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My book says that by varying Vgs the transconductance varies in a non linear fashion (this all happens in the "linear" or ohmic region of the FET) and it is constant in the saturation region.I just cannot get it!!

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Take a look at this, the (fairly) standard characteristic of a FET: -

enter image description here

Transconductance or "current out to volts in" is quite different between the linear region and the saturation region. In the saturation region if you lift the gate voltage from 4 V to 5V you get a corresponding change in the drain current of about 17mA to about 24mA and both ratios are about the same - not perfectly the same but enough to say that "transconductance is fairly constant in the saturation region".

The saturating transconductance varies a little bit with drain-source voltage and so it's not a perfect thing to say BUT people do say it and design circuits assuming it is a reasonable axiom.

Go to the linear region and note that for a given gate voltage (say 4V) the drain current is near enough totally dependant on drain voltage. People use this area as variable resistors - the gate controls the resistance between drain and source. Increase the gate voltage and the resistance lowers. It's more appropriate to call this section the linear (ohmic) region because there is no singular dependancy of drain current on gate voltage.

As a footnote, if you see a FET characteristic drawn like below where all the lines from 0,0 seem to merge into one until the saturation region begins to break them out individually, I have one thing to say and that is "THIS IS DRAWN WRONG": -

enter image description here

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  • \$\begingroup\$ But how is the transconductance non linear in the ohmic region?That is the reason the FET's are biased in the linear region when operating as mixers.. \$\endgroup\$ Commented Aug 15, 2015 at 10:27
  • \$\begingroup\$ Because it isn't mainly dependant on Vgs. It's also of little use to refer to transconductance in any way when in the linear region. I haven't seen the book you mention but there are probably better ways of stating things rather than labelling it as non-linear. Maybe you can take a picture of the page? \$\endgroup\$
    – Andy aka
    Commented Aug 15, 2015 at 10:31
  • \$\begingroup\$ You could argue that the saturation region is "current out with volts in" and the linear region is "conductance out for volts in". \$\endgroup\$
    – Andy aka
    Commented Aug 15, 2015 at 10:34
  • \$\begingroup\$ I have edited my post.This is from Microwave by David M Pozar!! \$\endgroup\$ Commented Aug 15, 2015 at 10:36
  • \$\begingroup\$ If Vds is held constant, then the transconductance is fairly constant (and proportional to Vds) in the ohmic region. \$\endgroup\$ Commented Aug 15, 2015 at 10:43
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What is transconductance gm? This parameter tells us how much the drain current Id will vary when the controlling voltage Vgs is changed.

Therefore: gm=d(Id)/d(Vgs)

This differential quantity is nothing else than the slope of the input charcteristics Id=f(Vgs). It can be shown (from the transistor physics) that

Id=Id,s[1-(Vgs/Vp)²].

Of course, the slope of this curve depends in a non-linear fashion from the voltage Vgs.

(Explanation: Id,s: Current Id for Vgs=0; Vp=Pinch-off voltage with Id=0).

Added: When building the above differential quotient and after some mathematical manipulations, we finally get:

gm=(2/|Up|)[SQRT(Id*Id,s)]

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