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23rd March 2019, 07:47 #1
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Deriving mosfet differential current expressions
Could anyone help to derive mosfet differential current expression (9.4) ?
Note: Screenshot taken from book "Lowpowerwirelesscommunicationcircuitsandsystems60GHzandbeyond"

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23rd March 2019, 09:30 #2
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Re: Deriving mosfet differential current expressions
Could be a bit hard, because Lambert W function is not an elementary function.
If you would like to deriv similar formula using square law approximation, check Gray, Hurst, Meyer book "Analysis and Design...", chapter related to diff pairs.

23rd March 2019, 09:39 #3
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Re: Deriving mosfet differential current expressions
Last edited by vivekroy; 23rd March 2019 at 09:49.
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23rd March 2019, 14:24 #4
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Re: Deriving mosfet differential current expressions
In the proof for BJT , why do you add Io (DC bias point current) ?
I thought gmc*V1 is the total current flowing through the bottom mosfet (or in your proof, a current source) ?

23rd March 2019, 15:02 #5
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Re: Deriving mosfet differential current expressions
Io + gmc*V1 is just copied from post #1...

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23rd March 2019, 16:26 #6
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Re: Deriving mosfet differential current expressions
@FvM
Io + gmc*V1 is just copied from post #1...
I have checked the whole section of the chapter, there is no mention about Io.
Why you call "Io" as DC bias point current ?

23rd March 2019, 17:47 #7
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Re: Deriving mosfet differential current expressions
But that is just the small signal current. All of these expressions were derived NOT assuming small signal models (and thus all the complicated expressions)... And thus, I assumed the DC component of the tail current is Io.
EDIT 1: (Some more comments)
I cannot see it being anything other than a DC component anyway.
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23rd March 2019, 18:55 #8
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Re: Deriving mosfet differential current expressions
The nature of Io as bias current is suggested by using a capital letter, also by symmetry considerations, you have i0a=Io+gmc*v1 and i0b=Iogmc*v1.
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