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.