[sdiy] 90-degree phase displacement network calculations
David G Dixon
dixon at mail.ubc.ca
Mon Jan 11 21:42:04 CET 2021
Hello Ian,
Well, I'm getting a bit tired about arguing about this, so my official
answer is... whatever.
Cheers
Dave
-----Original Message-----
From: Ian Fritz [mailto:ijfritz at comcast.net]
Sent: Monday, January 11, 2021 6:44 AM
To: David G Dixon; 'Bernard Arthur Hutchins, Jr'; synth-diy at synth-diy.org
Cc: 'Brian Willoughby'
Subject: Re: [sdiy] 90-degree phase displacement network calculations
[CAUTION: Non-UBC Email]
That looks not to be true. The difference between two successive k'(i)
values clearly can not be zero. The process is a (rapidly) converging
iterative one.
In case you can't see this, the proof is trivial:
Suppose k'(i) = k'(i-1)
Then from the second equation, k(i) = k(i-1) Now the first equation yields 0
= k(i)-k(i-1) = [1-k'(i-1)]/[1+k'(i-1)] -
[1-k'(i-2)]/[1+k'(i-2)]
This can be generally true only if k'(i-2) = k'(i-1) So by induction, all
the k'(i) values are the same.
A sequence either iterates or it doesn't -- it can't just drop dead in the
middle of the street.
Ian
(math minor, including some pretty tough analysis courses)
On 1/11/2021 2:23 AM, David G Dixon wrote:
> ........ There are no "approximate" answers, and this problem is not
> one where one gets closer and closer to the true solution with each
> step. That would be an iterative solution, and as I've said ad
> nauseum, this is not that problem.
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