 What's one thing that all of these devices have in common? Well, they all filter something. We filter the air we breathe with air conditioner filters, the water we drink with water filtration systems. We filter the air, the oil, and the gas that our cars use, and then we try to filter out the pollutants that result when we use the car. We filter light with sunglasses and shades, and we even put filters on some things that we shouldn't even be using in the first place. As a matter of fact, you name it, and I'll bet you that somebody's thought of a way to filter it. We use a lot of filters in electronics, too, and all of them basically serve the same purpose as the other filters we've been talking about. They pass what we want to pass and reject everything else. Electronic filters keep noise and interference out of your radio and TV sets. They allow you to listen to high fidelity recordings and FM stereo. They make certain that a radar set electronically sees only what it's supposed to see. As a matter of fact, it's probably safe to say that there's not a single piece of electronic equipment that doesn't use a filter of some type. Basically, filters are designed to do one of four jobs. One, to pass all frequencies below a specified value and reject all those above that value. Two, to pass all frequencies above a specified value and reject all those below that value. Three, to pass a selected band of frequencies while rejecting all others. And four, to reject a selected band of frequencies while passing all others. All electronic filters fall into one of those four categories except for a few very specialized cases. And it's made possible by these simple components, capacitors and inductors. In this lesson, we'll discuss how these components can be connected together in series to provide filtering action. In a later lesson, we'll discuss parallel filters. Before we begin, let's look at the terms we'll be using in discussing filters and define those that are new to you. This response curve shows all of them. Band pass, band width, cutoff frequencies, and the attenuation bands. The band pass, you'll recall, are those frequencies that fall within this area on the response curve between the half power points. In this case, the band pass is from five to seven kilohertz. The band width then, or the width of this band of frequencies, is two thousand hertz or two kilohertz. The cutoff frequencies are those frequencies below or above which there is no usable output from the filter. Here, below the cutoff frequency of five kilohertz, there's no usable output. And above the cutoff frequency of seven kilohertz, there's no usable output. The attenuation band is used to describe all those frequencies that do not pass through the filter. All those frequencies above and below the high and the low frequency cutoff points. A basic filter circuit is the inverted L configuration. So-called because it looks like an upside down or an inverted L. By plugging into the series and the shunt positions of this circuit, the correct values of inductance and capacitance, and in some cases resistance, we can accomplish all four basic filtering actions. Now in this circuit, total current will always pass through the series component. However, only part of total current passes through the shunt component, the rest going through the load impedance. The important point to note in this arrangement though, is that the voltage felt in the output, the output voltage, is the same as the voltage across the shunt because they're in parallel. And the voltage across the shunt is dependent on the voltage developed by the series component. Because the voltage across the shunt is equal to the total applied voltage minus the voltage drop across the series component. Thus, this circuit acts like a simple voltage divider. Now we can easily demonstrate this basic principle of filters on our trainer. The equipment that we'll be using for our demonstration is an oscilloscope, a little circuit board, or a trainer, and a signal generator. Now the signal generator will deliver a 10 volt signal to the trainer. We can control the frequency out of the signal generator with this knob. But the output voltage is fixed at 10 volts and will be supplied to the trainer from this test point up to this connector. Now from this point the 10 volt signal is supplied to two places, the upper connection here and a lower connection here. Now the upper connection goes directly over to this point. And as you can see it's tied directly in to the A-trace or the top trace of the oscilloscope. Now this shows or displays the output from the signal generator at all times, the top trace of the scope. And it's connected with this connector to this point. Now the middle connector here is used to provide a synchronization voltage for our oscilloscope, which as you can see we need. I'll just plug that back in. That's the top trace. Remember it always displays the output directly from our signal generator. Now the lower connection here, this is where we'll connect our filter components. The series component here, the shunt component here. We'll take our output across the shunt component and it will be displayed on the B-trace or the lower trace of our oscilloscope. Now as you can see we have no output at this time because of course we have no components plugged into our filter circuit. Notice also that the oscilloscope, a little trainer and the signal generator are all grounded together. To show how a simple voltage divider can provide filtering, we'll use two variable resistors just like this one. Now you'll note that this is nothing more than a variable resistor that I've