floating inductor

[Don Tillman]

   Date: Wed, 29 Nov 1995 17:35 -0800 (PST)
   From: Barry Klein 714-932-7493 <KLEIN_B at A1.WDC.COM>

   You might want to investigate using a phaser circuit like in my book
   on page 134, where you output the phase shifted signal only, it sounds
   like vibrato.  I don't know how it sounds compared to the hammond
   circuit you are working on though.

I'm guessing the reason JH is doing this is simliar to the reason I
would (if I had enough time): each type of phase shifter
implementation has a different sound with a different "soul".
FET/opamp phase shifters (MXR Phase90) sound different from OTA phase
shifters (Small Stone) sound different from ladder phase shifters (ARP
Quadra) sound different from emitter-collector phase shifters
(UniVibe).

So the goal here (if I might be so bold as to speak for JH) is to grab
the soul specific to the Hammond flying chorus and implement it in a
more appropriate technology.  The theory is that the soul of this
beast has to do with the phase and delay characteristics of the LC
delay line.

This interests me an awful lot (Lord knows why) so I spent some time
scratching my head and thinking about it.  Okay JH, I got something
here.  Check this out:

You can implement a floating inductor with three OTAs and a cap
like this:

-----+------------------------+
     |                        |
     |             gnd--|+\   |
     |                  |  >--+
     |             +----|-/
     +---|+\       |
         |  >--+---+
     +---|-/   |   |
     |         =   +----|+\
     |         |        |  >--+
     |        gnd  gnd--|-/   |
     |                        |
-----+------------------------+


Note the lovely aethetics of symmetry.  If the first OTA has gm1 and
the other two OTAs have gm2, the effective inductance is:
L = gm1 gm2 C.

Cool, eh?  But not good enough.  Still too many components.  How about
a single JFET:


----+-------+
    |       |
    |       /
    |       \   R
    |       /
    --|     |
      |<----+
    --|     |
    |       |
    |       =   C
    |       |
----+-------+

This circuit is equivalent to an inductor in series with a resistor.
The inductance is L = R C / gm and the resistance is R = 1 / gm.
You might want to deal with biasing the gate down a little of course.

  -- Don