Power to the People
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As mentioned in the pre-lab, this lab will explore a couple of different circuits designed with the same goal in mind. Our context for this lab will be powering the familiar Teensy microcontroller we've used before, but we'll try powering it from a source with a higher voltage. This is an incredibly common application, taking a high voltage (for example, the 120V power mains) and converting it down to a lower voltage needed to power a device (for example, 12V or 5V); and our goal is to do this conversion both accurately and efficiently.
For our purposes today, we'll be stepping down an 11V source to around 5V to power our Teensy. The Teensy doesn't require exactly 5V to work; in fact, it accepts quite a wide range of possible voltages. To start, let's target making approximately 8V from our 11V source.
1) Resistor Divider
We've already seen one way of doing this, with a resistor divider:
The "load" is the thing that we're providing power to with our converter. Later in the lab, the Teensy will take that spot. But for now, so that we can do some calculations, let's model the Teensy as a 110\Omega resistor. It's a crude approximation, but actually kind of close in some ways.
Using this model, we can make a voltage close to 8V by choosing R_1 = 10\Omega and R_2 = 33\Omega.
Now let's do an experiment to see how this matches up against reality. Build this circuit (using the big chunky power resistors we have up front) on your board, and using a regular 110\Omega resistor from the cabinet to represent the load, temporarily. Use the benchtop power supply (set to 11V, 1.2A) to power it it for a short while only, and while it's on, make note of the following:
- the voltage and current indicated on the power supply (these are the source voltage and current, which we can use to compute the power sourced by the supply),
- the voltage across the load resistor
Turn off the benchtop supply when you've written these things down. Be careful with the resistors, too, because they get very hot very quickly.
Don't tear this circuit apart; we'll need it for some more experiments later.
Demonstrate your results to a staff member. How did you
compute the efficiency in theory land, and how did you measure it in your real
circuit? How did your theoretical efficiency compare against your measured
efficiency?
2) Buck Converter
Now let's look at a more-efficient power converter, a "buck converter:"
To start with, let's ignore the load and just think about how the buck converter itself looks.
In this circuit, the switches are intended to alternate. So, for a period of time, S_1 will be closed and S_2 will be open; and then for another period of time S_2 will be closed an S_1 will be open. Generally speaking, we flip these switches in sync with each other and at a rate that is much faster than the natural frequency 1\over \sqrt{LC} of the LC combination.
During that first period of time when S_1 is closed and S_2 is open, our circuit looks like:
If the capacitor initially started with 0 charge, then we suddenly have an 11{\rm V} drop across our inductor. As a result, some current will start to flow left-to-right through the inductor. This current will start the capacitor charging, which decreases the drop across the inductor; but ultimately, we will always have a drop across the inductor from left to right, meaning that we see a smaller voltage across the load than our original 11{\rm V}.
Then we flip the switches:
The current through the inductor cannot change instantaneously, so it continues to flow into the load, behaving something like a current source. The capacitor acts as a smoothing agent, making sure we don't see dramatic instantaneous changes in the voltage across our load.
From the prelab, we saw a couple of things:
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If we leave the switches on for DT seconds and off for (1-D)T seconds (where T, again, is short) and keep switching them on and off, we'll eventually see a voltage on the output that looks something like D\times 11{\rm V}, with some small oscillations sitting on top.
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This circuit, in theory, has 100% efficiency. Since neither the inductor nor the capacitor is dissipative (they merely store energy), all of the energy we put into this system is dissipated through the load.
Alas, though, that the real world is not so kind. In reality, we do lose power to a number of places. The most noticeable of these losses come from the fact that:
- the inductors and capacitors also have some amount of resistance, and
- it takes energy to flip the switches (which are implemented using transistors and diodes).
In the next section of the lab, we'll put this circuit together and see how well we can actually do (spoiler alert: it won't be 100% efficient).
2.1) Building the Buck Converter
Many of the components in the circuit are straightforward (we can grab inductors and capacitors from the cart/cabinet, for example); but some are not: in particular, we'll need to think a little bit about how we're going to implement the switches in this circuit. We need these switches to be able to be controlled electronically, and we need to be able to open and close them quickly.
For S_1, we're going to use a MOSFET. Before, we treated our MOSFET as a variable current source; but today we'll treat it slightly differently: as a switch. In short, if the gate of the MOSFET has a high-enough voltage on it, a path will open up for current to flow from the source to the drain; if not, then that pathway will be closed.
And for S_2, we're going to use a diode, which we'll model as allowing current to flow in one direction but not the other. So our circuit will actually end up looking like this:
Where V_{\rm sq} is an alternating signal we'll create with a separate circuit.
We have MOSFETs up front, and diodes too. There are a couple of things to be careful of here:
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Be careful putting things into the breadboard! Both the MOSFET and the diode can both be a little tricky to get into the breadboard, so please be careful!
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The MOSFETs we have available have their pins connected like so (GDS from left to right facing the thing from the front):
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The diodes have a little silver line printed on them, which needs to be oriented the same way as the line in their little symbol (i.e., that stripe should be conected to the inductor, not to ground).