connected with a couple of test leads so that I can plug it directly into my trainer for use during the demonstration. Now we'll put one here in the series position and one here in the shunt position to illustrate how the voltage dividing principle will work to affect the output voltage. Well here I'll just plug this one in, the shunt position like that and there and we'll put this one in the series position like this. Now that audio tone that you're hearing in the background, that audio tone results because I have a loudspeaker connected to this point on the trainer. Now this is the output of our trainer so that the tone will always indicate whatever is coming through the circuit. You'll also be able to see the output displayed on our scope so you'll have two checks to determine the effect of our filter components on our output voltage. I think in this way you'll be able to understand the operation a little better. Now remember the generator output which is applied here will go through the series component then down through the shunt component to ground and we'll be taking our output across the shunt component. Now first let's set our series resistor to zero resistance or opposition and we'll set our shunt resistor to maximum opposition just like that. We have a short circuit here in the series position and maximum resistance here in the shunt position. Now this should give us maximum output voltage and as you can see it does. You can also hear the fact that we're getting our audio tone clearly through this circuit now. We have 10 volts in our input, 10 volts directly from the signal generator and we also now have 10 volts in our output. So we can conclude that to have maximum output voltage requires minimum series opposition and maximum shunt opposition. Now let's set our series resistor to its maximum position and the shunt to its minimum position. Now as you can see we have no output at all and you can also notice by the fact that we have no audio tone that there is zero output. We have all our voltage now being dropped across the series component. Our conclusion is then that to have minimum output voltage requires maximum series opposition and minimum shunt opposition. This is what we want our filter to accomplish. For those frequencies we want to pass through the filter and on to the output say 500 hertz. We'll want the shunt opposition to be maximum like this and the series opposition to be minimum like this. Thus this frequency 500 hertz will pass through the filter and on to the output. Now for those frequencies we want to reject and not allow to pass through the filter say 700 hertz. We'll want the series opposition to be maximum like that and the shunt opposition to be minimum. Thus this frequency 700 hertz is now being rejected. The voltage dividing principle works. We can pass or reject specific frequencies but since resistors are not frequency sensitive devices this system is not very practical is it? The circuit is now rejecting 700 hertz alright but it's also rejecting all other frequencies as well. If we set it to pass one frequency say 500 hertz by selecting maximum shunt opposition and minimum series opposition like this. Well it not only passes the frequency we want to pass it passes every other frequency as well. What we need in our filter circuit then are components that will react automatically to input frequency changes by adjusting their own oppositions and thus offering the output voltage. In other words we need frequency sensitive components. Inductors and capacitors fit this need. They are frequency sensitive. Exabel inductive reactance is the opposition an inductor offers to current. At a low frequency the inductive reactance is small. At a high frequency it's large. Exub C or capacity reactance is the opposition a capacitor offers to current. At a low frequency it's high. At a high frequency it's low. By plugging these two components into our circuit we can meet the requirement for frequency sensitive components to operate the filter. The first filter action we will demonstrate is the passing of low frequencies and the rejecting of high frequencies. In other words we'll have a low pass filter. Now from what we've previously established in order for our circuit to pass low frequencies the series opposition must be low at the low frequencies. The inductor then must be our choice for the series component because at low frequencies its opposition is low. Then to the series component should be able to reject the high frequencies. The inductor can also do this because its opposition is high at the higher frequencies. So the series inductor is always used to pass low frequencies and to reject high frequencies. The shunt opposition however must work the other way. That is it must be large at low frequencies so it can develop our output voltage and it must be small at high frequencies to shunt them away from the output. The capacitor fills the bill for our shunt component. At low frequencies it offers a large opposition. At high frequencies a small opposition. So the shunt capacitor is always used to pass low frequencies and reject high frequencies. This circuit then a series inductor and a shunt capacitor serves as an inverted L low pass filter. It passes low frequencies rejects high frequencies. Alright now let's hook up the trainer in the configuration we've just illustrated that of the low pass filter. First we need a capacitor in the shunt position. Okay then the inductor goes in the series position and there's our output from the filter. At this frequency we do have an output. Now let's check the overall frequency response of this filter circuit the low