[sdiy] MOSFET ANGST

[Magnus Danielson]

From: Scott Gravenhorst <music.maker at gte.net>
Subject: Re: [sdiy] MOSFET ANGST
Date: Sun, 18 Jul 2004 08:08:22 -0700
Message-ID: <200407181508.i6IF8LZ27667 at linux6.lan>

> Peter et al,
> 
> Yes, I made much of it go away using the linearizing resistor technique, but
> I got unsatisfactory results with respect to amplitude.  I couldn't get much
> more than 100 mV of input signal before I started seeing soft clipping of the
> triangle peaks.
> 
> So unless I get some brainstorm that presents an idea for allowing a much
> larger input signal (I need about 3 volts for my application, preferrably
> more), this method will be shelved.

Let us see... the MOSFET current in its "resistive" part is

                       2
I  = k [(V  -V )V   - V  ]	(1)
 D        GS  T  DS    DS

With the linearizing resistors we have

      1       1
V   = - V   + - V		(2)
 GS   2  CS   2  DS

The resistance we have is defined as

     V
      DS
R  = ---			(3)
 DS  I
      D

With (1) and (2) inserted into (3) we get

         2
R   = -------			(4)
 DS   k * V
           CS

Great. Thing is, this is only valid in the linear part, saturation is defined
as
                    2
            (V  -V )
              GS  T
I       = k ---------		(5)
 D(sat)         2

The voltage where the resistor hits saturation now can be expressed as

V        = R   * I	        (6)
 DS(sat)    DS    D(sat)

which becomes

                   2
           (V  -V )
             GS  T
V        = ---------		(7)
 DS(sat)      V
               CS

however, Vgs depends on Vcs and Vds and solving that mess results in

             V  -V         _______
              CS  T       /3      |
V        = - ------ + \  / - V  V	(8)
 DS(sat)       2       \/  4  CS T

which you probably guessed anyway.

This would mean that you'd have limits on Vcs and thus limits on suitable
Rds values. Besides, I don't have the Vt for the transistors at hand (they are
not given in the datasheets I was able do download and I am a bit too lazy to
derive them from the graphs).

Anyway, there's the core-dump from my paper and pen exercise. I'll see what
other lovely relations I can come up with.

Cheers,
Magnus