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Zero Temperature Drift biasing of JFET

In the last post, we studied different biasing techniques of JFET and we also saw some parameters and their importance while in the end, we concluded that self-bias and voltage divider bias circuit gives the best result while explaining those techniques
I mentioned that there are certain reasons due to which JFET needs to be biased and that particular reasons I will be discussing in this post.
Before starting with the post, I want to give you a brief idea of what concepts we will learn by the end of this post. 
1) Different parameters of JFET.
2) Effect of temperature on JFET.
   a) Concept of zero current drift
   b) Derivation of the equation for zero current drift.

1) Different parameters of JFET:-
There are certain parameters that you have to study first before moving further.
a) Transconductance (gm):- If you want to understand what exactly transconductance is then please do read my post on rpi model of BJT. there I  had explained the whole concept of transconductance in a detailed way. 
So according to the definition, gm = ΔId / ΔVgs
Now if we differentiate Shockley's equation then we will get the following result as shown in the image.
Thus we got the equation of maximum transconductance and at the end, we got the relation between transconductance(gm) and maximum transconductance(gmo).
b) Dynamic resistance (rd):- Change in drain-source voltage with respect to drain-source current when Vgs is constant is known as a dynamic resistance.
So according to the definition, rd = ΔVds / ΔIds ...... (When Vgs is constant)
c) Amplification Factor (μ):- Change in drain-source voltage with respect to gate-source current when the drain current is constant.
So according to the definition, μ =  ΔVds / ΔVgs ...... (When Id is constant)

2) Effect of temperature on JFET or Why JFET needs to be biased?
Before understanding the whole concept of the effect of temperature on JFET we have to make certain assumptions for our better understanding. Consider an N-channel JFET, we know that the electrons move from source to drain. Assume that during normal conditions i.e. at room temperature 10 electrons or 10e- are moving from source to drain.
Now, as the outside temperature increases the atoms or the crystal ions in the N-type region start vibrating. As the atoms vibrate it opposes the migration of electrons from source to drain due to which the number of electrons moving from source to drain decreases i.e. in normal conditions if 10e- were migrating from source to drain then as the temperature increases only 8e- may travel from source to drain due to which the current Id decreases. As fewer electrons travel from source to drain due to the vibration of atoms, therefore, it is assumed that the depletion region increases.
Experimentally, it is seen that Id decreases by 0.7% per degree rise in temperature.
Therefore, ΔId = 0.7% * Id.......(1)

a) Concept of zero current drift:-
To understand this concept you have to understand the concept of the self-biasing circuit first then it will be very much easy for you to understand this concept because this concept uses a self-bias circuit. As we saw above that if the temperature increases atoms vibrate and channel width decreases due to which Id also decreases by 0.7% per degree rise in temperature. Similarly, as temperature decreases the width of the N-channel region increases due to which the output current or Id also increases. This increase in drain current is equivalent to a change in Vgs by 2.2mv per degree rise in temperature. This value is calculated experimentally.
That is, we know that,
ΔId = ΔVgs * gm
ΔId = 2.2mv * gm........(2)

b) Derivation of the equation for zero current drift:-
So we need to conclude some of the things before going to the equations. From all of the above explanations, we conclude that the increase in drain current becomes equal to the decrease in drain current. Such biasing is known as zero temperature drift bias. While the self-bias circuit plays a very significant role in between increment and decrement of Id w.r.t temperature.
So, from the above explanation
Decrease in Id w.r.t temperature = Increase in Id w.r.t temperature
ΔId decreasing w.r.t to temperatureΔId increasing w.r.t temperature
0.7% * Id  =  ΔVgs * gm .......... [From (1) & (2)]

In the end, I would like to conclude the whole concept with this 15-minute video please watch it, because I had shown the working in the animated form I hope it will help you to boost up your concept in a much more detailed way.


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