Ok, we're continuing our discussion of operational amplifier applications and we're going to be looking at the subject of active filters. Active filters could be differentiated from what we would call a passive filter. A passive filter is a filter that is going to be a filter that is based on resistors, capacitors, inductors, and there will be … no … a passive filter doesn't have any voltage or any amplification whereas an active filter we'll going to use additional voltage and additional amplification to cause a more precise filtering. Now passive filters can be quite accurate but they do not amplify the signal at all and they do not use … they simply take the frequency they send in and filter it and provide an output. Often times the output will be quite severely attenuated and in active filters, there's an amplifier ball so the signal can be boosted in the process. Again there are four types of filters. First of all, there all low pass filters. They pass only the low-frequency signals and these are used, one example is that they are used in DSL lines. High pass filters, they pass only the high frequencies. Band pass active filters, they pass only a specific band of frequencies. You might see something kind of like that. They are used in radio and TV transmissions. Band-Reject Filters, they chop out a specific frequency. Might have a band of frequencies or suddenly … a certain band of frequencies just suddenly cut out. They're used to filter out 60 Hertz hum. Sometimes they're used in some cable systems; they're used to block certain channels.
Low Pass Filter
The first one we're going to look at is the low-pass filter. What we have here is a graph of the output of a low-pass filter and so you get the idea of what is going on and in here we have frequency going from zero up to whatever frequency that we're filtering. Here is the amplitude of the signal and what we have here is … in this band here, we're passing everything but when we get up to a certain frequency we begin to lose the signal. This part here...lots of different types of low-pass filters but this is one of the common configurations that will give us low-pass filtering.
The frequency of concern is called the critical frequency and the critical frequency on this graph is this point right here. We call that the point where the signal is … prior to this point, we're going to pass this signal at this point, we're going to begin to severely attenuate that signal. The formula is one over two pi r times the square-root (I guess I could draw this out) times the square-root of C1 times C2. This is the actual calculation; we're using the values that we have here. If you do that, you'll find that the frequency is 7.04 K-Hertz. At the critical frequency, the output will be 70.7 percent of the input volt. Now, this value isn't in your textbook. From this graph that is in your text, you can kind of ascertain that that is actually the value.
The reaction of the two capacitors is such that they look like and open for frequencies below 7.04K-Hertz. Above 7K-Hertz they short and the input does not get to the output. If you look at the position of the capacitors in this, one is right here at the input and one is in the feedback loop. Now as we apply a signal here at low frequencies, they will both have high reactants and they won't be passing this signal. This input, in this case, will get to the op amp, it will amplify … this will be a resistance in parallel with this, so there will be a feedback loop and we will have a passing of a signal over here. Now when this gets to a sufficiently high frequency, in this case, it is seven K, these capacitors will begin to conduct, they'll begin to look like a short and this signal, instead getting the op amp, it is going to have an alternate path to grab on so it won't be conducting, it won't be getting passage of signal. This capacitor will begin to short, so the feedback loop will begin to look like a straight short, and so there won't be much amplification there. What we'll end up with is that in the low band of frequencies it will pass as soon as it gets up to the critical frequency we will begin to lose and it will be severely attenuated. This is an example of a low-pass filter, some of you may have seen these if you're using a DLS line, you would plug this into your telephone and then you, you know, when you're using your phone, this will eliminate some of that potential high-frequency noise in the DLS line. DLS lines and data invoice over the same line, the high-frequency data is in the range of 25 to 1.5 Mega-Hertz.
The voice data is below four K-Hertz. Low pass filters are used prior to the phone to reject the high-frequency data so the user hears only the voice so if we look at a graph here, we'd find that going up to 1.5 Mega-Hertz possibly, then this would pass only those frequencies that are below four K-Hertz where the voice data is, in this stuff up here which would potentially generate a lot of noise, is rejected.
High Pass Filter
Then this is a high-pass filter and what we'll note here is the high-pass filtering is accomplished by swapping the positions of the resistors and the capacitors. That low-pass filters, we had resistors here and we had capacitors here. By simply changing positions of those components, we can build a high-pass filter. In this case, the capacitors look like an open, until the input frequency approaches the critical frequency and the formula is one over two pi times the capacitance times the square-root of R1 times R2. In this case, what we're going to have is just the opposite of the low-pass and the low frequencies … we're not going to pass anything until we get to the critical frequency and then we're going to begin to pass everything and this would indicate the high-frequency rates so everything above a certain frequency will be passed.
The idea here, and it's fairly straight forward, is we have a signal coming in and the reactants of the capacitors are such that at lower frequencies they're going to look open. It's not going to pass anything until it gets to the critical frequencies, then these capacitors will begin to conduct and then we will pass the frequency. The higher the frequency is the capacitors are just going to conduct. They're going to pass everything above a certain frequency so you have this characteristic curve … a high pitch frequency. Now here, this is a simulation from you multi-sim package, and this is a high-pass filter. Let's look at this … let's see, why don't we start … we'll look at the calculation of the … what frequencies are actually being passed. Here we have the critical frequency formula, and if we plugged in these numbers, and the numbers we're going to be using here … there's the 0.05 Micro-Farads capacitor and the 11K- and the 22K-Ohm resistors. If we plugged those into this formula … draw a little line there to make sure the square-root goes across that hole to those two items … we would get about 205 Hertz. What this is saying is that this filter will block those frequencies below 205, and then it will pass everything above that. This filter is available in your multi-sim package. Now let's look specifically at the circuit and see what we have here. Here we have the op amp. Pin four goes to the negative. Pin-seven goes to the positive. Then we have the two capacitors and the two resistors. Now we also have a device called a bold plotter connected to this. A bold plotter is a very interesting instrument. What it does is as the user you go in and you plug in the values that you want to use, and what we're looking at horizontally … we're looking at a frequency range … this is the initial frequency and this is the final frequency.
The initial frequency we're starting at is way down at 100 Milli-Hertz and the final frequency is ten K-Hertz. We're looking at a frequency from close to zero to ten K-Hertz. What we see here is the relative amplitude of that signal. Up here we're going to be at amplitude probably about zero dB actually. Then below this, we're going to experience signal attenuation and you can see I have stopped this simulation at this point and you see this blue line and you know this is the blue line we're down three dB; actually, that is 70.7 percent value. We're at a frequency of 204 Hertz and you'll note our calculated value was 205. This is an excellent tool to assist you in looking at the output of filters. Remember going horizontally here we're looking at frequency, and going vertically you can adjust for the amplitude of the signal and it is actually in decibels over here. OK, so the bold plot, when you use this guy, you would connect the bold plot … the input and output of the bold plotter … one end would go into the input and the other would go into the output and of course, the negative on and the negative here are both going to ground. This will allow you to view what would this device produce over a range of frequencies and like I said, as the user, you can go in and you could put this up to one Mega-Hertz if you wanted to but then it would just kind of go up … go right up here and then it would be a cross. By making it more specific here you are able to really tune into that specific frequency. OK, in filters here we have a look at this high-pass filter and we looked at a little bit about the theory. Then we looked at a low-pass filter, we looked at an example of a low-pass filter, which is a DSL filter. Again we looked at the theory about low-pass and then we just introduced the subject of active filters. In the next section, we're going to look at the band pass and band reject.