04.05.2024

Okay hello everyone so this video is. about the examples of bode plot and as I. told you I'm going to do an example here. in this video but I thought that maybe. it's better to do more examples in class. other than in video so this one in this. one I'm going to do one example for you. so you can have some idea on how we can. sketch the bode plot and then on Tuesday. I'm going to do more examples in class. so this one is a practice problem 14.3. practice problem 14.3 so this is the. transfer function that we have in this. example were j omega x j omega plus 10. okay so we have to draw the bode plot of. this transfer function both the. magnitude bode plot and the phase 40. plug so we can open a table 14.3 on page. 623 because I'm using that table always. to draw the bode plot so that's what. that's one of the reasons that I want to.

Do more examples in class because I can. show you that tables on board while I'm. doing this while I'm sketching the bode. plot so the first thing that I told you. I'm sketching the bode plots is that. these numbers should be equal to one. right so I have to factor out 2 from the. numerator so 2 multiplied by 5 this will. be J Omega over 2 plus 1 over and then I. have to factor out 10 from the. denominator so 10 J Omega multiplied by. 1 plus J Omega over 10. and you can see that this 10 will be. canceled with this time so we do not. have any constant game here in this. transfer function so the final transfer. function that we have to draw the bode. plot for is 1 plus J Omega over 2 over J. Omega multiplied by 1 over 1 plus J. Omega over 10 ok so let's see first for. the magnitude plot let's see what each. of these factors are so what is this.

Factor this is a simple zero right and. then we have the same configuration but. in the denominator so this will be a. simple pole and this one 1 over J Omega. is pole at the origin by the D word so. now I have all the factors in the. transfer function distinguished from. each other and we can go ahead and draw. them so for the first example I'll just. do this do it on a plain paper but so in. class I'm going to do it on the semilog. paper so you can see how we can draw on. that paper as well because in the exam. I'm going to give you the semilog. papers to draw all right so for the. magnitude plot so you remember that we. said in sketching the bode plot we have. to sketch each of these factors. individually and then add them. graphically so I'm going to draw each of. these factors with one color and then. add them graphically for finding the.

Magnitude plot of bode plot so first one. is the simple zero so if you look at the. table that we have on page 623 you can. see that if we have a simple zero which. is one two three fourth row it says that. oh let me first specify the frequencies. that we have here on the axis. zero point one and then we have 110 and. 100 and then here is 20 decibels here is. 40 decibel so the good thing about. semilog papers is that they have all of. these already defined on them so your. graphs will be more accurate all right. so the first one was a simple zero so. for the simple zero we know that the. plot will be zero until this zero here. which is two so our zero Z 1 is equal to. 2 ok so if if this is 1 this is 10 then. this can be defined as 2 so it says that. it is 2 right and then after Z after the. zero it will increase with the slope of.

20 decibels per decade so it is. basically 20 n but n here is equal to 1. right so it is 20 decibels per decade it. means that from from the frequency of. 2 until the frequency of 20 ok the. magnitude should increase 20 decibels so. this will be our plot and then again. from 20 to 200 it has to reach a 40 so. the somewhere over here see since we. don't have the semi log plot it is a. little hard to draw them in the exact. place but it will be something like this. ok so this is our simple 0 then we can. go ahead and draw the simple pole or the. pole at the origin it doesn't matter so. I'm going to draw the simple pole first. let me change the color. what is our pole here it is 10 right so. p1 is equal to 10 so for the simple pole. in the table which will be Rho 1 2 3 4. fifth row it says that um. the plot is equal to zero until 10 and.

Then it will decrease with the slope of. negative 20 n and n is equal to 1 so it. is negative 20 so from 10 200 it has to. reach 20 which is here so it's a little. hard to draw excite line and then from. 100 mm which is another decade we have. to reach 40 okay so this is my simple. pole so the only thing that is left is. the pole at the origin which is 1 over J. Omega so let me throw it with another. color to orange okay so for the pole at. the origin it is the third row in the. table you can see that the slope is. negative 20 and it has to pass frequency. of 1 so when it is reaching frequency of. 1 the magnitude is equal to 0 right so. this is 10 and then this is 20 so this. will be my plot for 1 over J here's. something like this ok now we have all. our plots ready so we have 1 plus J. Omega over 2 which is the green one we.

Have 1 over 1 plus J Omega over 2 to 10. which is the pink one right and then we. have 1 over J Omega which is the orange. one so now we can go ahead and add these. graphs graphically so you haven't seen. this part before because the previous. ones were like the things that I just. talked about all right so let's add them. graphically see the frequencies that. something happens. in the bode plot are the frequencies. that these plots will um will meet each. other at those places so one of them is. frequency of one another one is the. frequency of ten and I think that's it. yeah that's it okay so let me draw this. it's not necessary to define these. frequencies but it will be easier for. you to find out where the bode plot has. to change so oh and also one at two. right they may or may not change at. these frequencies but if you define them.

Then um you'll work more accurately and. let me change this plot here it's a. little too thick so I get confused let. me change it oops. okay so from zero point one from the. frequency of zero point one until the. frequency of two you can see that we. have the green plot is zero the pink. plot is zero but the orange plot is. twenty and it is decreasing with the. slope of negative twenty right so if you. add these plots together if you add each. point of these plots together you will. get the same plot as this one right. because the other two plots or equal to. zero. so they don't have any effect on the. bode plot then when we reach the. frequency of two you can see that the. orange plot is decreasing with negative. twenty I will write here negative twenty. decibels per decade the key pink plot it. is zero but the green plot it has the.

