Welcome back to Linear Circuits. 
This lesson is going to be a lab demo. 
We're going to be looking at the 
frequency response of an RLC circuit. 
And basically trying to reemphasize some 
material that we learned in our last 
lesson, which was more general, the 
theoretical aspects. 
We are still in the topic of frequency 
response in this module. 
In module three we built an RLC circuit 
and we had a lab demo of it. 
And that was to look at a transient 
response, for we want to plot, look at 
the very same system and as you recall in 
the last. 
Module, we had to build a buffer circuit 
in there to be able to boost the power. 
So, if this is our function generator, we 
built in our little [INAUDIBLE] circuit, 
here, in order to be able to produce the 
correct signal that we needed here, with 
enough power to run this circuit. 
So, this is a circuit schematic of what 
we're building. 
So, the lab demo is the RLC circuit 
frequency response. 
 >> So, this is a RLC circuit that we've 
already built before. 
Recall in the lesson, in the last module 
when we were looking at transient 
response of second order systems. 
We built a circuit like this. 
So, this has an inductor in series with a 
resistor in series with a capacitor. 
And we are measuring the voltage source, 
which is across these green wires as our 
input to our circuit. 
And out output is the voltage across this 
capacitor. 
Looking at our screen and our actual 
response, if I gave it a square wave what 
I would see is the characteristic 
response of an over-damped system. 
So, with these values, it's an 
over-damped system. 
Now we're interested in the frequency 
response. 
So, we want to see sinusoidal responses. 
At this frequency of ten hertz the output 
looks very much like the input. 
So, the output is in blue. 
That's the capacitor voltage. 
The input is in green and that's the 
source voltage. 
I'm going to do a sine sweep. 
Where I change the frequency slowly in my 
input and you'll what happens to the 
output. 
So, as I increase it what you're seeing 
and I have wait till it reaches steady 
state so what you're seeing is the 
amplitude is decaying. 
Lets change my scale here. 
So, the amplitude is changing as I change 
the frequency and also there's a lag 
that's appearing. 
So, the amplitude, so the response of the 
system is a function of the frequency of 
the input. 
So you see as I'm changing that frequency 
in input. 
My amplitude actually is going lower, and 
my phase is changing. 
I can take these, this data. 
I can measure the amplitude change, the 
ratio of the output amplitude over the 
input amplitude. 
For each point frequency that I've looked 
at the forcing signal at. 
And I can also measure the phase lag for 
each point. 
So, if I measure it at each frequency and 
then plot it, I will get the frequency 
response. 
Well, fortunately, most instruments do 
that automatically for you and I'm going 
to close these and go ahead and open up 
the bode plot. 
So, this automatically does the 
calculations in the measurements to do a 
bode plot for you, automatically. 
So, I'm going to go from 10 hertz to a 
1000 hertz. 
And I'm going to run this. 
What you're seeing at each one of these 
point where it, it shows a point, it has 
input a sine wave into my circuit and it 
measured the output amplitude and it 
measured the phase. 
In the output amplitude, it divided by 
the input amplitude, took the log of 
that, and multiplied by 20 to get values 
in decibels. 
So, these are the amplitudes given in 
decibels and then its measured versus 
frequency on a log scale. 
And then these are the phase lags 
measured in degrees, and it did it 
automatically for you. 
Now let's go back and look at this same, 
experiment but within under damp system. 
So, an over damp system, you see 
something that tails off like this. 
And I want to mention one other thing is 
that, we can calculate the bandwidth as 
being the value at which this is three 
decibels below the low value, low 
frequency value. 
So, three decibels is about right here. 
So, I would say the bandwidth of this 
particular circuit is in the range that's 
about 20,30. 
In the range of about 40 hertz, that's 
when I'm down three decibels from my low 
frequency value. 
So, let's go back to this circuit. 
I am replacing this resistor, which was 
20K, with a much smaller resistor. 
And, as we've seen before, if I decreases 
resistance, that will lower my damping to 
the point where this is now an under 
damped response. 
So, this particular case. 
Change my values here, want to look at 
the response due to square wave. 
And, I need to enable the, any other 
thing I need to do is check the trigger 
so that my display looks better. 
You can see that it oscillates there, it 
over shoots and then comes back. 
That characteristic of an under damped. 
Response, that means I've got complex 
roots. 
Now lets look at the frequency response 
of an under damped case. 
First of all lets do a sine sweep. 
Start out with a frequency of 100 hertz 
and I'm going to be increasing the 
frequency. 
My two signals, one in green is my. 
Input voltage, and one in blue is my 
output voltage. 
You see here, in this frequency range 
there is a difference. 
My output is lagging my input. 
My output starts lagging my input, but 
one thing you'll see is that my output 
has a higher amplitude. 
Than my input. 
See the output amplitude's getting larger 
and then it goes smaller. 
So, this is a difference between an a 
under damped system and the over damped 
system. 
The under damp system, the output starts 
becoming a little bit larger, and then it 
gets smaller. 
So, this is a case of my damping it's 
really, really small. 
I have that situation. 
Now let's look at the bode part. 
What I should see in the bode part is 
that my frequency response should pick up 
right above this frequency, that's about 
the frequency at which I get may be the 
largest. 
Value, that's around 4, 4000 hertz, and 
we call that a resonant frequency, is 
when my output frequency my output 
amplitude becomes the largest relative to 
my input amplitude. 
And that would be resonance. 
Let's look at our bode plot now. 
Okay, I'm going to go ahead and run this. 
It is automatically doing a sine sweep. 
You see this is the output amplitude over 
the input amplitude in the log scale. 
And you see how it peaks up. 
This, in this range it means that the out 
put amplitude is lager than the input 
amplitude. 
And this happened, the peak happened at 
about, it's 2000, 3000, around 4000. 
Around 4000 hertz. 
Is when we hit that resonant right there, 
and we call that the resonant frequency. 
When we run this with a few more points 
in there, so get better resolution. 
[SOUND] So, it's just checking more 
frequencies. 
A smoother plot. 
Okay, so checking a little bit better, 
it's still. 
It's now between, that's two, three, 
four. 
Really between four and five K hertz is 
what my resonant frequency looks like. 
And the other thing to notice is that my 
phase goes from zero down and it's 
approaching minus 180. 
So, the characteristics of an under 
damped system with low damping is that 
the frequency response peaks up. 
Now, what's the bandwidth in this case? 
Well it's a frequency at which we're at 
three decibels below my low frequency 
value. 
Low frequency is at 0 db and my bandwidth 
is right around here which looks to be 
around, around 8K, I would call that my, 
my bandwidth around 8K. 
So, in summary we've looked at the 
frequency response. 
We generated it automatically using a 
bode analyzer which is a very common 
instrument in, in electronic 
applications. 
Thank you. 
 >> So, in summary what we found is that 
in low R in an RLC circuit. 
Means that you've got low damping. 
And a high resonant peak. 
And that resonant peak means that my 
output amplitudes, when I've got 
frequency, a sine wave at that frequency, 
my output amplitudes are going to be very 
large compared to my input amplitude. 
And we've found that we can generate the 
bode plot by a sine sweep. 
Where we input sine waves of different 
frequencies, and then we calculate the 
amplitude ratio. 
The amplitude of the output signal versus 
that of the input signal. 
And we also look a the phase lag for each 
response, and then we plot that. 
In doing a bode plot you have to first 
take 20 times the log of that ratio 
before you plot it. 
Would plot both the magnitude and the 
phase versus frequency and that gives us 
a bode pot. 
And this can be done automatically and 
there're a lot of instruments that do 
that. 
Our next lesson with be an introduction 
to filtering.  Thank you.