COMMAND RANGING & TELEMETRY UNIT CORTEX
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Page 45
3.3.3.
IF Carrier Tracking
Once the carrier frequency is acquired as per previous section, tracking is launched using Phase-Locked Loop
technique.
Cortex CRT XL Quantum uses a 2nd order PLL for carrier tracking.
CRT eXplorer can be configured to 2nd order PLL or 3rd order PLL, using the PLL order registry parameter (see
chapter 4.2.8.2.6). This section describes the performances for tracking only, acquisition performance is not
depending on the loop order and is described in chapter 3.3.2.2.
3.3.3.1.
2
nd
Order PLL
This is the most commonly used PLL. However, for demanding applications, this loop has one drawback:
Expected C/N0 is sizing the loop bandwidth
Loop bandwidth is sizing the Doppler rate
Example: The C/N0 drives the choice of the Loop Bandwidth. If you want to track a signal with a low C/N0, you
have to choose the narrowest loop bandwidth in order to increase the ratio S/N.
With this hypothesis, reducing the bandwidth implies a lower tracking performance for the Doppler rate.
And finally, the Doppler generates a phase error bias in the loop of
𝝓𝜺 ≈
𝜶
(𝟐𝑩𝑳)
𝟐
× 𝑫𝒐𝒑𝒑𝒍𝒆𝒓𝑹𝒂𝒕𝒆
𝛼
is a constant value (approx. 7.05) and it is relative to damping factor (0.7 in case of Cortex).
The total phase error is composed with
ϕε
and
σ
which is the standard deviation.
𝛔 = √
𝟐𝐁
𝐧
𝟐
𝐒
𝐍
𝟎
with
𝑆
𝑁
0
Signal Noise ratio input (dB.Hz)
The PLL cannot manage a bias error superior to
𝜋
2
, so the maximum admissible Doppler Rate cannot exceed:
𝐃𝐨𝐩𝐩𝐥𝐞𝐫𝐑𝐚𝐭𝐞 <
𝛂(𝟐𝐁𝐋)
𝟐
𝟕. 𝟎𝟓
× (
𝛑
𝟐
− 𝟒𝛔)
Example: With
2BL = 100 Hz
, and
S
N
0
= 40 dB. Hz
, the maximum Doppler Rate is :
𝐑 =
(𝟐𝐁𝐋)
𝟐
𝟕. 𝟎𝟓
(
𝛑
𝟐
− 𝟒√
𝟐𝐁
𝐧
𝟐
𝐒
𝐍
𝟎
)
=
(𝟐𝐁𝐋)
𝟐
𝟕. 𝟎𝟓
(
𝛑
𝟐
− 𝟒
√
𝟐𝐁𝐋
𝟐. 𝟏𝟎
(
𝐒
𝐍
𝟎
)
𝟏𝟎
⁄
)
< 𝟏𝟖𝟐𝟔 𝐇𝐳/𝐬