Slope of 20 decibels per decade so what. will happen here we have one negative. twenty we have one positive 20 so if we. add them together it will be zero so. we're going to have a plot with slope of. zero okay until we reach frequency of. ten and then at the frequency of ten we. will have all three waveforms all three. plots right we have negative 20 and. again the pink one is negative 20. decibels per decade and then we have the. green one which is 20 decibels per. decade so we have we're going to have 20. 20 plenty these will be negative 20. decibels per decade so we're going to. get a plot which is decreasing with the. slope of negative 20 per decade and from. this frequency on we do not have any. other changes so as you can see we add. these three plots graphically and we got. the black one which is our body plot.

The magnitude bow tip like this so let. me just make it a little thicker so the. black one is what we are looking for so. in the exam for sure you have to show. all these steps and for sure all of them. have some points the partial credit but. to get the full credit you have to be. able to sketch this black one as well so. this was the magnitude plot let's go. through the phase plot as well for this. transfer function so the transfer. function was H of Omega please equal 1. plus J Omega over 2 over J Omega. multiplied by 1 plus J Omega over 10. okay so this time we have to look at the. phase plots in table fourteen point. three so you can see table fourteen. point three it has three columns first. one is the factor so the factors that we. have in the transfer function second one. is the magnitude plot and third one is.

The phase plot okay so go ahead and look. at the phase bus all right so let's draw. the phase plot for each of these factors. here in our transfer function so Omega. by 0.1 and then 1 10 100 and thought why. am I writing this like why is the. intervals from zero point 1 to 1 1 to 10. because frequency is increasing in. decade in bode plot don't forget that so. let's start from 1 plus J Omega over 2. which is a simple zero which is the. fourth row in the table you can see that. the phase plot is going to remain in it. will be 0 until Z over 10 sorry I was. looking at the wrong. so what is the over 10 C 1 is equal to 2. so Z 1 over 10 will be equal to 0.2. right so it says that if this is Z zero. point two it will remain at zero point. two right and then at ten Z which is. what is ten Z is 2 multiplied by 10. which is 20 okay so at 20 it has to.

Reach 90 n and n is equal to 1 so this. is my plot right so from zero point two. to 20 okay so how can I find the slope. of this plot before it reaches 90 see. from zero point two to 20 it's not one. decade it is two decades right first. from zero point two until two is one. decade and then from 2 to 20 is another. decade so in two decades so in two. decades we reach as we goes from 0 to 90. so we can easily say that in one decade. we would go from 0 to 45 degrees okay so. this plot here it has slope of 45. degrees per decade so for sure here it's. not accurate here but at 2 we're going. to have 45 degrees ok now let's go and. draw for the pole so 1 over M sorry 1. plus J Omega over 10 so P 1 is equal to. 10 and P 1 over 10 will be equal to 1. and 10 P 1 is equal to hundred ok so. and one two three four fifth row in the.

Table it says that the plot should. remain zero until P / 10 P / 10 is equal. to 1 so until the frequency of 1 my plot. will be 0 and then it has to decrease. and reaches minus 90 degree at 10 P so. 10 Pease hundred so in hundred it has to. reach negative night okay if I want to. be consistent with the one that I drew. for 0 I have to do this it goes down and. we know that this one is the same as the. other one only the negative so minus 45. degrees predict ok and then we have to. draw the phase plot for the pole at the. origin which is easy it is negative 90. so you draw it with and it is negative 9. ok so these three are separate plots for. each factor and now I have to add them. graphically so let me specify the. frequencies that something is happening. in them so it is zero point two which is. here so as I said there might be not and.

Not nothing or now for we can't we can't. say that for sure at these frequencies. the bode plot will change because if. they for example other ones are zero. then nothing will happen so this goes to. and 20. these another frequency and then 100. okay so let's see what is happening here. so from zero point one until zero point. two the green plot is zero the pink plot. is zero but the orange plug is negative. 90 so we're going to have this because. negative 90 plus zero plus zero will be. negative nine then from zero point two. until one we have the pink one is zero. so it doesn't have any effect but we. have a green one with negative with. positive 45 degrees per decade while we. have the orange one in negative 90 okay. so the green plot will be shifted down. here right okay and then from 1 to 2 or. C from for example here is the example.

That I said they may not change so from. 1 to 2 and from 1 to 20 we have the same. three plots so the green plot the pink. plot and the orange plot are not. changing in the interval of one until 20. right so we have the green one with 45. degrees per decade we have the pink one. with negative 45 degrees per decade and. then on the orange plot which is at. negative 90 so those two will cancel. each other so we're going to have the. same slope as we have for the orange. plot right and then. from 20 we have the green plot at 90 and. we have the orange plot at negative 90. and then the pink plot is negative 45. per decade so it goes down like the pink. one okay and then add 100 we're going to. have negative 94 the pink one negative. 94 the orange one and positive 90 for. the green one so we're going to have. negative 94 our imported plot so for the.

phase plot you may be a little confused. in the beginning but I'm going to talk. more about it on Tuesday because I want. to draw it on the semi log paper so you. can see what's going on better okay so. please watch these videos before Tuesday. class because I want you to have an. overview on what the bode plot is and. how we can draw them thank you