[sdiy] Shift register sequence period

[Tim Stinchcombe]

Hi list,
	I've been trying to establish the length of the sequence from a
particular 4006 shift register setup. It is used in the Doepfer A-117, which
is where I came across it; Ken Stone also uses it in his 'Digital Noise'
module:

http://www.cgs.synth.net/modules/cgs31_digital_noise.html

and the earliest reference I've found to it so far is in a 1990 book by Ray
Marston, 'Integrated Circuit and Waveform Generator Handbook'.

At first I thought the inverter in the feedback (middle 4030 gate in Ken's
circuit above) would mean that the length of the sequence would be some what
less than 2^18-1. Then in attempting to translate the gates into polynomials
(if I've got it right) the inverting action seems to make the feedback
non-linear, and so the normal theory of LFSRs no longer applies. So I
'captured' a few bit sequences on my scope (the longest being 59 bits), and
ran it through the Berlekamp-Massey algorithm, which appears to say that the
length of the minimum *linear* feedback shift register which could generate
this sequence is actually 19 stages, i.e. one more than the 18 available in
the 4006! I'm hoping that this 'anomaly' *is* due to the non-linearity...

Has anyone done any analysis of this or similar circuits, i.e. with an
inverter in the feedback? Or if anyone steer me in the right direction, or
toward a decent analysis of this circuit, then I'd appreciate it. (I can't
find anything similar in Electronotes; not much seems to turn up in the
Synth DIY archives; but I note the EDP Wasp and Gnat use similar circuits,
but with a different arrangement of taps and inverter.)

Cheers,
	Tim

P.S. I have a copy of Golomb's 'Shift Register Sequences', but I'm kinda
hoping to get at least a semi-cogent sense of what is happening without
resorting to 3 months hard graft...
__________________________________________________________
Tim Stinchcombe 

Cheltenham, Glos, UK
email: tim102 at tstinchcombe.freeserve.co.uk