Buck Converter
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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. In practical applications we may be further limited by volume, mass, cost or reliability, making the design of each power converter an interesting and fun optimization!
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 120\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 120\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. But for now, disconnect the resistor divider from our input voltage so we aren't dissipating unecessary power in the next section.
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 the time domain.
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.
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.
2.1) Filter
From the prelab, we found that inductor and capacitor in this circuit can also be thought of as a filter. Where we can replace the switches and source with an equivalent input source (V_{IN}).
Enter your answer as a Python expression, using omega for \omega, j for j, R for R, L for L, and C for C.
HINT: Using the impedance method lets us treat this like a voltage divider!
We call the rate at which S_1 and S_2 turn on or off, the switching frequency (f_{SW}). If we want to decrease the output voltage ripple which happens at a frequency of f_{SW}, we could think about choosing our values of L and C such that f_{SW} is filtered or attenuated.
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).
2.2) Building the Buck Converter
Many of the components in the circuit are straightforward (we can grab inductors and capacitors from the table/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. Like in the boost converter lab, we're going to treat our MOSFET as a 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.
We are also going to do a little trick to make our circuit a less complicated, and instead of placing S_1 on the positive terminal of the source, we are going to place it on the negative terminal. This allows us to turn on and off the switch with a simpler drive circuit (take 6.220, 6.222 or 6.622 to learn more!). The analysis we have completed so far will hold for this version of the buck converter; however, since the load ground is now different than the input ground, we just need to be careful to measure the output voltage differentially (i.e. two probes and the math function or a multimeter), but more on that later.
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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Try to keep things relatively compact on your breadboard if you can.
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The inductor for today is on the table near the front of the room, but the capacitors are in the cabinet as usual. The legs of the inductor are kind of flimsy; please be careful with them!
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The MOSFETs we're using (same as last week) are ultra cute and should fit right into the breadboard. Along with lots of other useful information, their datasheet will tell you which pin is which (if you have trouble finding it, let us know).
- Note also that, like the op-amps we've used, these MOSFETs are perfectly sized to cross the gap in the middle of the breadboard; you shouldn't need to bend any pins to hook things up.
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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.
With all that in mind, go ahead and maybe wire up the main body of the circuit now. Up front, we have a 2.2 mH inductor, and you should grab a 0.1\mu{\rm F} capacitor from the cabinet for C_{OUT}.
As before, we'll use a 120\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.
2.2.1) 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. Start with 1nF for C_{555}.
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. Measure the voltage across the output resistor by using two probes with their ground clips connected to the input ground, as shown below.
You should see a roughly-constant voltage across the load resistor, with some wiggling around that point.
2.3) Voltage Ripple
Now we are going to try changing the output capacitor (C_{OUT}) value and measure how the peak-to-peak ripple changes. Make a table in your notes that looks something like this, for each capacitor value predict the peak-to-peak ripple and then measure the result across the load resistor. Be ready to talk about this table at your check off.
Now let's try increasing our switching frequency, modify your 555 circuit swapping out the 470 {\rm pF} capacitor for C_{555}.
Now measure the new output on pin 3.
The duty cycle should be similar to what you found with the previous configuration. Add back in the 0.1\mu{\rm F} capacitor at the output.
2.4) Efficiency
Now, go back to an output capacitance of 10 \muF and you can keep the frequency the same as the last section (C_{555} = 470 {\rm pF}).
What is the impact of output capacitance on ripple? What is the impact of switching frequency on ripple? 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 the supercapacitor "battery" to power our circuit; we'll try both power converters (our original resistor divider and the buck converter we built) to step the voltage down from the 11V we get from the supercap, and we'll compare how long each one can power the Teensy for.
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. It will also blink a little orange LED once every second while it is running, which you can use to estimate how long it runs for.
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 the input of either your buck converter or the resistor divider, whichever one you're currently testing.
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 be hooked up in parallel with the power supply, which will cause it to charge up (at this point the battery is disconnected from your power converter and the Teensy; it's just charging).
Then 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 120\Omega load, connect up the Teensy instead (make sure to remove the 120\Omega resistor). The Teensy pin labeled "5V" should be connected in between your two resistors (the output of the power converter), 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 (you can plug jumper wires into the little while connector on the speaker to see it work).
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, and/or counting blinks, and/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 5 V pin should then go on top of the capacitor, and the G pin should go to the bottom of the capacitor (not the - side of the battery!).
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 70-80% 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.
Bonus: If you want to observe the effects of this parasitic inductance and capacitance, try measuring the switch voltage (drain-to-source) while it is operating. Whoa! We see a lot of overshoot and ringing, this looks similar to some of the measurements we have seen for a series RLC circuit. Turns out you can model the effects of turning off a MOSFET with a series RLC circuit, where the L is the parasitic inductance of your circuit and C is the capacitance of your MOSFET. Here you can try and decrease the wire length you used to wire the MOSFET to the rest of the circuit and see if you can reduce this overshoot.
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).
Bonus: If you want to try and increase the efficiency of your buck converter you can try and decrease the inductor loss by placing two inductors in parallel. Or you can try changing the switching frequency by adjusting the resistors in you 555 timer. Or you can try two diodes in parallel to decrease their conduction losses. Or many other things, talk to a staff member if you want help trying out some ideas.
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.