With all that in mind, go ahead and maybe wire up the main body of the circuit now. Up front, we have a 15\mu{\rm H} inductor, and you should grab a 47\mu{\rm F} capacitor from the cabinet.
As before, we'll use a 110\Omega resistor as our load.
Feel free to ask for help if you need it as you're building, or if you want us to double-check things once it's built.
2.1.1) Making a Square Wave
Now we have all the machinery in place, but we need a mechanism to turn the switches on and off electronically. To do this, we'll make a square pulse that we'll stick on the gate of our MOSFET. When this square pulse is high, S_1 will be closed and S_2 open; and when the square pulse is low, S_1 will be open and S_2 will be closed.
We'll use a famous chip called a 555 (pronounced "five five five") to accomplish this. Page 3 of the LM555's datasheet that shows you the pin numbers. Note that there is a little notch on one side of the package that you can use to break up the symmetry and tell the pins apart.
Grab yourself a 555 from the cart and wire up the following little circuit on it, paying careful attention to the pin numbers from the datasheet:
You can then measure the output on pin 3. You should see something that looks like a square wave, kind of. Answer the following questions about this wave:
Once you have that working, you can hook up pin 3 of this little circuit to the gate of your MOSFET in your buck converter. After doing so, you should see a roughly-constant voltage across the load resistor, with some wiggling around that point.
2.2) Efficiency
Now, as we did before, measure the efficiency of your circuit. You should be able to figure this out by measuring the voltage across the load resistor and by looking at the voltage and current that the power supply is outputting.
What is the efficiency of your new circuit? How does this compare against
the circuit from before? How does it compare against our theoretical result?
Show your results to a staff member.
3) Comparison
So why do we care about efficiency? Well, one place we care is when we're powering a device from a battery; in short, a more efficient power converter means longer battery life! In this section, we'll put that idea to the test a little bit, using supercapacitors as little rechargable 11V batteries.
In this section, we'll use our converters to power the Teensy. Before we get rolling, download song.zip and flash it to your Teensy; then DISCONNECT your computer from the Teensy. This program plays a fantastic song on a little loop.
Up front, we have some little boards that we made for you to help hook things up to the battery for this experiment; they look like this:
You should hook the 11V benchtop power supply up to the top rails on this board (labeled "power supply"). And then you should connect the bottom rails to your circuit (we're using those instead of the benchtop supply to power your circuit).
Also use a multimeter to measure the drop across the battery; we'll use this both to know when the battery is fully charged, and to get a sense of how quickly it's discharging.
When the little switch is thrown to the left, the battery will charge up. And when the switch is to the right instead, the battery will power your circuit. We're going to compare how long we can power the Teensy with one circuit versus the other. These batteries don't have a lot of juice, so they won't be able to power anything for very long; but they'll hopefully allow us to do some experiments to compare our two circuits (the resistor divider from before, and the buck converter).
To start, hook up this little board to the resistor divider that we started with. But now, instead of a 110\Omega load, connect up the Teensy instead (make sure to remove the 110\Omega resistor). The pin labeled "5V" should be connected in between your two resistors, and the pin labeled "G" should be connected to your circuit's ground. Connect up a speaker between pins 11 and G of the Teensy as well.
So now let's do an experiment:
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With the switch thrown to the left, wait for the battery to charge up to 11V.
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Then throw the switch to the right, making note of how long the Teensy runs for (either by listening to how far we get through the song, or using a stopwatch or something).
Repeat this process a couple of times, keeping track of how long the progrem runs for.
Then run the experiment again, using your Buck converter instead of the resistor divider. To do so, disconnect the your resistor divider; then hook up your buck converter to the "your circuit" rails. The Teensy's 5V pin should then go on top of the capacitor, and the G pin should go on ground.
As before, repeat it a few times to get a sense of how long things run for.
When you're done, please return: Any other wires or fixed-value resistors you can just throw away.
Discuss your results with a staff member.
4) Additional Food for Thought
OK, so our buck converter was a big step up from our resistor divider. But you might still be concerned. Given the theoretical 100% efficiency we calculated, shouldn't we have been able to do better than the maybe 60-70% efficiency you found for your circuit? The short answer is that yes, there is still a lot of room for improvement here (carefully-designed buck converters can often exceed 90% efficiency). We've built a prototype, and we hope that it was fun and instructive; but if we wanted to actually try to maximize efficiency, there are a number of things we would want to do differently.
For one, we wouldn't build this circuit on a breadboard. Those little parasitic capacitances between each row of the board are problematic, as are parasitic inductances from any loopy wires sticking up from the breadboard. We would want to keep things flat to the board, but even better, we would want to lay something like this out on a PCB and avoid the breadboard altogether.
We could also use better components. As one example, using the 555 to generate our square wave is somewhat wasteful, and there are much better ways (though they are beyond the scope of this class).
Buck converters also generally work best in high-power applications; for powering the Teensy, there are likely better options in the first place.
Making some of these changes, it's possible to make a much more efficient buck converter than the one we built today. If you're interested in exploring these ideas further in the future, you might be inerested to take 6.222 (Power Electronics Lab) and/or 6.622 (Power Electronics) at some point; both are classes about power electronics and likely explore some of these issues in much more detail.