[sdiy] 90-degree phase displacement network calculations

[Michael E Caloroso]

Well that was a highly analytical and thought provoking conclusion

MC

On 1/11/21, David G Dixon <dixon at mail.ubc.ca> wrote:
> 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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