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Â Welcome back to Linear Circuits, this is Dr. Ferri.

Â I wanted to finish our little sequence of lessons on

Â filters to talk about Bandpass and Notch filters.

Â Let's give an overview of all the Common Filters we are looking at.

Â This is a Lowpass Filter where it passes through frequencies that are low,

Â then the Highpass Filter passes through frequencies that are high.

Â A Bandpass Filter is one that passes through frequencies in a region

Â right here.

Â So, that's the band of frequencies and

Â a Notch Ffilter is one that stops frequencies in a certain region.

Â 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,

Â starting with a Bandpass Filter.

Â So let's define the passband as the region during which we pass through frequencies,

Â now where does these defined?

Â These are defined, again, as three decimals below the passband gain.

Â So this is the pass band gain, G sub DB here, this is plotted on a plot and

Â so this point right here is three decimals below that.

Â And again, over here, this is three decimals below that,

Â then this is the passband.

Â Sometimes we use this, for example, in communications.

Â We're interested in certain frequency bands.

Â We want to pass through those frequency bands and attenuate everything else.

Â Now, a Notch Filter looks like this.

Â This is what we'll call the stopband.

Â That's the region of interest, that's where we stop frequencies.

Â Again, we have the passband gain.

Â Sometimes this is different on one side verses the other side, but

Â we'll call that the passband gain and this is stopband region.

Â Where we might us a stopband is when we have a particular frequency that

Â bothers us, so we want to get rid of it.

Â 60 hertz comes to mind, because a lot of times a measurement signals 60 hertz

Â shows up as a measurement noise.

Â And in other countries, 50 hertz might be, because that's the line voltage.

Â Now if I want to implement this with an RLC circuit,

Â I would take the voltage across resistor and this being a bandpass filter.

Â The center frequency of that band is 1 over the square root of LC and

Â the width of that bandpass is R over L.

Â So I can use these variables,

Â these parameters to try to select a particular frequency band that I want.

Â 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

Â across this combination, the inductor and the capacitor.

Â And that gives me the Notch Filter with a center frequency, again,

Â 1 over the square root of LC.

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Out 60 hertz.

Â So this right here, in other words, I want 60 hertz to be here.

Â But this is in terms of radians per second, so

Â I have to convert that to radians per second.

Â So it's 60 times 2 pi,

Â which is 377 readings per second.

Â So then I just use this formula back here and let's see,

Â I tend to be able to find more commonly inductors than I do capacitors.

Â So, I'm going to pick the inductor first and I have more choice over capacitors.

Â So I let L = 10 millihenrys,

Â then I've got going to this formula,

Â I've got omega 0 squared = 1 over LC.

Â If I solve for C, I get 1 over omega squared L and

Â that is equal to 700 microfarads.

Â To summarize, we've introduced two very important types of filters,

Â a Bandpass Filter and a Notch Filter.

Â Now the Bandpass Filter passes through frequencies in a certain passband region,

Â where a notch filter or

Â sometimes we call bandstop filter stops frequencies in a certain stopband range.

Â Now we've talked about applications where these are important and

Â we've introduced RLC circuits that can be used to implement these sorts of filters.

Â But typically, when I have to actually implement a bandpass or a notch filter,

Â I'll build it out of op-amp circuits.

Â They're a little bit more useful and a little bit more flexible in the design,

Â but the basic concepts that we've covered in introducing these filters hold

Â whether it's an RLC circuit or an op-amp circuit.

Â Thank you.

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Â