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Welcome back to Linear Circuits, this is Dr. Ferri.
I wanted to finish our little sequence of lessons on
filters to talk about Bandpass and Notch filters.
Let's give an overview of all the Common Filters we are looking at.
This is a Lowpass Filter where it passes through frequencies that are low,
then the Highpass Filter passes through frequencies that are high.
A Bandpass Filter is one that passes through frequencies in a region
right here.
So, that's the band of frequencies and
a Notch Ffilter is one that stops frequencies in a certain region.
Sometimes people call this a band stop filter as well.
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Let's look at a little bit more about the characteristics,
starting with a Bandpass Filter.
So let's define the passband as the region during which we pass through frequencies,
now where does these defined?
These are defined, again, as three decimals below the passband gain.
So this is the pass band gain, G sub DB here, this is plotted on a plot and
so this point right here is three decimals below that.
And again, over here, this is three decimals below that,
then this is the passband.
Sometimes we use this, for example, in communications.
We're interested in certain frequency bands.
We want to pass through those frequency bands and attenuate everything else.
Now, a Notch Filter looks like this.
This is what we'll call the stopband.
That's the region of interest, that's where we stop frequencies.
Again, we have the passband gain.
Sometimes this is different on one side verses the other side, but
we'll call that the passband gain and this is stopband region.
Where we might us a stopband is when we have a particular frequency that
bothers us, so we want to get rid of it.
60 hertz comes to mind, because a lot of times a measurement signals 60 hertz
shows up as a measurement noise.
And in other countries, 50 hertz might be, because that's the line voltage.
Now if I want to implement this with an RLC circuit,
I would take the voltage across resistor and this being a bandpass filter.
The center frequency of that band is 1 over the square root of LC and
the width of that bandpass is R over L.
So I can use these variables,
these parameters to try to select a particular frequency band that I want.
The width and the center frequency of my design.
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In terms of a Notch Filter, I get the Notch Filter by taking the output
across this combination, the inductor and the capacitor.
And that gives me the Notch Filter with a center frequency, again,
1 over the square root of LC.
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Out 60 hertz.
So this right here, in other words, I want 60 hertz to be here.
But this is in terms of radians per second, so
I have to convert that to radians per second.
So it's 60 times 2 pi,
which is 377 readings per second.
So then I just use this formula back here and let's see,
I tend to be able to find more commonly inductors than I do capacitors.
So, I'm going to pick the inductor first and I have more choice over capacitors.
So I let L = 10 millihenrys,
then I've got going to this formula,
I've got omega 0 squared = 1 over LC.
If I solve for C, I get 1 over omega squared L and
that is equal to 700 microfarads.
To summarize, we've introduced two very important types of filters,
a Bandpass Filter and a Notch Filter.
Now the Bandpass Filter passes through frequencies in a certain passband region,
where a notch filter or
sometimes we call bandstop filter stops frequencies in a certain stopband range.
Now we've talked about applications where these are important and
we've introduced RLC circuits that can be used to implement these sorts of filters.
But typically, when I have to actually implement a bandpass or a notch filter,
I'll build it out of op-amp circuits.
They're a little bit more useful and a little bit more flexible in the design,
but the basic concepts that we've covered in introducing these filters hold
whether it's an RLC circuit or an op-amp circuit.
Thank you.
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Dr. Bonnie H. FerriProfessor
Dr. Joyelle HarrisDirector of the Engineering for Social Innovation Center
