Hi TI Team,
Based on the SmartRF Studio 7, CC1101 has differnet data rate vs deviation on GFSK, but what is the reason that 4.8kBaud has wide deviation 25.4KHz vs 10kBaud, 19kHz deviation?
The transmitted signal will have a certain signal bandwidth (BWsignal), which depends on the data rate and modulation format. This bandwidth can be approximated by Carson's rule:
BWsignal = 2*fm + 2*fdev (= data rate + frequency separation)
where
- fm is the highest modulating frequency. 2*fm = data rate
- fdev is the frequency deviation. 2*fdev = frequency separation
BWsignal for 4.8 kbps and +/-25.4 kHz deviation is then approximated as 55.2 kHz
BWsignal for 10 kbps and +/-19 kHz deviation is then approximated as48 kHz
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 (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.
BWchannel has to be larger than the maximum signal bandwidth BWsignal plus the maximum frequency error due to crystal inaccuracies. Worst case scenario will be for the crystal errors on Tx and RX side to be of opposite signs
BWchannel > BWsignal + 4* XTALppm* fRF
- XTALppm is the total accuracy of the crystal including initial tolerance, temperature drift, loading, and ageing
- fRF is the RF operating frequency.
BWsignal is more or less equal for the 4.8 kbps and 10 kbps cases above and can have the same frequency error. The deviation is set to get the same signal bandwidth and thus the same crystal accuracy requirements for the two data rates.
The crystal accuracy, assumiing operation at 868 MHz, will be roughly 15 ppm for the 2 cases above: 4.8 + 2*25.4 + 15*868 = 108 kHz.
Finally: For a fixed RX filter BW, sensitivity vs separation/datarate decreases with about 1.5-2.5 dB per halving down to a certain limit where the loss increases very fast. Thus, you can trade sensitivity for crystal accuracy. (crystal cost)
Hi Sverre,
Below is the customer feedack and thanks again for your response.
Thanks for the help on Carson's rule: BWsignal = 2*fm + 2*fdev (= data rate + frequency separation)
But Carson’s rule does not answer the relationship between fm and fdev posted:
4.8 kbps, 2FSK, 25 kHz deviation,
DC filter. RX filter bandwidth = 101kHz
no DC filter. RX filter bandwidth =101 kHz
10 kbps, 2FSK, 19 kHz deviation,
Can I set the data rate to be 38.4 kbps while dev is 5 KHz with RX filter bandwidth to be 101 KHz as Cason’s rule suggested?
Gary Lin
Gary,
The chosen frequency deviation will impact sensitivity and occupied bandwidth in opposing directions.
The CC1120 operates well at modulations indexes of 0.5 and above a slight improvement is seen at modulation indexes more than 1 (symbol rate = frequency deviation), however if the RX bandwidth has to be increased due to occupied bandwidth of the resulting signal then it ends up reduces the performnace more than the increase by modulation index.
Therefore.
Regards,/TA
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Hello,
I see all posts here about calculating BW, but:
In Carson´s rule is FM highest modulating frequency. For rectangular pulse, on the internet is lot of considerations to its bandwith.
B=2*Rate (http://zone.ni.com/devzone/cda/ph/p/id/20), or B=R (http://ece.utah.edu/ece3300/labs/lab6/FSK.pdf) or B=R/2 which is used in yours Carsons, (http://www.dip.ee.uct.ac.za/~nicolls/lectures/eee482f/13_fsk_2up.pdf ) . This make indecisive bandwodth of RX filter, but yours used BW is probably main lobe or spectrum or what.
//edit , I found that ansewr is using NRZ coding with 0-1 sequence, which gives B=Rb/2 (B=1/2Tb)
Also, how to calculate bandwidth for GFSK (if need more approach as Crason´s gives) and MSK used in CC1101 / CC430 ?
Regards