hi everyone in this video you are going to learn the linear wave shaping which is a part of pulse and digital circuit so with this video I am going to start a subject called pulse and digital circuits this comes generally in second year of b-tech ECE or triple branches so this subject is very helpful in learning how a pulse circuits and digital circuits are going to be operated with several inputs like a senseoidal input um ramp input pulse input exponential input and step input these are the general available waveforms that we are going to give input at various linear and non-linear circuits so as a part of this pulse and digital circuits the first and foremost concept we are going to learn is linear wave shaping linear wave shaping what do you mean by linear wave shaping so before going into this linear wave shaping and non-linear view shaping let me first explain what do you mean by linear Network and in non-linear Network so a linear network is a network which consists of all the linear components like resistance capacitance and inductance so linear Network linear network is made up of linear network is made up of pure linear components like resistance inductance and capacitance with one active Source active source is to give energized energy to the Circuit so that the circuit can operate with a signal okay active source is nothing but either voltage source or current Source in order to pass some current through these components so linear network is nothing but it is a network made up of completely a pure linear components all these are linear components we can say linear components okay linear components are going to be operated with the help of an active Source definitely active Source should be there actosource now and the second one is in non-linear Network the name clearly tells that non-linear Network it is a network it must be made up of is made up of non-linear components non-linear components in addition to linear components like RLC plus Active Components plus active component is nothing but active sources like voltage source or current source hope you understand how a linear network is differentiated from the non-linear Network linear Network consisting of only active source and any of these components like resistance capacitance and inductance any of these combinations we can say a RC network or we can say RL network card simply we can say RLC Network okay so in such type of networks we can call it as a linear Network whereas coming to non-linear Network non-linear component is there in addition to any one of these components see in all linear Network what do you mean by non-linear Network non-linear Network example is example for the non-linear Network non-linear um component is like a diode or a transistor are in scr or a triode whatever it is any type of non-linear device is considered as a non-linear component here so along with these non-linear components additionally we will be having definitely a resistance maybe there are a capacitance maybe there are an inductance may be there plus some active source to give the current passing through the network so this is the way how generally a linear Network and a non-linear network is defined and now coming to the definition where we have started that is linear wave shaping linear wave shaping so remember in pulse and digital circuits the first unit most of the universities will be having linear wave shaping and the second unit is non-linear wave shaping linear wave shaping means what do you mean by linear view shaping the process of the process of changing the shape of a the process of changing the shape of a non-sinusoidal signal non-sinusoidal signal when passing through when passing through a linear Network this is called linear wave shaping so linear wave shaping means if you are taking a linear Network linear Network and we are giving an input which is a non-sinusoidal input a non-sinusoidal input I am giving non sinusoidal input when we are giving a non sinusoidal input to a linear Network the output of that nonsenseoidal signal is a distorted or a changed waveform so it is a changing shape of input signal so definitely the shape of the input signal is changed when it is passing through a linear Network okay this is regarding to a non-sinusoidal signal suppose if you are taking the same linear Network I am taking the same linear Network now I am giving a sinusoidal signal a sinusoidal signal when a sign signal is passing through a linear Network the output is also is sinusoidal signal that means linear network will not change the shape of a sinusoidal signal it changes the shape of a signal which is a non-sinusoidal signal that is the meaning of linear wave shaping the shape of the signal the shape of a non sinusoidal signal changes according to behavior of the component what we are using inside a linear networker okay but if you are passing a sinusoidal signal definitely the output is also a sinusoidal signal that means we are giving a sinusoidal signal output is also a sinusoidal signal but here in the lean uh in the first case when an on sinusoidal Signal is given depending upon the type of the signal whether it is a ramp or step or pulse or exponential whatever the signal the output is changing according to that input signal okay this is what the linear way of shaping what is the meaning the process of changing the shape of a non sinusoidal signal when passing through a networker that is a linear network is called a linear wave shaping now coming to the first and foremost network of this linear Network so we can say now I am taking a linear Network I am taking a linear Network consisting of resistance and capacitance a linear Network consisting of a resistance and capacitance here I am constructing the circuit in such a way that resistance is connected at the input side and capacitance is connected at the output side that means the input is applied between resistance and ground and output is taken across the capacitor output is taken across the capacitor for our Simplicity first I am applying a sinusoidal signal okay is it a linear Network a non-linear Network it is a linear Network because when active source is there and the remaining are resistor and capacitor nothing but linear components so as the circuit consisting