So, we
1:02:32already know about quantization error.
1:02:34We showed a slide on it before. We
1:02:35talked about quantization error uh, back
1:02:38when James was here uh, talking about
1:02:40uh, analog signals in general. And so,
1:02:43we still have those same error types.
1:02:46>> [clears throat]
1:02:46>> Um, the offset error here, this is um,
1:02:50basically you have this ladder that's
1:02:52going up and if everything's just
1:02:53shifted along some analog voltage,
1:02:56that's actually not too bad. That might
1:02:58mean that like the tail resistor
1:03:00on your ladder was not quite right.
1:03:03Maybe it's malformed. Or maybe there's
1:03:05some, you know, analog offset. This
1:03:08error is common, but it's also
1:03:10recoverable cuz all you have to do is
1:03:12calibrate your device. And then you're
1:03:14going to have a nice stairstep effect.
1:03:15So, this one is uh relatively easy to
1:03:18deal with.
1:03:21Um and this is also why they have the
1:03:24the they often ship It's not even by
1:03:26error, but to get the most effect out of
1:03:29your SAR set, they often shift uh the
1:03:31bottom and the top by 1/2 LSB.
1:03:34Um the one that's a little bit harder to
1:03:36deal with is full scale
1:03:38uh error, and this is kind of like gain.
1:03:40So, this is where the stair step is, you
1:03:42know, you wanted it to be a digital
1:03:44value to be a particular analog value,
1:03:46but it's just uh diverging. Maybe it's
1:03:48diverging on the bottom on the low
1:03:50voltage side or the high voltage side,
1:03:51but there's this constant diverging of
1:03:53it. And so, full scale error uh is not
1:03:56also not that bad. This is calibratable,
1:03:58right? You can go and at factory time
1:04:01sometimes they'll do it. Sometimes
1:04:02they'll have a subset of points that are
1:04:05calibrated, and then you can interpolate
1:04:07between those points. And how they do
1:04:08that is at the factory, they'll have a
1:04:10known voltage uh input or they'll
1:04:13command a digital output and measure the
1:04:14output voltage, and then they'll have a
1:04:16lookup table. They'll show you those
1:04:17offset values. Um
1:04:20and then it's probably not practical for
1:04:22them to do all the voltages, but they'll
1:04:24do some.
1:04:25Um
1:04:27and so, like uh it's not obvious, but
1:04:30uh the amount of time it takes to test
1:04:32your chip
1:04:33and actually make sure that it is uh
1:04:36fully functional. So, that's like
1:04:37checking all the D flip-flops and that
1:04:39the
1:04:40thing can boot and all those sort of
1:04:41things and check all the analog
1:04:42peripherals is actually a real
1:04:44bottleneck for most um microcontrollers
1:04:47and um high-end processors. So, they're
1:04:50not going to do the full um
1:04:52calibration for you.
1:04:54But that one you could calibrate uh if
1:04:56you if you had to as part of some
1:04:58startup sequence uh some way on a on a
1:05:00product. It's not impossible. Or if you
1:05:02had a very special like one-off system,
1:05:04you could just do the full lookup table.
1:05:08The errors that are much worse are the
1:05:11kind of the ones we talked about that
1:05:12are more susceptible with a weighted
1:05:13binary
1:05:14uh value uh DACs where the non- the size
1:05:18of the bits vary as a function of the
1:05:20code. Now, these are much harder to deal
1:05:23with um because it would take a whole
1:05:25bunch of mapping of every single thing
1:05:27to figure this out. Um so, there's these
1:05:30uh type of errors and typically the
1:05:33manufacturer's going to
1:05:34uh
1:05:35uh specify that uh what the worst-case
1:05:39differential non-linear error error is
1:05:40going to be. So, they're going to say
1:05:41like how much error do they expect in
1:05:44their ladder under normal operating
1:05:46conditions.
1:05:47And so, that would be added into your
1:05:50quantization uncertainty as well. And
1:05:52I don't know if James said this, but I
1:05:53typically think of a DAC or an ADC as I
1:05:55just throw away the last bit anyways,
1:05:57maybe the last two bits just because you
1:05:59have noise, you have system noise,
1:06:02um you know, you put a constant voltage
1:06:04in and you look at your ADC reading and
1:06:05you can just watch the thing wiggle
1:06:07around.
1:06:08You can track down all that noise, but
1:06:10that's effectively your your system
1:06:12noise and you can't get around that. So,
1:06:14uh you just expect that uh the signals
1:06:16aren't going to be perfect.
1:06:18Um these are like other examples of
1:06:20differential non-linearity.
1:06:22Um some of these are, you know, okay.
1:06:24There's little offset errors, maybe you
1:06:26skipped uh an analog step, uh just not
1:06:29reliable. And then, these are like the
1:06:31really bad ones where somehow you
