[sdiy] 90-degree phase displacement network calculations
Bernard Arthur Hutchins, Jr
bah13 at cornell.edu
Fri Jan 8 04:05:10 CET 2021
The “design” of 90-Degree Phase-Differencing Networks (90-degreePDNs) can involve some deeper theoretical discussions as well as practical ”plug and chug” equation summaries. The earliest offerings in EN involved references to academic presentations from which practical equations were largely just cribbed {D. Weaver, "Design of RC Wide-Band 90-Degree Phase-Difference Network," Proc. IRE, Vol. 42, pp 671-676 (1954); W. Albershein & F. Shirley, "Computation Methods for Broad-Band 90° Phase-Difference Networks," IEEE Trans. Ckt. Theory, CT-16, pg 189 (1969) }. See a summary at:
http://electronotes.netfirms.com/MEHCh6aPart.PDF
with details at: http://electronotes.netfirms.com/AN167-AN170.PDF
and a quit important contribution to practical implementations at: “Design of Wideband Analog 90° Phase Differencing Networks Without a Large Spread of Capacitor Values”; http://electronotes.netfirms.com/EN168-90degreePDN.PDF
The offering here from David seems to be (like our own!) deficient in theoretical explanations. Is there a link/reference? Perhaps no one cares? But some notion of a “UNIQUE-BEST ” (UB) (can’t do better) solution requires theory – in this case it seems to be the “alternation theorem” (AT) as applied to the phase error.
The AT allows us to RECOGNIZE the UB equi-ripple solution in terms of the finding of a correct SET of “extremal frequencies” as found by ITERATING an “exchange algorithm” (Remez or Parks-McClellan). No closed form is possible, but convergence is very rapid.
I have not attempted this.
-Bernie
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