swra181

Design Note DN021

By Sverre Hellan

CC2500 and CC2510/CC2511 Sensitivity versus Frequency Offset and Crystal Accuracy

Keywords

• • • •

Sensitivity

Frequency Offset Crystal Accuracy

PER (Packet Error Rate)

• CC2500 • CC2510

• CC2511

1 Introduction

This design note provides plots of CC2500 sensitivity versus frequency offset for different data rates. The results are also applicable for CC2510/CC2511.

The required crystal accuracy is calculated from these plots. Throughout this document, CC25xx is used to refer to both CC2500 and CC2510/CC2511.

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Design Note DN021

Table of Contents

KEYWORDS..............................................................................................................................1 1 INTRODUCTION.............................................................................................................1 2 ABBREVIATIONS...........................................................................................................2 3 RECEIVER CHANNEL FILTER BANDWIDTH AND CRYSTAL INACCURACIES......3 4 PER VERSUS FREQUENCY OFFSET..........................................................................4 5 CRYSTAL ACCURACY..................................................................................................5 APPENDIX A: SENSITIVITY VERSUS FREQUENCY OFFSET.............................................6 5.1 2.4 KBAUD.................................................................................................................6 5.2 10 KBAUD..................................................................................................................7 5.3 250 KBAUD................................................................................................................8 5.4 500 KBAUD................................................................................................................9 6 GENERAL INFORMATION..........................................................................................10 6.1 DOCUMENT HISTORY................................................................................................10

2 Abbreviations

2-FSK Frequency Shift Keying IF Intermediate Frequency MSK Minimum Shift Keying PER Packet Error Rate PLL Phase Locked Loop ppm parts per million SoC System-on-Chip

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Design Note DN021

3 Receiver Channel Filter Bandwidth and Crystal Inaccuracies

A phase locked loop (PLL) is used to generate the RF frequency in the CC2500 transceiver and CC2510/CC2511 SoC. 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 1.

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 CC25xx is programmed for a carrier frequency of 2440 MHz, there will be an error in the carrier frequency of 2440 MHz·10/1·106 = 24.4 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, i.e. 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 (CC25xx 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 2.

If the transmitter crystal error is +10 ppm and the CC2500/10 is programmed for a carrier frequency of 2440 MHz, there will be an error in the carrier frequency of 24.4 kHz. If the receiver crystal error is -10 ppm and the CC25xx is programmed for an LO frequency of 2439.7 MHz (300 kHz IF frequency) there will be an error in the LO frequency of –24.397 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 2·24.4 kHz = 48.8 kHz.

Receiver channel filter BW

-2·X ppm0+2·X ppmoffset

=signal bandwidth

Total error of 4·X ppm

Figure 1. Plot of IF versus Frequency Error

Figure 1 shows the required minimum receiver channel filter bandwidth BWchannel to account for crystal errors of opposite signs, which is a worst case scenario. BWchannel has to be larger

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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 ageing

• fRF is the RF operating frequency.

Example 3.

If both the transmitter and receiver crystal accuracy is ±10 ppm and the CC25xx is programmed for a carrier frequency of 2440 MHz with an IF frequency of 300 kHz, BWchannel must be larger than BWsignal + 4· XTALppm· fRF = BWsignal + 4·24.4 kHz = BWsignal + 97.6 kHz.

Design Note DN021

4 PER versus Frequency Offset

Figure 4 to Figure 10 plots the 1% PER for different data rates and modulation formats. The RF frequency is 2440 MHz in the measurements. Since 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). Since the IF frequency is programmed in steps of 25 kHz this is not always possible.

-91-93Sensitivity, PER 1% [dBm]3 dB degradation in PER-95-97Frequency offset for 3 dB degradationis smaller for the negative offset-99-101-120-100-80-60-40-20020406080100120140160Frequency offset [kHz] Figure 2. Definition of Frequency Offset which gives 3 dB Degradation in PER

(unsymmetrical frequency offset)

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-90-92Design Note DN021

-94Sensitivity, PER 1% [dBm]-96Frequency offset for 3 dB degradation equal for negative and positive offsets-98-100-102-104-106-40-30-20-100Frequency offset [kHz]10203040

Figure 3. Definition of Frequency Offset which gives 3 dB Degradation in PER

(symmetrical frequency offset)

5 Crystal Accuracy

Appendix A 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

Ö Crystal accuracy (in ppm) = Total frequency offset·106 / (4 · fRF)

Case

Figure

3 dB Bandwidth (total frequency offset) 100 kHz 100 kHz 130 kHz 150 kHz 140 kHz 140 kHz 200 kHz

Crystal Accuracy (@ 2440 MHz) ±10 ppm ±10 ppm ±13 ppm ±15 ppm ±14 ppm ±14 ppm ±20 ppm

2.4 kBaud, 2-FSK, 38 kHz deviation, DC filter. RX filter bandwidth = 203 kHz.

