[sdiy] 90-degree phase displacement network calculations

David G Dixon dixon at mail.ubc.ca
Sun Jan 10 02:38:05 CET 2021

Incidentally, for all you math-heads, the Landen transformation technique is
discussed in Chapter 16, Jacobian Elliptic Functions and Theta Functions, of
the Handbook of Mathematical Functions by Abramowitz and Stegun (if you like
math and you don't have this book, you are missing out!).  Section 16.12 is
Descending Landen Transformation (Gauss' Transformation) (which is what I'm
doing), and Section 16.14 is Ascending Landen Transformation.  In the
descending form, one ends up with k=0 and sn = sin.  In the ascending form,
one ends up with k=1, and sn = tanh.
So, I just created an Excel function that calculates the elliptic sine given
any angle and modulus.  From that, the poles are calculated directly, in
closed form.  The mathematicians were wrong, Bernie.
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