Welcome back, this is Dr Ferri. In this lesson we will look at another
lab demo, this one on RLC circuits. Just to remind you where we are in this
module, we've looked at the analysis of an RLC circuit, now we are going to look
at a demonstration of it. We would like to measure the response of
this circuit. Now this circuit, we would like to have a
voltage source right here, but there's a bit of a problem with this.
The problem is that if I want to give this a square wave input, So, I want to
trigger the transient. I've got sharp and abrupt changes in the
voltage. Well, sharp and abrupt changes in the
voltage here are going to require sharp and abrupt changes in the voltage over
here. And, because the current is equal to c
times DVCDT. I'm looking at the derivative of
something that changes very quickly. So that means it's going to require large
currents. And this is a problem when you're trying
to build a circuit. A lot of times this causes problems.
If I'm going to require a lot of current here, my source Has to be able to give a
lot of current, have the high current limit.
And a lot of sources function generators don't.
It, it's equivalent to having a, a triple a battery.
You're trying to, to power a circuit with a triple a battery.
Well, triple a battery has 1.5 volt value to it, but it's very current limited,
very power limited compared to a D size battery, which is also 1.5 volt, but it
can pack a lot more power to it. So what we have to do is get a circuit,
you know, put a, some sort of conditioner on this, so that we can give the power
that we need. And the particular circuit we're going to
build is, it's going to be what I would call a buffer circuit built out of an op
amp. This will be the output of my function
generator here, and I'm going to put it through a buffer circuit that amplifies
the power, so that V sub S right here is the very same voltage level as it is
here, but it's able to draw more current. And in case you're interested, the actual
circuit that I built is an up amp, it's a common device.
And it has it's own power supply, and because of that it's able to provide more
power than the function generator. So that's just a common problem that you
sometimes have in building a regular circuit.
So the lab demo is on RLC circuits. We're going to be building an RLC circuit
on this proto-board. And demonstrating its response.
And I notice that I've already got something hooked up here.
This is our op amp circuit. Remember that the op amp helps us to
boost the power. So I've got the input to the op amp
circuit from the function generator. And the op amp itself is inside this
integrated chip. And it's got metal pins out the side of
the integrated chip that allow us to hook up to the internal components.
The output the op amp goes here, and that's going to be the input to my ROC
circuit. Here's our schematic here.
The function generator is hooked up here. And I've got a common ground.
My voltage source to my circuit I'm going to define as being right here, V sub S.
Recall that has the same waveform as function generator waveform, the same
voltage level, but it's able to provide more current.
So I'm going to hook this up as, to my oscilloscope to display it, and it's
going to be channel zero. And I'm also interested in the voltage
across the capacitor, and I'm going to hook that up to the oscilloscope channel
1. Nathan has already examined this circuit
and shown the equations for the circuit, and they're given here.
If we want to find what sort of response it is, we have to find the roots of this
polynomial right here. For these values of L, R, and C, I get
real roots. These are the roots right here, the real
and distinct roots. That means that this is an overdamped
system. And just as a, sort of beyond the scope
of this particular course, but, if you understood about differential equations,
you could write down what that response looked like.
And with an overdamped system, it would look like these.
The 2 roots show up as exponentials. And notice, that one of them is very,
very negative. And if I were to plot this, it decays so
quickly that it becomes negligible very quickly.
And the response looks more like a first-order exponential response.
So that's what we predict will happen here, that we're going to get an
overdamped system that looks more or less Like this one right here.
Now let's go back and build our actual circuit.
This comes from my op amp, and that's [INAUDIBLE].
I connect that to this Inductor, remember that inductor is just a coil of wires.
In series with that inductor, I put a 20 k resistor.
In series with that resistor, along this same row, I'm going to insert a
capacitor. Ok, so I've got those three in series
now, and I have to finish my circuit by connecting it to ground.
So that's my ground wire. Now I want to hook up the oscilloscope
channels. I'm going to zero out channel zero that I
connected to ground and the low side of channel one, again, to ground.
Remember, along the rails of a, side rails of a Try to avoid the raw
connectors. Everything all in here are connected
together, so all these wires are connected.
The plus side of channel zero, I want to hoook up to [UNKNOWN] s.
Plus side of channel one I want to hook up to [UNKNOWN] c.
So now I have my circuit hooked the way I showed in the schematic.
Let's go to the function generator and oscilloscope panels and I've got my
function generator set to a square wave at 700Hz We start that running, and let
me run the eselescope. And I see that my response looks this way
that the. Let me go ahead and change that.
There it is. I'm displaying channel 1 and channel 0.
So channel 0 is in green and channel 1 is in blue.
Channel green is my voltage source, and channel blue is my capacitor voltage.
So, you see I, I predicted that it would look exponential, and it does.
Because my roots are, it's an overdamped system with my 2 roots that are very
different in magnitude with respect to another.
And so the result looks like a first order system, and I can actually come up
with a time constant here. So this is an overdamped response.
Going back to this slide is schematic. If I changed my, my 20K resistor to 100
ohm resistor, and recalculate what the roots are, I now find that the roots are,
are imaginary or complex, where j is the square root of minus 1.
So, this is the imaginary part versus the real part.
The smaller the value of R, then this becomes, this gets to be low damping.
So, as R is decreased, decreased to some value at which.
I have complex roots, and then if I continue decreasing R, then my system
becomes, has lower and lower damping. So right here, looking at the root,
complex roots meets its under-damped. Low values of r means that the imaginary
part becomes large with respect to the real part.
Where does that happen with regard to the response that I see?
So, what I want to do is take out the 20 k resistor.
So, you're seeing what the 20 k resistor is.
That's an overdamped case. We take that out, and put in 100 ohm
resistor. Can you see that response.
That's an underdamped response. You see that oscillation?
Let me expand the time scan here, so you can see it a little bit better.
You see the oscillatory behavior. The smaller the value of R, in the
circuit, the smaller the resistance, the higher peaks I have.
The more oscillatory that behavior is. The lower ends also known as lower
damping in my system. So, over damp system comes from real
roots, under damp system comes from complex roots.
Thank you. So in summary, we've seen that an
underdamped RLC circuit has the small r value, and results in large peaks.
An over-damped RLC circuit has a large R value and doesn't have any peaks to it,
no oscillatory behavior. In the next lesson, we will look at
applications in inductors and capacitors that exploit mechanical components.
Thank you.