Shigeo Yamase, JA7UHV

**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 = 650.782.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 Deviationfrom 90 degrees |
Relative Frequency |
Example 1.Frequency in Hz |

1 |
-0.0100 degrees |
fl = 0.039199658493 |
fl*Fo = 19.5998 |

2 |
0.0000 |
0.040389462375 |
20.1947 |

3 |
+0.0100 |
0.044031100092 |
22.0155 |

4 |
0.0000 |
0.050345633857 |
25.1728 |

5 |
-0.0100 |
0.059716379881 |
29.8582 |

6 |
0.0000 |
0.072712173665 |
36.3560 |

7 |
+0.0100 |
0.090121892817 |
45.0610 |

8 |
0.0000 |
0.11300232841 |
56.5011 |

9 |
-0.0100 |
0.14274230101 |
71.3711 |

10 |
0.0000 |
0.18114689293 |
90.5734 |

11 |
+0.0100 |
0.23054686667 |
115.273 |

12 |
0.0000 |
0.29393982172 |
146.977 |

13 |
-0.0100 |
0.37517146967 |
187.586 |

14 |
0.0000 |
0.47916763781 |
239.584 |

15 |
+0.0100 |
0.61223026097 |
306.165 |

16 |
0.0000 |
0.78241360945 |
391.207 |

17 |
-0.0100 |
1.0000000000 |
F0 = 500.000 |

18 |
0.0000 |
1.2780963776 |
639.048 |

19 |
+0.0100 |
1.6333723825 |
816.686 |

20 |
0.0000 |
2.0869522921 |
1043.48 |

21 |
-0.0100 |
2.6654478840 |
1332.72 |

22 |
0.0000 |
3.4020569045 |
1701.03 |

23 |
+0.0100 |
4.3375128643 |
2168.76 |

24 |
0.0000 |
5.5203817402 |
2760.19 |

25 |
-0.0100 |
7.0056317778 |
3502.82 |

26 |
0.0000 |
8.8493751774 |
4424.69 |

27 |
+0.0100 |
11.096082969 |
5548.05 |

28 |
0.0000 |
13.752855259 |
6876.44 |

29 |
-0.0100 |
16.745824211 |
8372.92 |

30 |
0.0000 |
19.862695598 |
9931.35 |

31 |
+0.0100 |
22.711219976 |
11355.6 |

32 |
0.0000 |
24.758933177 |
12379.5 |

33 |
-0.0100 |
fh = 25.510426327 |
fh*F0 = 12755.2 |

**Figure 1. Differential Phase-Shift Characteristics of the optimized network.
The graph has a twofold symmetry.
So the left half of the graph is exactly the same as the right half
with respect to the axis of symmetry,
as your right hand is the same as your left hand in a mirror.
**

Copyright (C) 2004 - 2016 @Shigeo Yamase JA7UHV

** **