We can also find the Bode plot from experimental data.

The key is to remember how the transfer function relates to input and

output magnitudes.

So the amplitude of the output signal divided by the amplitude of the input

signal, is the magnitude of the transfer function at that frequency.

And similarly, the phase angle is defined as the difference between

the input waveform and the output waveform.

Now let's look at some experiments relating that.

Here is an oscilloscope trace of an input and an output of an RC circuit.

The input is shown in green and the output is shown in blue.

For this particular frequency, the frequency is at 1,000 Hertz.

And you can see that the output amplitude

over the input amplitude is a ratio of 0.8.

So the transfer function at that frequency is 0.8,

magnitude of the transfer function.

If an instrument like a Bode

plot instrument, electronic instrument wants to find a Bode plot automatically,

what it does is it inputs a frequency like this.

Find its ratio of amplitudes,

finds the phase angle between them at that frequency, and then records it.

And then it changes the frequency, and does those recording again,

the amplitude ratio and the phase lag.

Let me show you an example of running a Bode Plot instrument.

So here's with the same circuit hooked up.

And I'm going to hit run on this and you'll see it building it up.

For each of those points, it's finding the amplitude ratio and

taking 20 times the log of it, and plotting it.

This is gain in decibels and down here is the phase angle in degrees.

Again, found numerically or found experimentally by looking at the angle

difference between the input signal and the output signal.

So this again is an automatic generation of the Bode Plot experimentally,

without even having to worry about the explicit formula for H of omega.

Now I want to take a look at our other circuit where I take the output across

this resistor.

Now this is a transfer function and

we can get the transfer function similar to what we did before.

We used the impedance method, where we use the voltage divider law.

So it's R over R plus this impedant, one over j omega c.

And that would be to find V out given Vs.

So this is a transfer function and if I clear my fractions I get this.

Now if I plot the magnitude versus frequency and

the angle versus frequency, I get these two Bode plots.