of all the linear components we can say we can classify this circuit as a linear circuit okay now what is the shape of the output signal output signal is also a sinusoidal signal this is in terms of time period that means in terms of time period we can expect the same input shape but when we are going to the frequency response of the same circuit because see here I am giving a sinusoidal signal means a sign means continuously varying with respect to time the amplitude of the signal continuously varying with respect to time that means it is having some frequency it is having some frequencies there that frequency when it is passing through this network it will be attenuating higher order filters higher order frequencies okay this network especially designed to pass only low frequencies that's why this low this network is also known as low pass Network or low pass filter only low frequencies are passing through the network and all other higher order filter higher order frequencies are eliminated so if you draw the frequency response characteristics of this Network they will be like this so on x-axis we are taking frequency and on y-axis you are taking the gain now the frequency response characteristics will be like this see this is the pass band this is pass band where the signal is passed and this is called stop band this is called stop band see pass band is there in the lower order frequencies and stop band is there for the higher order frequencies and this frequency we are taking it as higher cutoff frequency or we can also say this F H as f l sorry F2 okay if any response is having two frequencies F1 and F2 generally higher frequencies you have to and lower frequencies F1 okay and here we are having maximum response is one and we can say it is 1 by root 2. if the maximum response is 1 it is 1 by root two times so that means zero point uh sorry 0 0.3 or 0.7 DB 0.7 down okay that means 3 DB down we can say it is 3 DB down okay 0.707 of this gain value okay this is the frequency response of this particular low pass RC network why it is low pass RC network because this network is helping us to pass only lower cutoff frequencies all other higher order frequencies are being eliminated see here if you see the operation of this particular Network we are giving a sinusoidal signal the output is also a sinusoidal signal so there is no change in the shape of the network okay now let us calculate the gain mod a okay how much is the gain of this particular networker and similarly how can you calculate the expression of a higher cutoff frequency f h from this particular Network okay these two terms you are going to see now now see here if you convert this particular Network into its LaPlace Transformer Network simply the circuit components will be changed like this we are having a resistor followed by a capacitor and here the input voltage is applied we are taking it as v i of s because every parameter is converted into its LaPlace Transformer Network and it is the voltage across capacitor output we can say V naught of s and it is 1 by c s it is R there is no change in the resistance value okay so because resistance is independent of frequency and all other components are dependent on the frequency that's why v i of s here and one by CS here and V naught of s and assume that some current I of s c is passing through this network now gain of this RC network gain a is equal to gain a is equal to what is the formula of gain output voltage by input voltage output voltage by input voltage output voltage is nothing but what is output voltage output voltage is nothing but we are calculating the voltage across the capacitor voltage across capacitor so we can write it as 1 by c as into I of s voltage across capacitor is 1 base yes into ifs is the current flowing through that capacitor and now v i of s we can write V AFS as the total components into ifs so R plus 1 by c s into ifs so that is equal to this ifs if gets canceled and if you take LCM in the denominator Now 1 by cscs gets canceled and 1 by 1 plus RC yes okay but we know we know s is equal to J Omega and J 2 pi f Omega is nothing but 2 pi f so a is equal to 1 by 1 plus J 2 pi f r c J 2 pi f r c okay now from this waveform at particular frequency f h yet f is equal to f h what is the amplitude it is 1 by root 2. okay so if you take f is equal to F2 this a becomes 1 by root 2 before that let us write the magnitude form of the same mod a is equal to 1 by square root of C A Plus J B how can we write modulus of this one a square minus b square okay here J square is there J becomes minus 1 J Square becomes minus 1 so it is 1 minus minus plus 2 pi f r c whole Square okay generally this one is a square minus b square a square minus b square minus here J square is minus 1 so minus minus plus now at frequency that frequency f is equal to f h see in textbooks you may write it as F2 FH is equal to F2 whatever you name it this is a higher order frequency okay I can say higher cutoff frequency simply cut off frequency okay at frequency f is equal to f h what happens mod a is equal to 1 by root 2. mod a is equal to 1 by root 2 substitute that here so 1 by root 2 is equal to 1 by root 1 plus 2 pi f h r c whole Square okay this root root cancel and now 2 pi f h r c is equal to 1. okay and f h is equal to 1 by 2 pi RC FH is equal to 1 by 2 pi RC this is what the higher cutoff frequency of this low pass filter you can say it is higher cutoff frequency of the low pass filter FH is equal to 1 by 2 pi RC okay if you substitute the same FH in the equation we can say it has some equation number one and this has equation number two okay so from equation 1 we can write it as a is equal to 1 plus 1 by 1 plus J into F by f h F by FH are mod a is equal to from this second equation here 1 by 1 plus F by FH whole Square here square is there whole Square this is under root okay so this is the way how to write the magnitude and as well as a normal form of this gain with the help of higher cutter frequency letter we can also write angle Theta is equal to tan inverse of B by a 10 notes of here B by a b f by f h so F by f h anverse of V by a so this is the way how to calculate the response gain of this low pass RC network when a sinusoidal signal is applied at the input okay thank you