[sdiy] 90-degree phase displacement network calculations

Ian Fritz ijfritz at comcast.net
Mon Jan 11 15:44:20 CET 2021

```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.

```