2.4 kBaud, 2-FSK, 38 kHz deviation, no DC filter. RX filter bandwidth = 203 kHz.

10 kBaud, 2-FSK, 38 kHz deviation, DC filter. RX filter bandwidth = 232 kHz.

10 kBaud, 2-FSK, 38 kHz deviation, no DC filter. RX filter bandwidth = 232 kHz. 250 kBaud, MSK, DC filter. RX filter bandwidth = 541 kHz. 250 kBaud, MSK, no DC filter. RX filter bandwidth = 541 kHz. 500 kBaud, MSK, DC filter. RX filter bandwidth = 812 kHz.

Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10

Table 1. Crystal Accuracy Requirement for Selected Data Rates and Modulation Formats 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 a lower IF frequency and thereby lower noise floor and improved sensitivity. As an example, for 2440 MHz, 250 kBaud MSK, enabling the DC filter gives 2 dB better sensitivity at the expense of an increased current consumption of 2.2 mA.

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Design Note DN021

Appendix A: Sensitivity versus Frequency Offset 5.1 2.4 kBaud -85-90-95-100-105-110-80-70-60-50-40-30-20-1001020304050607080Frequency offset [kHz]

FOCCFG.FOC_LIMIT[1:0] 10b

FSCTRL1 0x08

Figure 4. 2.4 kBaud, MDMCFG2.DEM_DCFILT_OFF = 0 -80-85-90-95-100-105-80-70-60-50-40-30-20-1001020304050607080Frequencyoffset[kHz]

FOCCFG.FOC_LIMIT[1:0] 11b

FSCTRL1 0x0B

Figure 5. 2.4 kBaud, MDMCFG2.DEM_DCFILT_OFF = 1

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5.2 10 kBaud -80Design Note DN021

-85Sensitivity, PER 1% [dBm]-90-95-100-105-110-100-90-80-70-60-50-40-30-20-100102030405060708090100110Frequency offset [kHz]

FOCCFG.FOC_LIMIT[1:0] 10b

FSCTRL1 0x06

Figure 6. 10 kBaud, MDMCFG2.DEM_DCFILT_OFF = 0

-75-80-85-90-95-100-100-90-80-70-60-50-40-30-20-100102030405060708090100Frequency offset [kHz]

FOCCFG.FOC_LIMIT[1:0] 10b

FSCTRL1 0x0B

Figure 7. 10 kBaud, MDMCFG2.DEM_DCFILT_OFF = 1

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5.3 250 kBaud -70Design Note DN021 -75Sensitivity, PER 1% [dBm]-80-85-90-95-100-80-60-40-200Frequency Offset [kHz]20406080100 FOCCFG.FOC_LIMIT[1:0] 01b FSCTRL1 0x0A Figure 8. 250 kBaud, MDMCFG2.DEM_DCFILT_OFF = 0 -70-72-74-76-78-80-82-84-86-88-90-100-80-60-40-200FrequencyOffset[kHz]20406080100

FOCCFG.FOC_LIMIT[1:0] 01b

FSCTRL1 0x12 Figure 9. 250 kBaud, MDMCFG2.DEM_DCFILT_OFF = 1

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5.4 -60Design Note DN021

500 kBaud -65-70-75-80-85-90-150-130-110-90-70-50-30-101030507090110130150Frequency Offset [kHz]

FOCCFG.FOC_LIMIT[1:0] 01b

FSCTRL1 0x10

Figure 10. 500 kBaud, MDMCFG2.DEM_DECFILT_OFF = 0

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Design Note DN021

6 General Information

6.1 Document History

Revision Date Description/Changes SWRA181 2008-03-10 Initial release

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