In this lesson, we're going to design an active filter. So, first thing we're going to do, click here and use a mask. And then I show you how the structure of this filter supposed to be, just so that's the equation are shorter later. That's the field that we're going to implement to right forward as it stores. These, these two these other two and two capacitors and then Op Amp operational amplifier, we're going to use this structure. So let's put the components like these these we need two capacitors.

These, let's see what else more Op Amp let's put an ideal Op Amp ideal single pole operational amplifier most but don't leap up and dotsub Okay. And then click here we see that in this structure there is if the no invert, II know inverting input above, not below. So regards your cricket know the hand and Greek culture he controls air. So, we've got this and then we have two registers here So, let's take care of it for you Must you've got to read well enough then. Yeah. So let's do the connections.

Ask. They must use two resistors here. Let's bring it here. Connect all these things. voltage, voltage sauce like this as key, ground net, ask and then let's add a label V out. Let's add the label V in standing for input.

And then let's see if it's correct to register stars Paragon are true our capacitor like this, a second capacitor and juice over resistors. And then we must know, veterans first trust transfer function of this filter. If you do the analysis of this secret use the theory of electric circuits, you're going to find these equation. So it's the second order transfer function. You've got two poles here, and you can control the position of this pose by means of setting up these values of resistors, capacitors and the key. The key is This relation and aren't you and Aaron, these little air little air is defined by these words the stars.

So this is a cane. This is a gain constant, we're going to set up using these registers. Recall that it must be higher than one greater than one because this is greater than zero, so he must be greater than one. And then we're going to implement a second order by means of this formula, a second order Butterworth filter. So this filter is going to represent a maximally flat future Caracas risks. So, the second or the denominator for a buck dwarf response is it as square plus square root of two as plus one.

So, what one simple way of joining this is taking these equation and setting all the resistors and capacitors are not always those but only Aaron, Aaron and Archer and both capacitors to one and then we have this equation which he's left waiting for us to set the key value. So, let's get to One on one on one foreign one foreign IDs. And then we must put some directive here, please dot o b dot leap up. That's this recommendation was written when we choose the op amp, so we must follow it. And then what we must do next, we must set these register values. Remember we want to make this free minus key equals true this prayer root of two.

So the correct value for the key. Key is key Brzeski key is one dot 586 approximately. So let's put it here. Key equal key equal one dot 586 approximately, we must, we must use it. So in order to use it What must we do keep this expression must equal one dot 586. So our true of r1 must equal zero dot 586.

So, what are we going to do and make Archer Archer equals zero dot 586 Aaron click ok so In our case air one, this little air one is air free and little air two is air four. So what can we do we can put here like one kilo ohm, and then but here 586 ohms. We do this we use AC amplitude one volt because we're going to do AC analysis. We're going to simulate a did simulation comment, AC analysis, decades, number of points 100 start frequency let's but really small frequencies zero dot one and all the one kilohertz and budget here Remember this secret is a normalized filter, it means that it its response will be given by these second order logic or for response, which has these denominator, these will have the cutoff frequency of one Rajon per second. So it's so far it's only for us to understand how it works.

So, and then we're going to do something called frequency calling. So in order to operate in the frequency we want, so let's click the running man and click V out. We see that In this position we have nearly zero decibels not zero. In fact, it has free dot 177 decibels We must find where does these decreases to minus three decibels. So the very beginnings free that free forum four decibel. So let's find four zero dot 349 decibels 00 it's in here zero that's free for a nine Free foreign nine.

Let's do these zoom zero dot zero dot free. Free hundred free hundred and 49 449. It's here. It's 170 million hertz. If we multiply this by to buy 100 That's 70 nearly heads times two times by equals approximately running rads per second. That's because it's a normalized circuit.

It's a it's made for the run rat per second Rajan cutoff frequency. Let's put an equation here. Rhydian frequency equals two times b times frequency. You must remember this. So what happens in one ad per second happens in our frequency which is equal to one divided by two bye Then click zoom to fit. And we see that some fee we can make out we can learn about it is that when we go one decade, that is when they multiplied the frequency by 10.

