Party Lights
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Today we're going to do something quite magical. We're going to light up a little string of lights. Well, maybe that doesn't seem so magical, but it is, trust me. Start by grabbing yourself a little string of lights from up front, and a AA battery (1.5 Volts) and holder.
Each of the bulbs in our little string of lights is an LED (a "light emitting diode"). We haven't covered diodes too much in class, but the s that when a voltage of the proper polarity and magnitude is applied, current will flow, the LED will light up, and it will maintain a roughly-constant voltage drop across it. For the lights we're using, they'll turn on when the voltage drop across them is around 2.4V (though it depends on the color of the LED).
1) This Little Light of Mine
To start, let's hook up the lights to our battery. You can plug the battery leads into a breadboard, and then you can use alligator clips to connect up one end of the lights to a little piece of wire that you can jam into the board, like so:
Also note that the lights have a polarity (i.e., it matters which side is connected to + and which is connected to -). A little protrusion on the plastic casing of each LED marks the + side:
OK, so hook up your battery across the string of lights. Do they light up? No they don't. How sad. But has your day been ruined? Of course not! During the remainder of the lab, we're going to light up the darkness and push the bad feelings away through the magic of power electronics.
Why didn't the bulbs turn on? Well, remember that in order to turn on, each bulb needs about 2ish Volts across it. So we need a much bigger voltage in order to turn the lights on. Let's test a little bit more to figure out what we're aiming for.
Turn the power supply on and slowly, SLOWLY and carefully turn the voltage
up. DON'T GO ABOVE LIKE 20V, the lights won't like that. What voltage is needed to make the lights start to light up? What is
needed to make them light up nice and bright? Make a note of these voltages.
2) Boost!
OK, so yep, we need substantially more than 1.5V to light up the lights. What are we going to do? Well, conveniently (almost as though we planned it that way), we saw a circuit in lecture yesterday that will be very useful here: a Boost Converter, which can produce a large voltage from a small voltage.
As a reminder, here is a conceptual model of the circuit:
The circuit generally operates in three stages:
- In stage 1, S_1 is closed and S_2 is open.
- In stage 2, S_1 is open and S_2 is closed.
- In stage 3, both switches are open.
These stages are repeated in quick succession, forever; so after stage 3, we proceed back to stage 1. Let's take a look at how the voltages and currents in the circuit evolve during each of these stages, theoretically.
2.1) Analysis: Stage 1
During stage 1, switch S_1 is closed and switch S_2 is open; so the inductor has one side shorted to ground and the capacitor is completely disconnected from the circuit, like so:
Let's think about the case where, just before entering stage 1, the system was at rest (i.e., no current through the inductor and no voltage across the capacitor). Then we enter stage 1 at time 0.
Answer the following questions, assuming these initial conditions;
use V_IN, T_1, C, L, and whatever mathematical constants you need in order to
answer the question.
i_{\rm L}(0^+) =~
We stay in stage 1 for some arbitrary amount of time T_1.
i_{\rm L}(T_1) =~
Sketch out how both i_{\rm L} and v_{\rm C} are changing as functions of time over the course of stage 1. We'll add more pieces to this sketch in a moment, and you should be prepared to discuss your sketch during the first checkoff.
2.2) Analysis: Stage 2
Next, we enter stage 2! During this stage, switch S_2 is closed and switch S_1 is open, meaning that the inductor and capacitor are connected to each other directly (during this stage, this looks like the driven LC oscillator we saw in lecture before!):
i_{\rm L}(T_1^+) =~
We stay in stage 2 until the inductor current reaches 0 (call this time T_1 + T_2).
i_{\rm L}(T_1+T_2) =~
Sketch out how both i_{\rm L} and v_{\rm C} are changing as functions of time over the course of stage 2. We'll add more pieces to this sketch in a moment, and you should be prepared to discuss your sketch during the first checkoff.
2.3) Analysis: Stage 3
Finally, in stage 3, both switches are open.
i_{\rm L}((T_1+T_2)^+) =~
We remain in this state for some arbitrary amount of time, until t = T_1 + T_2 + T_3.
i_{\rm L}(T_1+T_2+T_3) =~
Sketch out both how i_{\rm L} and v_{\rm C} are changing as functions of time over the course of stage 3.
Discuss your results from above (and your sketches!) with a staff member.
3) Build It!
Phew! Now that we've done some analysis to know what to expect, we can carry on with actually building the circuit! In order to do so, we're going to need to make a few small changes/additions to our circuit. The main difference is that we'll need to use real components to create switches that can be controlled electronically (rather than mechanically).
As we did last week, we'll use a MOSFET for one of our switches. When the voltage on its gate terminal is high enough, it will open a path for current to flow (closing the switch).
