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.