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<DIV dir=ltr align=left><SPAN style="FONT-SIZE: 12pt"><FONT face=Arial><SPAN
class=346354400-13012021><FONT color=#0000ff
size=2> -- </FONT></SPAN>I understand what you did and for the third
time state that there is nothing wrong with what you
did.<O:P> </O:P></FONT></SPAN></DIV>
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class=MsoNormal><SPAN style="FONT-SIZE: 12pt"><O:P></O:P></SPAN><SPAN
class=346354400-13012021><FONT size=3 face="Courier New">I already knew that,
Bernie. I wasn't seeking your approval. I was just presenting a
technique for everyone to use as they wish.</FONT></SPAN></P>
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class=MsoNormal><FONT face=Arial><SPAN style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021><FONT color=#0000ff
size=2> -- </FONT></SPAN>But you have avoided my repeated questions
about what the error plot looks like if you do fewer iterations. <SPAN
style="mso-spacerun: yes"> </SPAN>[ Neither have you commented your program
or (despite saying there were several errors along the way) provided a full
corrected copy.<SPAN class=346354400-13012021><FONT color=#0000ff
size=2> ]</FONT></SPAN></SPAN></FONT><FONT face=Arial><SPAN
style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021> </SPAN><O:P></SPAN><SPAN
style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021> </SPAN></O:P></SPAN></FONT></P>
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face=Arial></FONT></SPAN></P>
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class=MsoNormal><SPAN style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021><FONT face="Courier New">OK, I'll say it one more time:
There are no iterations. If one does not take the necessary number of
steps to complete the Landen transformation, then one gets inaccurate numbers
for the elliptic sine and cosine. I see no purpose to calculating anything
if the elliptic functions are not accurately calculated. Once the
necessary elliptic functions are calculated, then the pole values are calculated
simply from those.</FONT></SPAN></SPAN></P>
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class=MsoNormal><SPAN style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021><FONT face="Courier New">To do what you request would
be like calculating a trigonometric function with sines and cosines, but instead
of actually using those functions, using series expansions truncated at the
third step. Why would anyone do that?</FONT></SPAN></SPAN></P>
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class=MsoNormal><SPAN style="FONT-SIZE: 12pt"><SPAN
class=346354400-13012021><FONT face="Courier New">Orchard presents an equation
to calculate the maximum error in the phase angle directly. However, it
does not seem to give the correct answer. For phase angle, I am
calculating it directly from the RC factors of the filter, and summing up the
total phase angle for all stages in each chain, then subtracting one phase angle
from the other. I have benchmarked my results against the QuadNet program,
and the two results are identical. The equation
in Orchard dramatically underestimates the maximum error.
For example, a 16-stage PDN with a bandwidth of 4 decades
will generate a maximum phase error of 0.133 degrees. The Orchard equation
gives 0.066 degrees. With a bandwidth of 5 decades the maximum error
increases to about 0.5 degrees. The Orchard equation gives 0.116
degrees. So, that's a fail. It bears noting that the equation given
in Darlington for this purpose is different, so the old guard were not all on
the same page, evidently.</FONT></SPAN></SPAN></P></DIV></BODY></HTML>