Theory and Calculations

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From the course by University of California San Diego

Internet of Things: Sensing and Actuation From Devices

84 ratings

University of California San Diego

Internet of Things: Sensing and Actuation From Devices

84 ratings

Have you wondered how information from physical devices in the real world gets communicated to Smartphone processors? Do you want to make informed design decisions about sampling frequencies and bit-width requirements for various kinds of sensors? Do you want to gain expertise to affect the real world with actuators such as stepper motors, LEDs and generate notifications? In this course, you will learn to interface common sensors and actuators to the DragonBoard™ 410c hardware. You will then develop software to acquire sensory data, process the data and actuate stepper motors, LEDs, etc. for use in mobile-enabled products. Along the way, you’ll learn to apply both analog-to-digital and digital-to-analog conversion concepts. Learning Goals: After completing this course, you will be able to: 1. Estimate sampling frequency and bit-width required for different sensors. 2. Program GPIOs (general purpose input/output pins) to enable communication between the DragonBoard 410c and common sensors. 3. Write data acquisition code for sensors such as passive and active infrared (IR) sensors, microphones, cameras, GPS, accelerometers, ultrasonic sensors, etc. 4. Write applications that process sensor data and take specific actions, such as stepper motors, LED matrices for digital signage and gaming, etc.

From the lesson

Amplifier Build

Time to build your very own amplifier! In order to interact with a wide variety of components, including many of the components that will be used throughout this course the voltage output from the DragonBoard™ 410c low speed expansion header will need to be amplified. In this lesson we will talk about a very basic voltage amplifier design. This design will be used to boost the signal voltage from the GPIO’s located on the DragonBoard™ 410c low speed expansion header. Once familiar with this basic amplifier, one can make adjustments to create personalized amplifiers geared toward specific future projects.

Introduction to Lesson 21:36

Specification matching2:07

Theory and Calculations5:25

Amplifier Diagram (NTE987)1:36

Weighing your options1:58

A look back at Lesson 20:51

Meet the Instructors

Ganz Chockalingam
Principal Engineer
Qualcomm Institute of Calit2, UC, San Diego
Harinath Garudadri
Associate Research Scientist
Qualcomm Institute of Calit2, UC, San Diego

We've explained amplifiers, we've explained op amps.

We've brought it all together as to why we wanted to build this amplifier from

the get go, and now we need to show you how to calculate your resistor values.

So that just in case you don't want to build the exact amplifier that we built,

you could actually go in there, calculate other resistances,

change the factor of amplification up or down, and do it on your own.

So we're gonna go ahead and show you how to do that.

>> Yeah, so we quickly wanted to give you a little bit of theory behind an op amp

and how it works.

Normally when you're doing calculations for

an op amp you take an ideal consideration towards it.

And so there's, there's a few things that are involved with that, but,

it's basically you're just gonna assume that no current actually flows into

the inputs, but it does flow out.

And you're gonna make, the ideal assumption is that the voltage difference

is zero between the input and output, even though that's not true, and you're gonna

assume that there's, it has to do with the gain, but, it's kinda complicated.

We're just gonna make some of these assumptions while doing the calculations

so that it'll make it a lot easier.

And the values that we're gonna calculate are gonna be very close to the actual

values so that it works very well.

But we're basically, you can see here on the right that's the setup of our circuit.

And so we have the plus is the non-inverting input,

the negative is the inverting input, and the point on the triangle is the output.

And so the chip also has to be grounded and powered but

we have these resisters set up in this fashion so that we can get the gain,

which is gonna be AV over there is gonna be equal to one plus R1 over R2.

And so we're gonna calculate that in a second, but

what that means is you can take the value of R1 divided by R2 added to one, and

that's gonna be the gain of the system.

And so, in our case, I think we chose R1 to be 10,000 Ohms and

R2 to be 5,000, so that you get a gain of three.

>> Yeah and just to note, a side note, you can see up there that,

what he was just talking about, that little triangle being the op amp,

the chips that we have, they're quad op amps, right?

So, quad op amps.

>> Yeah, so there's four of them in each chip.

>> There's four of those diagrams in each chip.

Which is why you're basically going to mirror, you're gonna build it once and

then you're just gonna mirror it four times or eight times or

12 times based on how many GPIOs you wanna amplify.

>> Yeah, and then one last thing to note is that you do have to power the chip, and

depending on what power you give for

the VCC rail is gonna determine how much you can amplify it.

So we typically have been powering it with five volts,

which means you can't get higher than five volts.

And in fact,

you can't get higher than about 4.3 would be the maximum you can get.

If you want to go higher than that, then you do need to use a 12 volt or

something from the DC in jack.

>> Yeah, fully capable with this port.

Actually, there's plenty of options to change your amplifications,

not only just the resistance but, like he said, just changing the power to the chip.

>> Yeah, and we didn't need it to go any higher than that so

we just used the five volt and that gets it right to where we want it to be.

All right. So

we wanted to take you through some of the calculations here.

And so this is, again, our amplifier diagram and how we had it set up.

We can change it around and you can see how this is ideally how it's gonna work.

And so we have, this is the setup, it's almost like a voltage division setup

because, again, we're gonna be using those ideal assumptions

that no current is actually flowing through the v negative terminal there.

All right? And, so now, again,

our other assumption is that the difference between the non-inverted and

inverted input is zzero, so that they're actually the same voltage level, and

then we also assume that the current going into the amplifier is zero.

Now, we've used Ohm's law and kind of rearranged it and

then we've added them together and used the voltage division, and

you can see how we're working out the steps to get to the v out.

And then we want the transfer function basically,

which is gonna show how much it's being amplified by.

So we get v out divided by v in, and that's where we get our AV right there,

and so that's basically how much we're multiplying the input by to get to v out.

And so it works for us, and it's gonna basically multiply,

in this case, it's gonna multiply the input voltage by three, and

get us an output actually gonna be capped off around 4.2 or so.

>> Yeah, so again, this is just showing you how we worked it out.

But you could literally go to that last step where it says AV equals R1 over R2

plus one, and plug in 15,000 over 5,000, and

then that's just three plus one, so then you'll be having a gain of four

which means you'll be amplifying your signal by four times.

>> As long as you increase the power rail so they can go higher.

>> So if your power rail is capable of amplifying 1.8 volts four times

then you can do that, and that's all you really need is that last formula there.

Yeah. >> Yep.

>> All right?

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