We have here 300 kilohertz and we're going to free kilohertz. The decrease in the amplification is approximately 40 decibels 40 it is shown that left bottom corner. That's because this is a second order secret. So first of all, the secret first order filter is going to roll roll off at 20 DB database for decades. A second order sequence is going to roll off at a rate of 40 decibel spurs for decades, furred or the future is going to roll off at a rate of 60 decibels per decade and so on. What are we going to do now is we must change the frequency in which this circuit operates.

So, what can we do here? We can increase the cutoff frequency by means of decreasing the capacitors. If we decrease the capacitor true true on amounts which permits us true. have a say thank you the heads of cutoff frequency What is very Rogen equivalent of 10 kilohertz? It is given by this frequency. So we're going to multiply two times by times.

Thank you, that's an intro equal six to two. Let's write it here. 6228 fri one dot eight, Brad for a second seconds. That's the frequency, we want to achieve the cutoff frequency we want to achieve. So what what are we going to do? We're going to divide this one file by this value in order to move the frequency characteristics for files.

So these accounts gives 15 dot nine. Let's write it 15 dot dot nine micro Fatah, it sorry going to use these values these new values for the capacitor right here 15 dot nine Meeker 15 dot nine Meeker and then we're going to simulate it again. We see we have something weirds going on. We must increase these range of frequencies because we have extended the If not extended a scale the frequency, the frequency of cutoff so we must let's say an increase at 100. Okay. And then we see here here we have ad nearly DC we have free dot 946 decibels so we're going to see why do we which free this bells fall.

It's gnarly. Wait, free dot not free dot 946 sorry Lu 409460946 0946 you the nine is in this range. Here the nine or six it's gnarly G's value. So it's brought him out to very close to 10 kilohertz. So we've achieved our specifications. So let's zoom to fit and see it, give it a closer look here.

We see that we have a very flat Batman response which is what happens here. As we had before 40 decibels went from one decade to another, decreasing you can see on the left bottom corner, then to fit but we have one small problem in the circuits. Eat isn't very achievable. Very fries, go to use one omega one omega resistors, one ohm resistors. So what we're going to do, we can increase it multiply both registers only this true because this is these two are gang controlling. Whereas those we're going to do now only with these twos.

So let's but it's one kilo on one kilo on But if we do this, let's see what happens only changing there these whereas the stores, let's see what happens, we get a very strange response. That was not the thing I was hoping for. So what was wrong, we must change the capacitors. Also, when we change these resistors in order to make them more practical we must do to use the scaling in the capacitors to, but how it's done. It's done in order to escape scale the abundances of resistor and capacitor. If we increase the register, we increase the register invaders but in order to increase their capacitor imbalance, we must actually decrease it.

So if we increase it by a thousandfold, we must divide this value by 1000. So the new value of capacitor is going to be 15 dot nine nano ferrets. And let's update it 15 dot nine nano and let's simulate it again. Now we have their response we're researching right salt response, which has approximately 10 kilohertz as a minus three DB cutoff frequency, which is the frequency in which the power falls to the half of the DC power wiki because it is a low pass filter. So basically, all these frequencies get amplified by approximated First mentally the same amount of free dot 946 decibels and when above these frequency of Thank you lights what happens is that the attenuation is higher and higher and higher as we increase the frequency with which rate we saw before 40 decibels its decade I mean each time you increase the frequency by 10 year decrease the attenuation you increase the attenuation effect by 40 decibels which is a large attenuation.

So, if we in 20 kilohertz we have for instance minus eight decibels attenuation. In short handed we've got you have minus 48 decibels approximately. So, this is a low pass filter, this range of frequencies is allowed to pass with an amplification of free dots 946 decibels and this value of amplification is given by this value of key, but this key factor key is also controls the pole positions of the transfer function, the pole positions because it changes these coefficients and then it must be clear that if a very high value of key we can even Make the filter unstable because we can move the poles to the right hand side of the s plane. So, in this equation, not these equation, if we have key value higher, they're free these equation, this filter is going to have balls on the right hand side of the s plane and then it will turn into an unstable circuit.

So you shouldn't do this if you want to do use a filter, he used it as a filter. So, in this lesson, we saw how to design a active filter, especially a selling key with this structure is called selling key which allows you to to achieve these response and we use these expressions to achieve that response. This kind of response, the second order Butterworth response. So we saw this and this is our last lesson.