Summary:
One of the sixteenth order PSN's
has been optimized with a successive approximation method.
It has the following characteristics: the 16th order, 90 degrees plus or
minus 0.010 degrees, and fh/fl = 650.784.The fh/fl is a frequency ratio
of the highest to the lowest over which differential phase shift of the
psn is maintained within 90 degrees plus or minus 0.010 degrees. The undesired
sideband suppression ratio is -81.2 dB (-81.18 dB) at each of the frequencies
having the maximum phase deviation of 0.010 degrees from the ideal 90 degrees
between fh and fl.
The average suppression of the undesired sideband is -87.2 dB (-87.23 dB) over the bandwidth of modulating frequencies between fh and fl.
Table 1.
| Nr | Phase Deviation from 90 degrees |
Relative Frequency | Example 1. Frequency in Hz |
| 1 | -0.0100 degrees | fl = 0.039199601 | fl*Fo = 19.5998 |
| 2 | 0.0000 | 0.04038943592 | 20.1947 |
| 3 | +0.0100 | 0.04403107740 | 22.0155 |
| 4 | 0.0000 | 0.05034562911 | 25.1728 |
| 5 | -0.0100 | 0.05971634119 | 29.8582 |
| 6 | 0.0000 | 0.07271207082 | 36.3560 |
| 7 | +0.0100 | 0.09012180955 | 45.0610 |
| 8 | 0.0000 | 0.1130022535 | 56.5011 |
| 9 | -0.0100 | 0.1427422220 | 71.3711 |
| 10 | 0.0000 | 0.1811468277 | 90.5734 |
| 11 | +0.0100 | 0.2305467345 | 115.273 |
| 12 | 0.0000 | 0.2939395439 | 146.977 |
| 13 | -0.0100 | 0.3751713466 | 187.586 |
| 14 | 0.0000 | 0.4791677826 | 239.584 |
| 15 | +0.0100 | 0.6122302397 | 306.165 |
| 16 | 0.0000 | 0.7824133735 | 391.207 |
| 17 | -0.0100 | 1.000000000 | F0 = 500.000 |
| 18 | 0.0000 | 1.278096763 | 639.048 |
| 19 | +0.0100 | 1.633372439 | 816.686 |
| 20 | 0.0000 | 2.086951661 | 1043.48 |
| 21 | -0.0100 | 2.665448758 | 1332.72 |
| 22 | 0.0000 | 3.402060120 | 1701.03 |
| 23 | +0.0100 | 4.337515350 | 2168.76 |
| 24 | 0.0000 | 5.520383725 | 2760.19 |
| 25 | -0.0100 | 7.005635655 | 3502.82 |
| 26 | 0.0000 | 8.849381040 | 4424.69 |
| 27 | +0.0100 | 11.09609322 | 5548.05 |
| 28 | 0.0000 | 13.75287471 | 6876.44 |
| 29 | -0.0100 | 16.74583506 | 8372.92 |
| 30 | 0.0000 | 19.86269747 | 9931.35 |
| 31 | +0.0100 | 22.71123168 | 11355.6 |
| 32 | 0.0000 | 24.75894939 | 12379.5 |
| 33 | -0.0100 | fh = 25.510464 | fh*F0 = 12755.2 |
Figure 1. Differential Phase-Shift Characteristics of the optimized network.The
graph is symmetric.So the left half of the graph is perfectly the same
as the right half with respect to the axis, as your right hand is the same
as your left hand in a mirror.
Copyright (C) 2004 - 2005, 2010 Shigeo Yamase
JA7UHV