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Biasing of MOSFET

We had studied biasing of BJTs and JFET. In the post of BJT biasing we had seen that there were four biasing techniques of BJT and JFET. So the same four biasing techniques are present for MOSFET. 
But as we had seen in the post on BJT biasing Voltage divider bias gives more stability than Modified fixed bias and I hope now you are very much familiar with the concept of biasing. 
So in this post, we will only analyze the Voltage divider biasing technique of MOSFET but before that, we need to understand the drain-source characteristics of MOSFET in little depth.
In the last post, we saw that MOSFET can be operated in 3 different regions. Now we will see how we can control it so that it can work in the desired region. So for that, we need to recall the graph which we studied in the last post.
In the above figure as you can see very clearly that when your input voltage(Vin = Vgs) is less than the threshold voltage(Vth) i.e. (Vgs<Vth) so in that case, your MOSFET is operating in the Cutoff mode. Now as you go on increasing the input voltage such that the input voltage is greater than the threshold voltage(Vgs>Vth) the MOSFET won't operate in the cutoff region rather it would operate in either the Saturation region or Linear region.
Now you may think that if Vgs is exceeding the Vth then what we should do such that the MOSFET will operate in either Saturation mode or in Linear mode. So now to understand this we need to understand one more concept which is pinch-off voltage (Vp).
So as you can see in the above diagram pinch-off voltage(Vp) lies in between the linear and saturation region. If you had read my post on MOSFET, at the end of the post I had explained the same condition. For your better understanding, I'm providing one image below by looking at the image you will get a clear-cut idea, of what I want to explain.
So as you can see in the above image input voltage is greater than the threshold voltage(Vgs>Vth). Now if we go on increasing the Vds then at some point depletion region increases and thus the conduction channel decreases or becomes narrow due to this a constant current Id flows through the channel. Thus the voltage at which the channel becomes narrow such that the drain current flowing through the conduction channel becomes constant is known as a pinch-off voltage. 
Mathematically, pinch-off voltage is given as Vp =  Vgs-Vth
So from the above graph if Vds is less than Vp and Vgs is greater than Vth then MOSFET operates in the Linear region. (Vds < Vp = Vgs - Vth)
Similarly, Vgs is greater than Vth and if  Vds is greater than Vp then the MOSFET operates in the Saturation region. (Vds > Vp = Vgs - Vth) 
Now, we will focus on the output current i.e. (Id). So the equation for the drain current is derived from the electronic devices. So basically you will learn the derivation part of this equation in electronic devices. Here you just need to understand the parameters involved in the equation.
ID = 0.5*μ*Cox*(W/L)*[2*Vds*(Vgs - Vth) - Vds^2]....(Linear region)
ID = 0.5*μ*Cox*(W/L)*(Vgs - Vth)^2.....(Saturation Region)
K = Conduction parameter = 0.5*μ*Cox*(W/L)
Thus the equation of the saturation current can also be written as 
ID = K*(Vgs - Vth)^2
Now, we will try to understand each and every parameter present in the above equations.
μ:- Mobility of electrons in the conduction channel
Cox:- Oxide layer of capacitance
W:- Width of channel
L:- Length of the channel

Now, I hope you know why biasing of transistors is important. We had done this topic in-depth in BJT so I hope now you don't have any doubt in your mind. So biasing is done to keep the Q-point exactly at the center of the load line.

@ Biasing of E-MOSFET
For biasing of any transistors there are 4 techniques but generally, we use the voltage divider biasing technique as it provides more stability than the other 3 biasing techniques and this we had seen in one of the posts on BJT. 
Now, as you can see with the help of voltage divider bias we can easily calculate the voltage VG. If you want to see how I calculated it, below I'm inserting one video don't forget to watch it.
We know that for an E-MOSFET to operate as an amplifier it should be operated in a saturation region and we know that for an E-MOSFET to operate in a saturation region, the output voltage(Vds) should be greater than the pinch-off voltage(Vp).
Saturation region. (Vds > Vp = Vgs - Vth)
So Vth of any MOSFET is known to us as it is present in any datasheet of a transistor, we can calculate Vds if the value of Id is known to us so now we are only left with the calculation of Vgs.
So for that, we need to apply KVL at the gate-source loop, also we know the equation for the output current i.e. Id.
Now that we know the value for Vgs, Vth and Id so we can easily calculate the value of Vds and compare it with Vp.
To calculate Vds we need to apply KVL to the drain-source terminal. 

Generally in the practical world, we don't prefer using D-MOSFET as its overall working is almost similar to JFET. So that's why I'm not explaining it over here if possible, I will make one short video on it.


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