 Welcome myself, Giridhar Jain, Assistant Professor in Electronics and Telecommunication Engineering, Valchan Institute of Technology, Sulapur. Now today I am going to deliver a lecture on MOSFET design equations. Now learning outcomes of the session are at the end of the session students will be able to draw phi i characteristics of E MOSFET and describe them. Second outcome is students will be able to write design equations for phi i characteristics of E MOSFET and elaborate. These are phi i characteristics of n-channel E MOSFET design equations. So these are the phi i characteristics of n-channel E MOSFET. So drain current versus VDS for different values of VGS. So VGS 1, VGS 2, VGS 3 and VGS 4. So you can see the characteristics and here a dotted line is drawn which is the condition or these are the dotted line is the set of points which will satisfy phi GS minus phi t is equal to phi DS. This is if phi DS is equal to phi GS minus phi t where phi DS is drain to source voltage, phi t is the threshold voltage and phi GS is get to source voltage. Now if you look at the characteristics you can see that towards the left hand side of this dotted line it is the non-saturation or linear region of characteristics. Towards the right hand side is the saturation region and for phi GS less than threshold voltage it is a cutoff region. So these are the three operating regions of the E MOSFET. So these characteristics are being drawn for the n-channel E MOSFET. Now this MOSFET has the three regions of the operation. First is the cutoff or the threshold region. Now for the cutoff region phi GS is less than or equal to VT and the drain current is 0 for the cutoff region. Means phi GS is less than threshold voltage less than or equal to VT. Hence the drain current ID equal, IDS equal to 0. Now second region is the non-saturation or the linear region where phi DS is greater than 0 and it is less than phi GS minus VT and phi GS is phi GS minus VT, right, phi DS greater than 0 and phi DS less than phi GS minus VT. So this condition is to be satisfied. And for this non-saturation or linear region the drain to source current IDS is given by IDS is equal to beta in the bracket, then phi GS minus phi T multiplied by VDS minus phi DS square by 2. So this is the equation for IDS. Now from this equation you can see that IDS is the relation of IDS with IDS depends on phi DS dependence. So there is a minus that phi DS square by 2, so this is a second order term. Now if phi DS is very small, then phi DS square by 2, so this term is negligible, right. And therefore, IDS linearly varies with phi DS, if phi DS is very small. Let us go back to characteristics and elaborate more. So in this characteristics you can see towards the left hand side of this dotted line that is your non-saturation or linear region and if phi DS is very small, then this characteristic is approximated by straight line because the second order term that is phi DS square by 2 is negligible, right. Then application of this linear region is that the MOSFET, this e MOSFET is used as a voltage variable resistance. So this is non-saturation or a linear region. Now next region of the characteristics is the saturation region. Now saturation region, the condition to be satisfied is that phi DS minus phi T is greater than 0 and phi DS minus phi T less than phi DS and drain to source current is given by IDS equal to beta in the bracket phi DS minus phi T bracket square divided by 2. So here if you look at the equation, you can see that the drain current depends only on phi DS because phi T is fixed for a given MOSFET, right. So IDS is a function of beta, phi DS, phi T. So beta and phi T are fixed for the given MOSFET and only phi DS is variable. So it does not depend on phi DS means as per this equation the drain current remains constant for given value of phi DS, ok. So go back to characteristics you can see. So in the saturation region, the drain current should be constant but practically it is slightly increasing. Now reason for this is the short channel effect. So that we will study later on. So this is non-saturation or linear region of characteristics. Then saturation region, ok. Now after saturation region, now pause this video and think on following question. What is a beta? So beta is a gain factor of the MOSFET and it is given by mu epsilon upon T o x into W upon L where mu is the mobility of channel. Epsilon is the permittivity of a gate insulator that is SiO2 layer that is epsilon, T o x is the thickness of the oxide layer as shown in the figure, W is width of channel and L is length of channel. Now here T o x, W and L. So these are shown in the diagram. So right hand side, so this diagram shows the geometric terms for the MOSFET. You can see substrate onto substrate drain and source are obtained by diffusion. Then there is an insulating layer of SiO2 shown by the dashed lines. So L is shown. So this is the length of channel and the depth that is the width of channel W as shown in figure. And onto insulating layer of SiO2 a polycrystalline silicon is used to make the contact with gate and for the drain and source the contact are made using the metals, ok. So these are the geometric terms for the MOSFET. So for this MOSFET you can see the beta is mu epsilon upon T o x as the thickness becomes small and small. As thickness of the oxide layer becomes small and small the gain of MOSFET increases, ok. Then beta is directly proportional to the mu and epsilon. Then it is directly proportional to the W and inversely proportional to the L. And depending on once beta is increased you can see the drain to source current will be increasing. You can see here. So ids is equal to beta phi gs minus vt square by 2 for saturation region. And for the cutoff region also it is ids is equal to beta in the bracket phi gs minus vt vds, ok. So beta depends on the MOSFET parameters, ok. That is geometry of the MOSFET and the material used for fabrication of the MOSFET, ok. And by controlling this mu epsilon T o x W and L you can control the beta as per requirement, ok. So these are the references. Thank you for watching the video.