[sdiy] ASM1 - MAT & caps

[Tom May]

Let's see how this shakes out.  Gray and Meyer say:

      q A Dn ni^2
Is =  -----------
         Wb NA

where

   q is q (constant)
   A is a contant area
   Dn is related to electron diffusion
   ni is the temperature-dependent intrinsic carrier concentration
   Wb is the width of the base (which varies with the terminal voltages,
      at least)
   NA is a constant related to doping

What we're interested in is the temperature dependence of the ratio
Is1/Is2 of the two transistors.

Is1   q A1 Dn ni^2     Wb2 NA2       Wb2 NA2 A1
--- = ------------ x ------------  = ----------
Is2      Wb1 NA1     q A2 Dn ni^2    Wb1 NA1 A2

A2, A2, NA1, and NA2 won't change so in theory we get:

Is1                  Wb2
---  proportional to ---
Is2                  Wb1

So we're down to the temperature dependence of Wb.  At this point it's
not clear whether this is "good enough", or whether matching Is1 = Is2
is better.  We're getting into second (or third) order effects here
with the base width modulation and temperature variation of Wb, which
I don't recall having been mentioned before, so I would guess Vbe
offset doesn't really matter.  I would obviously defer to empirical
evidence to the contrary, however.

Tom.

Ian Fritz <ijfritz at earthlink.net> writes:

> There has been some discussion of this point here before, and people never 
> really came to any agreement. A Vbe mismatch could be caused by material 
> variation and/or defects, in which case the measured dVbe could certainly 
> correlate with a mismatch in the Is temperature variation. However, it is 
> also possibe to have a mismatch in Vbe due to purely geometric effects 
> (different meas areas) without a temperature-dependent mismatch in Is. In 
> this case the Vbe mismatch produces an offset, but no temperature 
> problems.  So it's a question of which factor in Is is causing the mismatch 
> in Vbe.
> 
>    Ian
> 
> 
> 
> At 07:12 PM 2/6/2002, Scott Bernardi wrote:
> >There's actually two temperature dependencies in the Ic vs Vbe relationship:
> >Ic = Is*exp(-q/kT)
> >The Is term has a temperature dependence that approximately doubles every 10
> >degrees C. When you use two matched transistors in an exponentially converter,
> >they cancel each other out. What's left over is the -q/kT term that we use
> >tempco resistors to compensate for.
> >How well the Is terms cancel depends on the matching of the transistors and
> >the thermal coupling.  A delta Vbe is an indication of mismatch. 150uV is
> >plenty good, however.