We're continuing in op amp applications and in this section, we'll be looking at a band-pass filter and a band-stop filter. We begin with the band-pass. As its name implies, it passes only a specific band of frequencies and you can see from the graph here that that is exactly what it does; it passes a specific a band and sometimes you'll have several … well … a band of frequencies will be passed. This is widely used in TV … also in radio. Just as in the example with AM Radio, if you were looking at AM 950 K-Hertz, you know it comes in … and this would be 950, and that particular band is the transmission it will be ten K-Hertz … wide. So it will go from nine...actually from 945 to 955 and that would be, in this case, the band that is being passed.
In television, at least in analog television, the band is actually quite wide; it's six Mega-Hertz wide. So you'd come along and you'll have this band of frequencies and that contains the audio and the video, and the colour information takes quite a bit more data than does radio which is only voice and then if we went to FM, we'd find that this is actually 200 K-Hertz wide because FM is going to have a better sound quality … anyway, these are just some examples of what device or … systems that would utilize a band-pass filter. Now let's take a look at this circuit. What we'll notice here is that we have a cap in series with the op amp, and then we have another cap that's in the feedback loop. So what will happen is that this cap will be very reactive at low frequencies and more passive so no signal will get to the op amp. Then at a very specific frequency, this will begin to pass the signal and so it will send that signal into the op amp, we will have amplification. But notice that we have another cap in the feedback loop, and remember that the feedback loop will determine how much amplification we get. When this begins to conduct, this will begin to look like a short circuit and so then we will have zero ohms of resistance in our feedback loop and that will cause our gain to go to zero. So what we end up here is for a very short duration we have the passing of frequencies. Your text does not give you a formula for calculating this frequency. I happen to have one that will do it; it is one over two pi times capacitance times the square-root (I can draw this line across here) … the square-root of R1 in parallel with R2 times the value of R4. If you type that into a calculator, it will come out with this frequency and that would be the pass band if we were using this particular circuit.
Now I built a circuit in Electronics Workbench. This is in fact, that circuit, it was not in your package of circuits, but I just wanted to confirm the fact that this actually is the frequency and you'll note here is our signal source, here is the capacitor in the input, and then here's the capacitor in the feedback loop. You'll note here is the bold plot, and I have had the blue line as capturing the passing of the frequency. You'll notice down here that 968.9 … 69 Hertz is that passing frequency, and what was our calculated value was 973 so that is really quite close to the actual value that we see in simulation. OK then, we come to the band-stop filter. Sometimes this is called a band-reject filter. We have a circuit here and this is going to do, in fact, sometimes they call it the ‘notch filter' because what this typically looks like is you have a band of frequencies come along and suddenly there is a notch cut out and you no longer see the signal. We have a formula Fr here, this is a frequency that is rejected, and this will be one divided by two pi times R1 and C1. If we calculate this out, we find that this will create a notch at an about four K-Hertz. Let's talk a little bit about how this actually works. Low-frequency C3 has a high reactance and the signal is passed through R1 and R2, it looks like a low-pass filter so going along this branch this looks like a low-pass filter until you get to a frequency that is high enough that C3 starts to conduct and then that signal is shunted away from the input down through C3. So the top half looks like a low-pass filter then C1 and C2 act as a high-pass filter so when they get up to a certain value, C1 and C2 begin to conduct and it will pass it's signal to the input. The circuit acts as a low-pass filter in parallel with a high-pass filter. At a specific frequency, the leading and lagging signal applied to the input of the op amp will cancel each other out, resulting in a notch in the band. So here we have a signal coming in here, and a signal coming in here. The signal coming through here will … Ok it will come through here but it will also go through this RC; this is actually an RC network, which will cause the signal to lag a little bit behind. Then the signal passing through here will lead that signal. It will both reach the system and there will be a point where the two will tend to cancel each other out and we will end up with a notch.
This is the circuit, in fact, this is the circuit that comes from your textbook, and the calculated value was, again it was about four K.
When I did this in the simulation I couldn't put the blue line directly on the notch because it actually covered up the notch so you couldn't see it so I pulled it a little bit away from the notch, but you can see the frequency there is 3.981, which is very close to the value that we calculated … well the multi-sim that put it right on there, it was actually 4.09 but anyway, it is very close to the calculated notch. Now this one, it has a little spike right here. I have seen other filters that are a little bit cleaner than that; they will just come along and be a very specific notch. These are, as I mentioned earlier, these are used to filter out things like 60 Hertz hum. Sometimes in cable systems, they are used to actually notch out a given frequency a customer does not particularly want. So these have a number of industrial uses.
So in this section, we look briefly at a band-stop filter, looked a bit at the theory, and we looked at the band-pass filter. So this concludes this section.
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by Jake Hertz
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