[sdiy] 90-degree phase displacement network calculations

[Ian Fritz]

Hello --

I decided to have a quick look at this problem using a modern math 
package. I followed the Orchard paper's implementation of the 
Cauer/Chebychev approximation, starting from the beginning at the 
parametric equations 11a/b, and making no approximations from there.

Mathematica has built in all the elliptical/Jacobi functions needed for 
an exact solution. Including, most importantly, the somewhat mysterious 
"modular constant" and its necessary inverse.

There is no need for any approximations or complications such as 
multiple power law expansions and running back and forth through Landen 
transformations.

The results for the numerical example at the end of Orchard's paper came 
out exactly as given. (To better than six digits.)

Hopefully, this helps with any questions about rates of convergence, etc.

Ian


-- 
ijfritz.byethost4.com
-- 
ijfritz.byethost4.com