 Hello and welcome to the session on Colpitt's Oscillator, I am Mrs. Vaidehi Gulkarni. Learning outcomes are at the end of session students will be able to analyze Colpitt's oscillator, contents are like this, you can see figure one where amplifier has to be used with a common emitter configuration, in combination with that you must use tank circuit which consists of Z1 and Z2 which are one of the element of tank circuit and next is Z3. So, this Z1, Z2 and Z3 will provide the tank circuit which gives the 180 degree phase shift as well as amplifier give the 180 degree phase shift. Now if we replace the amplifier components by its equivalent circuit then it will look like this, you can see here this is base of transistor, collector of transistor, HIE which is a input impedance of amplifier, HFE and IB which gives the current source equivalent diagram where we have replaced this HOE as you can see 1 by HOE is very very large and equivalent of that will be over here and HRE is also very very small. So, this is the equivalent diagram for the amplifier Z2 and HIE are parallel which is in series with Z3 and that whole combination is in again parallel. So, which will give the output impedance of LC oscillator circuit. So, basic principle behind the LC oscillator is nothing but form a tank circuit with the appropriate reactive elements like inductor and capacitor, C1 and C2 are GAN capacitor nothing but which varies simultaneously R1, R2, RECE used to stabilize the amplifier gain. Collector circuit's output is coupled through this coupling capacitor to the tank circuit. So, tank circuit will act as a feedback circuit as well as it will determine the frequency of oscillation which is further stabilized and given to the base of transistor. So, in this way you can observe here total 360 degree phase shift is obtained with the help of these two circuit components and again we have to find what is the gain of amplifier so that you will meet the Barkhausen's criteria to get the sinusoidal oscillations at the output. This RF coil will blocks the AC signal over here and capacitor will blocks DC positive feedback over here. So, C2 provides a positive feedback RF coil permits DC output voltage is derived from the secondary of and this inductor expression of the colpid oscillator. So, you can see here this is the basic circuit diagram or block diagram of colpid oscillator where amplifier is wired through this tank circuit Z1, Z2 and Z3. So, equivalent resistance or output impedance is nothing but Z1 parallel with Z3 plus Z2 parallel HI as I told you at the time of basic configuration or basic building blocks of oscillator and as you know that without feedback amplifier gain is nothing but minus HFE by HI into ZL. V out is nothing but Z2 HI by Z2 plus HI plus Z3 into I1 this is output voltage of amplifier. Now feedback voltage is nothing but Z2 HI by Z2 plus HI into I1. So, you can see here beta is VF divided by V out. Now I am interested to get the sustained oscillations and as you know that for sustained oscillations beta AV should be greater than or equal to unity. Once you put the value of A as minus HFE by HI into ZL and beta value is VF by V out, VF and V out are known to you. Once you put these values you will come across the equation nothing but HI into Z1 plus Z2 plus Z3 plus Z1 Z2 into bracket 1 plus HFE plus Z2 Z3 equal to 0 minus J by omega C1 Z2 is minus J by omega C2 and Z3 is nothing but J omega L. We will come across the equation which consists of real part and imaginary part minus J into HI into bracket 1 by omega C1 plus 1 by omega C2 plus sorry minus omega L plus 1 by omega square C1 C2 into 1 plus HFE plus L by C2 equal to 0. Now here you have the imaginary part and the real part. When we equate this imaginary part to 0 you will get frequency of oscillation and this real part to 0 then you will get condition for gain for the sustained oscillations plus 1 by omega C2 minus omega L equal to 0. So, you will get equation as omega C2 plus omega C1 divided by omega square C1 C2 equal to omega L. Therefore, C1 plus C2 divided by C1 C2 L this complete quantity is under root. So, F equal to 1 by 2 by under root here L C1 C2 is there. So, if you separate out the terms it will come like this 1 by your C1 get cancelled. So, L C2 plus 1 by L C1 this is equation for frequency of oscillation part will be 1 by omega square C1 C2 into 1 plus HFE equal to L by C2 1 plus HFE equal to L divided by C2 into omega square C1 C2 1 plus HFE equal to value of omega square is C1 plus C2 divided by L C1 C2 and remaining part of the equation is L C2 L get cancelled over here C2 also get cancelled over here. So, we can write 1 plus HFE equal to C1 by C1 is 1 and here C2 by 1. So, HFE should be equal to the ratio C2 by C1 this is your condition for oscillation. So, if you follow this gain equation then you can get here equation for the gain nothing but HFE of amplifier call in call bits oscillator feedback is obtained from which element and the answer is from the center of slit capacitors. Next question to ensure that circuit oscillates condition for AV beta is yes as we have derived and that comes to applications of call bits oscillators are like this as you know that it is used for the high frequency of oscillations up to megahertz frequency. So, it is mostly used for high and wide range of frequency applications like RF and microwave it is also used with the saw device nothing but acoustic waves sawtooth acoustic waves can be used and that can be utilized as a sensor surface acoustic waves as circuit is highly sensitive it senses directly from its surface and so it is widely used for this kind of sensitive applications it is preferred to withstand high and low temperature frequently and it is mainly having applications for the commercial purpose. These are the references. Thank you.