For the other one, we'll use a diode. The diode will allow current to flow in one direction (from the side without the line toward the side with the line) but not in the other direction.
We'll also add another diode right next to the voltage source, to keep current from flowing back in that direction (this will keep things closer to the idealized model we analyzed above).
All told, our circuit will look like this:
Let's go ahead and build this. As you're laying our your circuit, take note of the following:
-
The 1.5V source in the diagram is a stand-in for our AA battery.
-
Build things without the battery connected first, and only connect it when you need to.
-
Try to keep things relatively compact on your breadboard if you can.
-
Both the inductor and the capacitor are up on the cart today, not in the cabinet (use the big chunky brownish/reddish/purplish capacitors, not the little black/blue cylinders).
-
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.
-
We're going to grab V_{\rm sq}, which will control the switch in our circuit, from the wave gen on the scopes. Use the following settings:
- square wave
- 75kHz
- 5Vpp
- 2.5V offset
- 50% duty cycle
If you want us to check your circuit before powering it on, let us know!
4) Measurements
Let's also connect up a load resistor, as a temporary stand-in for the lights we'll hook up in a second. For now, use a 4.7{\rm k}\Omega resistor, hooked up like so:
Before we move on to the lights, let's make some measurements to make sure that the behavior of the circuit agrees qualitatively with what we expect. For each experiment, it's a good idea to disconnect your battery before performing the experiment, and only to connect it when you're ready.
Please read each of these carefully, and actually do all the steps. We'll expect you to be ready to talk about all of these during your checkoff.
Experiment 1: Output Voltage
Let's hook up a multimeter to measure the voltage drop across the load, and then connect the battery up. What value does it reach?
Think about your sketches from above; what is different about this circuit,
compared to the one we analyzed earlier, and how does that affect how i_{\rm
L} and/or v_{\rm C} are changing in the various stages?
Experiment 2: Duty Cycle Effect on Output Voltage
Try adjusting the duty cycle of the square wave down from 50% (you can measure V_{\rm sq} with the scope probes to see the effect this has on the input wave if you want). What effect does this have on the voltage?
Try adjusting the duty cycle upwards as well; what effect does this have?
Make a note of all of these, and be ready to talk about them during your checkoff.
Before moving on, adjust your duty cycle so that the output voltage is sitting at around 15V.
Experiment 3: Effect of Load Resistance
Swap out the 4.7k\Omega resistor for a 1k\Omega resistor. What happens to your output voltage?
Experiment 4: The Approach
In lecture (and in last week's p-set), we saw that the output voltage should grow proportionally to \sqrt{n}, where n is the number of full cycles we've gone through. Let's see if that's really the case!
Put the 4.7k\Omega resistor back in (replacing the 1k\Omega resistor), and set up your scope as follows:
- Put the trigger at around 7.5V
- Set the timescale to be around 5ms/div
- Click "single" (which will cause the scope to wait for a single trigger event and then freeze.
Then, disconnect the battery, and then quickly reconnect it. This will show us how things are changing in the early moments.
Note that in order to make this work, the connection needs to be made quickly. What I would suggest is leaving the ground side of your battery connected and then, instead of plugging the + side into the breadboard, just touch it to the leg of the diode briefly, like so:
You don't need to leave it held there very long; just long enough to trigger (which should happen fast).
Take a photo of your scope screen so that we can discuss this shape during your
checkoff.
Experiment 5: Inductor Current
Let's also make sure that the inductor current is changing in the way we expect it to, from our graphs. Our scopes can't measure current directly, but we can use multiple voltage measurements to take care of this. Let's (temporarily) adjust our circuit to make a measurement by adding a little resistor, like so:
If we measure the voltage on the left side of this resistor on channel 1 and the voltage on the right side on channel 2, then their difference (which we can compute using the math functions on the scope) will be proportional to i_{\rm L}!
You should be able to get a nice, clear view of the inductor current's general
shape. Does it agree with your sketches from earlier? Can you pick out stage
1, stage 2, and stage 3 on it? As before, take a photo of your scope screen so that we can discuss it during
your checkoff.
5) Light Show
OK, now to (finally) put our circuit to use! What we'll do now is to use the circuit to power our light strip from earlier (there should be plenty of voltage now!), like so:
- Disconnect the battery
- Remove the 10\Omega resistor we just put in, so that the inductor is once again connected directly to the diode.
- Remove the 4.7k\Omega load resistor and replace it with our light strip (remember that the side with the little plastic protrusion should go on the + side of our output, and the side without it should go on ground).
- Connect the battery again.
- Adjust the duty cycle so the lights are as bright as you can make them.
Discuss the results of all of your experiments above with a staff member, and demonstrate your working lights.