Safran CORTEX CRT Quantum - Non-Integer Ratio between Q Factors

COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
© Safran Data Systems
This document is the property of Safran Data Systems.
It cannot be duplicated or distributed without expressed written consent.
Page 178
1
800 000
7 001
0.625
4 375.625
The one-way ambiguity distance is approximately:



3.6.9.4.2. Non-Integer Ratio Between Q Factors
The ESA-like and USB standards allow to select non integer ratios between minor tone « Q » factors. The
advantage of this solution is to increase the ambiguity distance much beyond the wavelength of the lowest virtual
minor tone. In this case, the one-way ambiguity distance can be directly derived from the Least Common Multiple
(LCM) of all « Q » factors.
Example: all real tones are in the range 47-53 kHz:
TONE RANK
(1 = FIRST)
Q
P
VIRTUAL TONE
(HZ)
REAL TONE (HZ)
7 (note 1)
10
1
50 000.0
50 000,00
6
170
16
5 882.4
47 058.8
5
180
19
2 777.8
52 777.8
4
850
88
1 176.5
51 764.7
3
4 250
449
117.6
52 823.5
2
21 250
2 249
23.5
52 917.6
1
106 250
11 249
4.7
52 936.5
The LCM is:
Qmin6 = 170 = 5x17x2
Qmin5 = 180 = 5x2
2
x3
2
Qmin4 = 850 = 5
2
x17x2
Qmin3 = 4250 = 2x5
3
x17
Qmin2 = 21250 = 2x5
4
x17
Qmin1 = 106250 = 2x5
5
x17
LCM = 2
2
x5
5
x17x3
2
= 1,912,500, corresponding to a virtual tone of (500,000/1,912,500) =
0.2614 Hz
The one-way ambiguity distance is approximately:


