Texas Instruments | CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy (Rev. D) | Application notes | Texas Instruments CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy (Rev. D) Application notes

Texas Instruments CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy (Rev. D) Application notes
Design Note DN005
SWRA122D – January 2007 – Revised September 2018
CC11xx Sensitivity Versus Frequency Offset and Crystal
Accuracy
Sverre Hellan
......................................................................................................... LPRF Applications
ABSTRACT
This design note provides plots of CC11xx (CC1100, CC1100E, CC1101, CC1110, and CC1111)
sensitivity versus frequency offset for different data rates. The required crystal accuracy is calculated from
these plots. The results are also applicable for CC430.
1
2
3
4
5
Contents
Abbreviations .................................................................................................................
Receiver Channel Filter Bandwidth and Crystal Inaccuracies .........................................................
PER Versus Frequency Offset .............................................................................................
Crystal Accuracy .............................................................................................................
Sensitivity Versus Frequency Offset ......................................................................................
2
2
3
4
5
List of Figures
1
Plot of IF Versus Frequency Error ......................................................................................... 2
2
Definition of Frequency Offset That Gives 3-dB Degradation on PER (Unsymmetrical Frequency Offset) ..... 3
3
Definition of Frequency Offset That Gives 3-dB Degradation on PER (Symmetrical Frequency Offset) ........ 3
4
4.8 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
5
5
4.8 kbps, MDMCFG2.DEM_DCFILT_OFF = 1
5
6
7
8
9
10
11
12
..........................................................................
..........................................................................
10 kbps, MDMCFG2.DEM_DCFILT_OFF = 0 ...........................................................................
10 kbps, MDMCFG2.DEM_DCFILT_OFF = 1 ...........................................................................
38.4 kbps, MDMCFG2.DEM_DCFILT_OFF = 0 .........................................................................
38.4 kbps, MDMCFG2.DEM_DCFILT_OFF = 1 .........................................................................
250 kbps, MDMCFG2.DEM_DCFILT_OFF = 0 ..........................................................................
250 kbps, MDMCFG2.DEM_DCFILT_OFF = 1 ..........................................................................
500 kbps, MDMCFG2.DEM_DCFILT_OFF = 0 ..........................................................................
6
6
7
7
8
8
9
List of Tables
1
Crystal Accuracy Requirement for Selected Data Rates and Modulation Formats With
FOCCFG.FOC_LIMIT[1:0] = 11b ........................................................................................... 4
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1
Abbreviations
1
Abbreviations
FSK
IF
MSK
PER
PLL
ppm
SoC
2
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Frequency shift keying
Intermediate frequency
Minimum shift keying
Packet error rate
Phase locked loop
parts per million
System-on-chip
Receiver Channel Filter Bandwidth and Crystal Inaccuracies
A phase locked loop (PLL) is used to generate the RF frequency in the CC1100, CC1101, and CC1100E
transceivers and the CC1110, CC1111, and CC430 SoCs. The PLL reference frequency is derived from
an external crystal. If the crystal frequency is incorrect, the transmitter carrier frequency and the receiver
LO frequency will also be incorrect. The crystal frequency error is due to initial tolerance, capacitive
loading errors, ageing, and temperature drift.
Example: If the crystal frequency has an error of ±X ppm (parts per million) the RF frequency also has an
error of ±X ppm. As an example, if the crystal error is +10 ppm and the CC11xx is programmed for a
carrier frequency of 868 MHz, there will be an error in the carrier frequency of 868 MHz×10/1E6 =
8.68 kHz.
The transmitted signal will have a certain signal bandwidth (BWsignal), which depends on the data rate and
modulation format. On the receiver side there is a channel filter, which is centered on the down-converted
received RF frequency; that is, the intermediate frequency (IF). The channel filter has a programmable
bandwidth BWchannel. The signal bandwidth has to be less than the receiver channel filter bandwidth, but we
also have to take the frequency error of the transmitter and receiver into account.
If there is an error in the transmitter carrier frequency and the receiver LO frequency, there will also be an
error in the IF frequency. For simplicity assume the frequency error in the transmitter and receiver is equal
(same type of crystal). If the receiver has an error of –X ppm and the transmitter has an error of +X ppm
the IF frequency will have an error of +2 × X ppm (CC11xx uses low side LO injection). Conversely, if the
receiver has an error of +X ppm and the transmitter an error of –X ppm the IF frequency will have an error
of –2 × X ppm.
Example: If the transmitter crystal error is +10 ppm and the CC11xx is programmed for a carrier
frequency of 868 MHz, there will be an error in the carrier frequency of 8.68 kHz. If the receiver crystal
error is -10 ppm and the CC11xx is programmed for an LO frequency of 867.7 MHz (300-kHz IF
frequency) there will be an error in the LO frequency of –8.677 kHz (approximately the same as the error
in the carrier frequency due to the low IF frequency used). The total error in the IF frequency, after down
conversion from RF, will be 2 × 8.68 kHz = 17.4 kHz.
Receiver channel filter BW
Offset
–2 × X ppm
0
+2 × X ppm
Total error of 4 × X ppm
= Signal bandwidth
Figure 1. Plot of IF Versus Frequency Error
2
CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy
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PER Versus Frequency Offset
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Figure 1 shows the required minimum channel filter bandwidth BWchannel to account for crystal errors of
opposite signs, which is a worst case scenario. BWchannel has to be larger than the maximum signal
bandwidth BWsignal plus the maximum frequency error due to crystal inaccuracies.
BWchannel > BWsignal + 4 × XTALppm × fRF
where
•
•
XTALppm is the total accuracy of the crystal including initial tolerance, temperature drift, loading, and aging.
fRF is the RF operating frequency.
(1)
Example: If both the transmitter and receiver crystal accuracy is ±10 ppm and the CC11xx is programmed
for a carrier frequency of 868 MHz with an IF frequency of 300 kHz, BWchannel must be larger than BWsignal
+ 4 × XTALppm × fRF = BWsignal + 4 × 8.68 kHz.
3
PER Versus Frequency Offset
Figure 6 to Figure 12 plot the 1% PER for different data rates and modulation formats. Register
FOCCFG.FOC_LIMIT[1:0] = 11b and the RF frequency is 868 MHz in the measurements. Because the
signal bandwidth is given, the plots can be used to estimate the maximum frequency offset and hence the
required crystal accuracy.
Assuming a 3-dB loss in sensitivity is acceptable, the total frequency offset is estimated as 2 times the
frequency offset where a 3-dB degradation in PER is first measured (see Figure 2). In the ideal case the
3-dB degradation in PER should occur at the same positive and negative frequency offsets (see Figure 3).
Because the IF frequency is programmed in steps of 25 kHz, this is not always possible.
-91
-93
3-dB degradation in PER
-95
-97
Frequency offset for 3-dB degradation
is smaller for the negative offset
-99
-101
-120 -100 -80 -60 -40 -20
0
20
40
60
80
100 120 140 160
Frequency Offset (kHz)
Figure 2. Definition of Frequency Offset That Gives 3-dB Degradation on PER (Unsymmetrical Frequency
Offset)
-90
-92
-94
Frequency offset for 3-dB degradation
is equal for negative and positive offsets
-96
-98
-100
-102
-104
-106
-40
-30
-20
-10
0
10
Frequency Offset (kHz)
20
30
40
Figure 3. Definition of Frequency Offset That Gives 3-dB Degradation on PER (Symmetrical Frequency
Offset)
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3
Crystal Accuracy
4
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Crystal Accuracy
Section 5 shows plots of sensitivity versus frequency offset for different data rates. The required crystal
accuracy is calculated from the total frequency offset as
Total frequency offset = 4 × XTALppm × fRF
Crystal accuracy (in ppm) = Total frequency offset × 1E6 / (4 × fRF)
(2)
(3)
Table 1. Crystal Accuracy Requirement for Selected Data Rates and Modulation Formats With
FOCCFG.FOC_LIMIT[1:0] = 11b
Figure
3-dB Bandwidth
(Total Frequency
Offset)
Crystal Accuracy
(868 MHz)
4.8 kbps, 2FSK, 25 kHz deviation, DC filter,
RX filter bandwidth = 101 kHz
Figure 4
50 kHz
±14 ppm
4.8 kbps, 2FSK, 25 kHz deviation, no DC filter,
RX filter bandwidth = 101 kHz
Figure 5
50 kHz
±14 ppm
10 kbps, 2FSK, 19 kHz deviation, DC filter,
RX filter bandwidth = 101 kHz
Figure 6
70 kHz
±20 ppm
10 kbps, 2FSK, 19 kHz deviation, no DC filter,
RX filter bandwidth = 101 kHz
Figure 7
70 kHz
±20 ppm
38.4 kbps, 2FSK, 20 kHz deviation, DC filter,
RX filter bandwidth = 101 kHz
Figure 8
110 kHz
±32 ppm
38.4 kbps, 2FSK, 20 kHz deviation, no DC filter,
RX filter bandwidth = 101 kHz
Figure 9
120 kHz
±35 ppm
76.8 kbps, 2FSK, 32 kHz deviation, DC filter,
RX filter bandwidth = 232 kHz
–
230 kHz
±66 ppm
76.8 kbps, 2FSK, 32 kHz deviation, no DC filter,
RX filter bandwidth = 232 kHz
–
260 kHz
±75 ppm
100 kbps, 2FSK, 47 kHz deviation, DC filter,
RX filter bandwidth = 325 kHz
–
220 kHz
±63 ppm
100 kbps, 2FSK, 47 kHz deviation, no DC filter,
RX filter bandwidth = 325 kHz
–
180 kHz
±52 ppm
250 kbps, MSK, DC filter,
RX filter bandwidth = 541 kHz
Figure 10
200 kHz
±58 ppm
250 kbps, MSK, no DC filter,
RX filter bandwidth = 541 kHz
Figure 11
220 kHz
±63 ppm
500 kbps, MSK, DC filter,
RX filter bandwidth = 812 kHz
Figure 12
120 kHz
±35 ppm
Case
NOTE: The ADC spectrum in the RX chain consists of a significant DC component. This puts a
lower limit on the IF frequency that can be used. For optimum sensitivity, a digital DC filter
can be enabled (MDMCFG2.DEM_DCFILT_OFF =0), and the ADC DC output is attenuated.
This opens for selection of lower IF frequencies thereby lower noise floor and improved
sensitivity. As an example, for 868 MHz, 250 kbps 2-FSK, enabling the DC filter gives 2 dB
better sensitivity, at the expense of an increased current consumption of 2.3 mA.
4
CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy
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Sensitivity Versus Frequency Offset
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5
Sensitivity Versus Frequency Offset
5.1
4.8 kbps
-100
Sensitivity, PER 1% [dBm]
-101
-102
-103
-104
-105
-106
-107
-30
-20
-10
0
Frequency offset [kHz]
10
20
30
Figure 4. 4.8 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
-100
Sensitivity, PER 1% [dBm]
-101
-102
-103
-104
-105
-106
-30
-20
-10
0
Frequency offset [kHz]
10
20
30
Figure 5. 4.8 kbps, MDMCFG2.DEM_DCFILT_OFF = 1
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5
Sensitivity Versus Frequency Offset
5.2
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10 kbps
-99
Sensitivity, PER 1% [dBm]
-100
-101
-102
-103
-50
-40
-30
-20
-10
0
10
Frequency offset [kHz]
20
30
40
50
40
50
Figure 6. 10 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
-95
Sensitivity, PER 1% [dBm]
-96
-97
-98
-99
-100
-101
-50
-40
-30
-20
-10
0
10
Frequency offset [kHz]
20
30
Figure 7. 10 kbps, MDMCFG2.DEM_DCFILT_OFF = 1
6
CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy
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Sensitivity Versus Frequency Offset
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5.3
38.4 kbps
-91
Sensitivity, PER 1% [dBm]
-93
-95
-97
-99
-101
-103
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency offset [kHz]
20
30
40
50
60
70
60
70
Figure 8. 38.4 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
Sensitivity, PER 1% [dBm]
-91
-93
-95
-97
-99
-101
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency offset [kHz]
20
30
40
50
Figure 9. 38.4 kbps, MDMCFG2.DEM_DCFILT_OFF = 1
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7
Sensitivity Versus Frequency Offset
5.4
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250 kbps
-88
-89
Sensitivity, PER 1% [dBm]
-90
-91
-92
-93
-94
-95
-96
-100
-80
-60
-40
-20
0
20
Frequency offset [kHz]
40
60
80
100
Figure 10. 250 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
-86
-87
Sensitivity, PER 1% [dBm]
-88
-89
-90
-91
-92
-93
-94
-120
-100
-80
-60
-40
-20
0
20
Frequency offset [kHz]
40
60
80
100
120
Figure 11. 250 kbps, MDMCFG2.DEM_DCFILT_OFF = 1
8
CC11xx Sensitivity Versus Frequency Offset and Crystal Accuracy
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Sensitivity Versus Frequency Offset
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5.5
500 kbps
-80
-81
Sensitivity, PER 1% [dBm]
-82
-83
-84
-85
-86
-87
-88
-89
-80
-60
-40
-20
0
20
Frequency offset [kHz]
40
60
80
Figure 12. 500 kbps, MDMCFG2.DEM_DCFILT_OFF = 0
SWRA122D – January 2007 – Revised September 2018
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9
Revision History
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Revision History
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from August 20, 2009 to September 27, 2018 ................................................................................................. Page
•
10
Formatting and editorial changes throughout document ............................................................................. 1
Revision History
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