1:06:33actually had a uh digital value was
1:06:36represented twice or more than once.
1:06:37It's not a linear step because of some
1:06:39process error. Maybe one of those uh
1:06:41resistor values got so far out of whack
1:06:44that it caused that sort of
1:06:45non-linearity. And
1:06:48you know, is that a problem for you? I
1:06:49have no idea, right? That's really up to
1:06:51your design. But imagine if you had a
1:06:53control loop which you were expecting
1:06:55that as you increase digital values, the
1:06:58analog values also uh increased and you
1:07:00had something that was tracking that.
1:07:02Well, in this case, you might get stuck
1:07:03in this uh local minimum uh not even
1:07:06realize why. It's rare, but you you
1:07:08should think about it if you're trying
1:07:09to do uh controls with analog uh
1:07:12signals.
1:07:13Um
1:07:15And this is just another the integral
1:07:17error as to uh make a a measurement over
1:07:20all the values compared to um
1:07:23the
1:07:25ideal versus the what was actually
1:07:27there. You can
1:07:29figure out the area under that curve and
1:07:31then you can integrate over it and
1:07:32figure out
1:07:33how much error is accumulated. So just
1:07:35another measurement. And maybe you know,
1:07:38maybe not the manufacturers of a
1:07:39microcontroller, but the manufacturers
1:07:40of an of a DAC or an ADC would should
1:07:43quantify that especially if you're in
1:07:45that like really nice audio place space
1:07:49or some other spaces where trying to
1:07:50sell you a really nice error
1:07:53DAC or ADC.
1:07:55Um let's see.
1:07:57Yeah.
1:07:59When this will come out,
1:08:01there are if you're going to take the
1:08:02FFT of something, right? This is a
1:08:04common thing. You have some signal. Now
1:08:06you're trying to do signal processing on
1:08:07it. You're analyzing some circuit coming
1:08:10in you're like, well, what's the most
1:08:11dominant frequency? Maybe that dominant
1:08:13frequency is human speed or something.
1:08:15There could be some radio signal or some
1:08:18Doppler shift.
1:08:20But you'll find is those errors will
1:08:21cause spurious signals. You This is your
1:08:24fundamental frequency. This is what's
1:08:25coming in. This fundamental frequency
1:08:27doesn't have these side lobes, but
1:08:29because of your ADC
1:08:31or DAC errors, these things start
1:08:34creeping into your signal processing
1:08:37pipeline where you're saying, oh wait, I
1:08:38get a lot of error over here. My signal
1:08:40coming in has all these spurious things.
1:08:43That doesn't meet the FCC spec. Well, it
1:08:45may be that your DAC is just
1:08:46interpreting that cuz it has some or
1:08:48your ADC cuz you have some
1:08:49non-linearities.
1:08:51So there's kind of like these follow-on
1:08:52effects that I'm just kind of giving you
1:08:53a heads up about.
1:08:55Um okay. So we're going to
1:08:59I don't really get to the eight to the
1:09:00DAC so everything I wanted to today, but
1:09:03we'll recap quickly.
1:09:04Um so we've
1:09:06reviewed voltage dividers and voltage
1:09:08ladders, three types of DACs.
1:09:10You can consider
1:09:13low-pass filter to be separated from the
1:09:15binary way and the R2R. They are
1:09:18different.
1:09:19Um
1:09:20maybe I wrote that wrong, but and then
1:09:22we talked about a bunch of errors in
1:09:24ADCs. I think the real rule of thumb is
1:09:26you have to figure out when you're
1:09:28working your system, how much do you
1:09:30trust those lower significant bits? Is
1:09:32it one bit you already know you can't
1:09:34trust it? Is it Is it two bits that you
1:09:36can't trust or three bits? You have to
1:09:37kind of figure out in a practical
1:09:39system, like what is that noise floor
1:09:41and can you trust those lower bits?
1:09:43All right. We'll end there and we'll
1:09:45pick up next week.

About this transcript

This page contains the full transcript of EECS 373 - Fall 2026 - Lecture 15: "DACs" by Interactive Sensing and Computing Lab , generated from the public captions YouTube serves with the video. The transcript has 11,232 words across 1,793 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

What you can do with it

Use the transcript to take notes, quote the speaker, build a study guide, generate a summary with ChatGPT or Claude via the YouTube Summary tool, or export it as a timed subtitle file with YouTube to SRT. You can also re-open it in the transcriber to translate the transcript into 100+ languages.

Free YouTube transcript tool

YouTube2Text is a free YouTube transcript generator — no signup, no daily limit. Paste any YouTube link and get the full transcript instantly, with timestamps, click-to-jump, translation to 100+ languages, AI prompts for ChatGPT, Claude, and Gemini, and exports to TXT, SRT, VTT, or Markdown.