% PLXBode
% This program takes the real and imaginary part of
% a complex pole (or zero) and returns the "knee"
% frequencies for the Bode phase plot, w1 and w2,
% and also the slope, in deg/dec, of the contribution
% between those two frequencies.
%
% By L.Linares 2011
%
%                   |(jw)
%         pole +----+b
%              |\   |
%              | \  |
%              |  \ |
%              |   \|
%         -----+----+---(sigma)
%              a    |
%                   
%

% USAGE: Enter a (level 2) and b (level 1) and
% [white shift] CONT. You receive:
%   W1: lowest "knee" frequency in the phase plot.
%   W2: highest "knee" frequency in the phase plot.
%   Wo: Undamped frequency associated with that pole (zero).
%   Xi: Damping factor (a number between 0..1).
%   degDec: slope of this pole contricution to the phase plot.

% VERY IMPORTANT: To type this program on a regular
%   text file, I had to replace some HP50 keys by
%   certain strings. So ...
%   Where I wrote        you type
%        *               [multiply key]
%        ACOS            [WHITE SHIFT] COS
%        ^               [y to the x key]
%        SQRT            press square root key (*)
%        ->TAG           [WHITE SHIFT] PRG/TYPE/->TAG
%        ->              [RED SHIFT] [zero key]
%        ALOG()          press the [WHITE SHIFT] 10 to x key
%   (*) Do NOT type the letters SQRT ... it won't work!

% This program is provided on a "as is" basis, for
% reference ONLY, and no warranty of its accuracy or
% correctness is made. If you use it, you use it at your
% own risk.

<< 
  "Cpx re,im -> a b" PROMPT
  -> a b
  <<
    'SQRT(a^2 + b^2)' EVAL 
    DUP a SWAP / ABS
    -> Wo Xi
    <<
       'Wo*ALOG(-Xi)' EVAL 'W1' ->TAG 
       'Wo*ALOG(Xi)' EVAL 'W2' ->TAG
       Wo 'Wo' ->TAG
       Xi 'Xi' ->TAG
       90 Xi / 'degDeg' ->TAG 
    >> 
  >> 
>>