Safran CORTEX CRT Quantum, User Manual

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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 30
3.3.1.3.
FM demodulation
3.3.1.3.1. FM Discriminator
The number of periods of the FM discriminator can be configured between 1 to 16. The output amplitude
depends on the selected Pre-Detection filter and the discriminator number of periods.
Let us take the example of an input IF carrier which is FM modulated by a pure sub-carrier, this signal being in
the Pre-Detection filter bandwidth.
-to-polar converter is:
𝝋(𝒏) =
𝟐
𝑵
𝟐𝝅
[(𝝎
𝒄
− 𝝎
𝑪𝑭
)
𝒏
𝑭
𝒔
+
∆𝑭
𝒇
𝒔𝒄
𝐜𝐨𝐬 (
𝒏
𝑭
𝒔
)] + 𝝋(𝟎)
Where:

𝑛
is the sample time index,

𝑁
is the number of bits on which the phase and the frequency are coded,

𝜔
𝐶𝐹
is the pulsation of the Center Frequency transposing synthesizer-NCO,

𝑐
is the pulsation of the input signal carrier,

𝜔
𝑠𝑐
is the pulsation of the input modulation sub-carrier,

𝐹
𝑠
is the sampling frequency,

𝑓
𝑠𝑐
is the frequency of the input modulation sub-carrier,

∆𝐹
is the FM frequency deviation.
The frequency output f(n) of the differentiator, where
𝐷
is the differentiator delay, is:
𝐟(𝐧) =
𝟐
𝐍
𝟐𝛑
{(𝛚
𝐜
− 𝛚
𝐂𝐅
)
𝐃
𝐅
𝐬
+
∆𝐅
𝐟
𝐬𝐜
× (−𝟐)𝐬𝐢𝐧 [𝛚
𝐬𝐜
𝐃
𝟐
×
𝟏
𝐅
𝐬
] 𝐬𝐢𝐧 [𝛚
𝐬𝐜
(𝐧 +
𝐃
𝟐
) ×
𝟏
𝐅
𝐬
]}
The frequency output
𝑓
𝑛𝑜𝑟𝑚
(𝑛)
normalized on Full Scale is :
𝐟
𝐧𝐨𝐫𝐦
(𝐧) =
𝐃(𝐟
𝐜
− 𝐟
𝐂𝐅
)
𝐅
𝐬
𝟐
⁄
+
𝐃 × ∆𝐅
𝐅
𝐬
𝟐
⁄
×
𝐬𝐢𝐧 [𝛑
𝐟
𝐬𝐜
𝐅
𝐬
𝐃]
𝛑
𝐟
𝐬𝐜
𝐅
𝐬
𝐃
× (−𝟏) 𝐬𝐢𝐧 [𝛚
𝐬𝐜
(𝐧 +
𝐃
𝟐
) ×
𝟏
𝐅
𝐬
]
The level of the sub-carrier on frequency output is (expressed in dBFS):
𝐟
𝐧𝐨𝐫𝐦
(𝐟
𝐬𝐜
) = 𝟐𝟎𝐋𝐨𝐠
𝟏𝟎
[
𝐃 × ∆𝐅
𝐅
𝐬
𝟐
⁄
] − 𝟑 + 𝟐𝟎𝐋𝐨𝐠
𝟏𝟎
{
𝐬𝐢𝐧 [𝛑
𝐟
𝐬𝐜
𝐅
𝐬
𝐃]
𝛑
𝐟
𝐬𝐜
𝐅
𝐬
𝐃
}