pass filter. Now you'll notice down at the low frequencies while I'm down around 200 hertz now you'll notice that I do have an output. I have 10 volts on the input directly from the signal generator and on the B trace the lower trace I show 10 volts of output from my filter circuit. So we're passing the low frequencies because this is a low pass filter. By increase the frequency though you'll note that at about 600 hertz the output starts dropping off. Now we're beginning to reject higher frequencies which again the low pass filter must do must reject the higher frequencies. Here at about 1200 hertz you can see that well I hardly have anything at all in the output so we're rejecting these higher frequencies. With a 10 Henry inductor and a .01 microfarad capacitor as my filter components I'm passing all frequencies from well about 1 hertz on up to about 600 hertz. On up to about this point but those frequencies above 600 hertz are not getting through. They're being rejected by our filter circuit. Plotted on a graph the output voltage looks like this. Here at about 600 hertz the output drops below 7 volts. Now remember I had an input of 10 volts so anything in the output less than .707 of this 10 volt value or in other words about 7 volts is not considered usable output from this filter. However this is not true in all cases. Actually the output voltage from the filter is still considered usable if it operates the low device. But in most cases the output voltage should be at least the effective value of the input voltage. So this then is the cut off frequency for this particular filter 600 hertz. Frequencies below this value are said to be in the band pass of this circuit. Those frequencies above this value are in the attenuation band. Of course the cut off frequency can be changed simply by changing the value of the filter components. Our next filter requirement is to pass high frequencies and reject low frequencies. In other words to reverse the action of the low pass filter we've just illustrated. Now it's only logical to assume that the action of the filter can be reversed simply by reversing the series and shunt components. In other words we'll put the inductor now in the shunt position and the capacitor in the series position. Alright let's do that then. Let's reverse the position of the series and shunt components on our trainer and then see what the frequency response will be. Now we'll just unplug the inductor and the capacitor. Now we'll place the inductor in the shunt position now just like that. And the capacitor will place in the series position. Alright capacitor in the series position inductor in the shunt position. What should we expect our output response to be? Well we know that in order to reject low frequencies the series opposition must be large at low frequencies. Well this is true of the capacitor. It offers very large opposition to low frequency currents. But at high frequencies the ones we want to pass the series opposition must be small. Again this is what the capacitor provides. So a series capacitor is always used to pass high frequencies and reject low frequencies. Now the shunt opposition must be minimum at low frequencies to shunt the output voltage. And maximum at high frequencies to develop the output voltage. And this is what the shunt inductor does. Now the shunt inductor is always used to pass high frequencies and reject low frequencies. This circuit then is an inverted L high pass filter. It passes high frequencies, rejects low frequencies. Okay let's check this out now with our demonstration. Now as I vary the input frequency from a low of about let's say 200 hertz you can see that nothing much below well about 600 hertz which is at this point is getting through our filter. Frequencies above 600 hertz are passing through though. We're passing the high frequencies. Now since we've not changed the value of the components our cutoff frequency is still the same. 600 hertz. That's our high pass filter. We're passing high frequencies, rejecting low frequencies. All the frequencies below our cutoff frequency of 600 hertz are being rejected by this filter. Those above are being passed. But suppose we want to reject both lows and high frequencies and only pass a small band of frequencies right around 600 hertz. You'll recall that this was the third filter configuration that we mentioned earlier. Using this inductor and this capacitor and with the addition of this resistor to the circuit let's design a filter circuit that will pass a band of frequencies between oh say about 500 hertz and 700 hertz. We're the center frequency of 600 hertz. We're only going to be passing this small band of frequencies. The rest of the frequencies we want to reject. Now what does this mean in terms of our series and shunt oppositions? Well we know that in order to pass 600 hertz our series opposition must be low at a frequency of 600 hertz. But at frequencies above and below that our series opposition must be very high in order to reject those other frequencies. Well at 600 hertz the inductor we've been using in our demonstration has an opposition of 31,400 ohms. The capacitive reactance of the capacitor we used at 600 hertz is also 31,400 ohms. Now individually neither component, neither the inductor nor the capacitor can do the job of passing a band of frequencies around 600 hertz. But when we place them together in series like this a rather remarkable thing occurs. Since inductive reactance and capacitive reactance are opposite forces they're 180 degrees out of phase and since in this case they're equal values, 31,400 ohms at 600 hertz the combined reactances exactly cancel each other. So the net effect of the combination is to offer a minimum opposition to 600 hertz. In other words it's simply a series tank circuit and as you've learned previously a series tank circuit offers minimum opposition to the resonant frequency and maximum opposition to all other frequencies. Now the shunt impedance in this case can be purely resistive, simply a resistor since its only use is to develop the output voltage. Now since the series tank opposition is minimum at the resonant frequency circuit current will be maximum. This current will flow through the shunt resistor and develop the output voltage. At all other frequencies however the series tank opposition will limit circuit current to the extent that very little current will flow through the resistor thus very little output voltage will be developed. Okay the generator is connected to the inductor these leads here, here's our inductor and then to our capacitor down through this resistor in this little shorting wire and to ground. Now at frequencies below 500 hertz the output drops to minimum as you can see. Now as I increase the generator frequency you'll note the output start to rise until at about 600 hertz the output is maximum. As a matter of fact it's about the same as our input frequency at this point. Now further increase in frequency causes the output voltage to decrease again so we're passing just this small band of frequencies between 5 and 700 hertz. Now on a graph you can see that at about 500 hertz the output voltage is 7 volts and again at about 700 hertz the output drops back to 7 volts. So in between these two frequencies we have usable output from the filter between 5 and 700 hertz. So 500 hertz and 700 hertz are the cutoff frequencies and the band pass of this filter is 500 to 700 hertz. The bandwidth is 200 hertz. These frequencies are in the band pass of this filter. All those above and below the cutoff frequencies are in the attenuation band. Now earlier we found that we could make a low pass filter perform as a high pass filter simply by reversing the position of the series and shunt components. Well the same thing is true of this band pass filter. By reversing the components as we've done we can cause the circuit to now reject a band of frequencies and pass all others. In other words it becomes a band reject filter. Let's see how. Okay we simply put the resistor in the series position. We're reversing its position and the LC tank goes in the shunt position just like that. Now the series component, the resistor has no effect on the input frequency because it's not a frequency sensitive component. However the shunt component, the LC tank is frequency sensitive. Remember at the resonant frequency the tank circuit's opposition is minimum. Now if we have minimum opposition then we'll have maximum current flow and the same current must flow through the series component. Thus the series component, the resistor will drop a maximum voltage drop. Now with maximum voltage dropped here then we must have minimum voltage dropped across the tank. This means of course that the output voltage is also minimum because they're in parallel. We're still dividing the voltage. Now remember at resonance maximum voltage is developed by the series component, the resistor. At frequencies above and below resonance however the tank opposition now becomes maximum. Now if the tank opposition is maximum it then will develop the maximum voltage drop across it. So at frequencies off resonance the output voltage will be maximum. Thus this filter configuration will reject frequencies right around resonance but pass all others. Let's demonstrate this. The output of the generator is connected to the resistor and through this little shorting wire. This is our series component. Then our shunt component the inductor and the capacitor and then on down to ground. The output is taken across the shunt component which in this case is the tank circuit. At frequencies below about 500 hertz the output from the filter is maximum. However when we approach 600 hertz the output drops off to practically nothing. Above 600 hertz though the output rises to maximum again. This filter then the band reject filter is now rejecting a band of frequencies around 600 hertz but passing all others. The graph of output voltage shows that this filter rejects frequencies from 500 to 700 hertz but it passes all others. Those below 500 hertz those above 700 hertz. The cutoff frequencies are here 500 and 700 hertz. Those frequencies from 0 to 500 hertz and from 700 hertz on up are in the band pass and those frequencies between 500 and 700 hertz are in the attenuation band. Alright that's our basic filters. Remember a low pass filter is designed to pass low frequencies reject high frequencies. The L-section filter uses a series inductor and a shunt capacitor. A high pass filter is made by simply reversing the position of the series and shunt components. Now the high frequencies are passed and the low frequencies are rejected. A band pass filter used a series tank circuit and a shunt resistor to pass a selected band of frequencies and reject all others. A band reject filter rejected a band of frequencies while passing all others. This was accomplished by reversing the position of the series and shunt components of the band pass filter. The resistor became the series component and the tank the shunt component. Now in this lesson we've discussed how series LC filters are nothing more than simple arrangements of the components in the series and shunt configurations. In our next lesson we'll discuss how parallel LC tanks can be used to accomplish the same filtering actions.