[sdiy] NICs, GICs, NLOs and all that

[Ian Fritz]

Hi listers --

It seems that there has not been much use of NICs and GICs (negative and 
generalized impedance converters) and related circuits in the synth-diy 
arena.  Recently JH reminded us that synthetic inductors constructed from 
classical gyrator circuitry may have important advantages in constructing 
fixed-frequency filter banks.  I've collected some interesting general 
information and circuit ideas in this area from the web and thought I would 
pass them along.  Of course, much of the basic information is also 
available in textbooks on network theory.

A Power Point presentation deriving the basic GIC equations with 
applications to synthetic inductors is given here:
http://madeira.physiol.ucl.ac.uk/people/richard/ele3031_4/drm.ppt

Applications of GIC-based simulated inductors (gyrators) and FNDRs 
(frequency dependent negative resistors) to filters are illustrated in the 
application notes for the AD713 op amp:
http://www.analog.com/UploadedFiles/Datasheets/70859332AD713_c.pdf

A BB application notes shows a clever linear-phase filter for anti-aliasing 
using FNDRs, along with a nice discussion of how to go about developing GIC 
circuits:
http://aldebaran.elo.utfsm.cl/datasheet/burr-brown/PDFFILES/AP-NOTES/AB-026.pdf

A recent EDN article demonstrated use of a modified GIC circuit to make an 
amplitude stable oscillator. It could possibly also be used to make stable 
hi-Q filters:
http://www.e-insite.net/ednmag/index.asp?layout=article&articleid=CA238420

The following link discusses NICs (negative impedance converters) and shows 
how to use a pair of them to make a simulated inductor and a bandpass filter:
http://ist-socrates.berkeley.edu/~phylabs/bsc/PDFFiles/bsc8.pdf

Another EDN article shows how to use negative resistors in filter and 
oscillator design.  A negative resistance can be used to cancel inductor or 
capacitor losses to make stable hi-Q filters:
http://www.e-insite.net/ednmag/archives/1994/072194/15di1.htm

Finally, here is a really great article on analog circuit realizations of 
non-linear dynamics.  The author shows how to start with arbitrary 
non-linear differential equations and implement them using various 
non-linear circuit techniques. He covers NICs and GICs, polynomial and 
linear-segment transfer functions, and the realization of Chua, Rossler and 
Lorenz oscillators.
http://www.fit.ac.jp/~itoh/geo/paper/ijbc1103.pdf

None of these references incorporate voltage control of parameters, but 
using OTAs as variable resistors to tune synthetic inductors and capacitors 
looks feasible.

Happy New Year to all!

   Ian