JFETs and Moog Ladder Filters

[Martin Czech]

> >What would a Moog Ladder low pass filter circuit look like if it used JFET
> >transistors in stead of NPN transistors?  Could such a thing even be made?
> 
> I'm tempted to say it's a s hard as building a ladder filter with t*bes (;->).
> I just don't see anything that coresponds to the exponential law of BJTs.
> (Unless you connect source and drain and use them as diodes ...)
> 
> More on the serious side: You can use them as VC resistors in a
> non-ladder configuration (with somewhat limited range, I guess).
> 

It`s early in the morning, but I try to figure out, what a 
JFET ladder would mean:

The bipolar transistor is used as a current controlled resistor in this way:

Ib=Is*exp{Ube/Ut} (base current dends exponential on base voltage Ube)

or Ube=Ut*ln(Ib/Is)

So far this is only base current and voltage, but we need
Uce and Ic. If the transistor is not starving from undervoltage
we can assume dUbe = dUce, and bipolar current gain beta:
Ib=1/beta*Ic

Simple exchange of variables gives:

Uce=Ut*ln(Ic/beta/Is)

then dUce/dIc= Ut*beta*Is/Ic/beta/Is=Ut/Ic

This means the resistance from colector to emitter
depends inversely proportional to the collector current.
This is very nice, because no other ugly factors like beta
are involved, only the temperature voltage Ut.

In the ladder filter the collector current is forced by a
exponential current source: Ie=Ic=K1*exp{Vc/K2)

Inserting:

dUce/dIc=Ut/K1*exp{-Vc/K2}

Voila: the collector-emitter resistance depends on 
our control voltage Vc in an exponential manner.

Now JFET:

Id=Ids*(1+Ugs/Up)**2  (Up=threshold voltage)

Ugs=-Up+Up*SQRT(Id/Ids)

and

dUgs/dId=Up/2*SQRT(Ids)/SQRT(Id)

This looks quite similar to the bipolar case, except
for the square root function for Id.

Again, in a ladder we force Id:

Id=K1*exp{Vc/K2) =>


dUgs/dId=Up/2*SQRT(Ids)*(K1*exp{Vc/K2))**-0.5
        =Up/2*SQRT(Ids)/SQRT(K1)*exp(-Vc/K2/2)

This is basicly the same structure than the one for
the bipolar case. 

So, in theory one could build an JFET-Ladder (you will need
of course one or two BJT for the expo control current).

But: we see some ugly factors in the JFET case, Up and SQRT(Ids). These
are not well defined, teperature dependend, matching will be hard.

And: the 2x4 ladder BJTs don't have to match in a first order approach in
order to get equal transconductance for the filter stages, see above. Only
the differential pair at the bottom (equal current distribution) and
at the top (offset suppression) have to match.  This is not the case
for the JFET ladder. All 2x4 ladder JFETs would have to be matched
for transconductance, and the 2 pairs for offset supression as above.
JFETs vary a lot more in parameters then BJTs, that makes things worse.
As long as we don't use a good matching JFET array chip, we'll have a
hard time.  But this is only a statistical argument.  If you have a lot
of of time and JFETs, you might be able to match them.

mc