How should I choose crystal frequency for my application using Si446x?
Before giving an accurate answer for the question, it is important to clarify a phenomenon called sampling spur (integer boundary spur). If the carrier frequency is near to an integer multiple of the crystal frequency, spurious contents (sampling spurs / integer boundary spurs) can appear below and above the carrier (the distance from carrier is the distance between the carrier and the integer multiple of the crystal frequency). The level of these spurs are getting higher with decreasing distance between the carrier and the crystal harmonic. This way, it is important to choose a crystal frequency that has no integer harmonic near the carrier frequency.
The minimum recommended distance between the carrier frequency and the integer multiple of the crystal frequency should be separated for low and high frequency bands. For low band frequencies (< 525 MHz) the minimum recommended distance is 2,2 MHz, for high frequency bands (> 850 MHz) this value is 2,8 MHz.
Let’s see an example: fc = 869,5 MHz, fxtal = 30 MHz. The 29th harmonic of the crystal frequency is 870 MHz, which is 0,5 MHz away from the carrier frequency. This way, spurious contents will appear 0,5 MHz below and above the carrier as shown in the following figure:
Considering the above mentioned recommended distance from the crystal harmonic, the carrier frequency should be below 867,2 MHz or above 872,8 MHz. The other option is to choose another crystal frequency which fits the recommendation (e.g. 26 MHz).
Other sampling spurs can appear if the nth harmonic of the carrier is near to an integer multiple of the crystal frequency. In this case the distance between the frequency of the sampling spurs and the carrier will be equal to the distance between the nth harmonic and the integer multiple of crystal frequency. Regarding carrier harmonics the recommended distance between the harmonic frequency and the integer multiple of the crystal frequency for low frequency bands is typically 2,2/n MHz, for high frequency bands the value is 2,8/n MHz, where n is the number of carrier harmonic which is near to an integer multiple of the crystal frequency.
Let’s see an example for a 3rd order sampling spur (the 3rd harmonic of the carrier is near to an integer multiple of the crystal frequency): fc = 909,8 MHz, fxtal = 30 MHz. In this case, the 3rd harmonic of the carrier (2729,4 MHz) is 0,6 MHz away from the 91th harmonic of the crystal frequency (2730 MHz). This way the side lobes will be 600 kHz away from the carrier:
To meet the recommendation for the 3rd order sampling spurs, the carrier frequency should be chosen to be below ~909 MHz (= 910 MHz – 2,8/3 MHz) or above 911 MHz (= 910 MHz + 2,8/3 MHz). The other option is to choose an appropriate crystal frequency for the desired carrier frequency.
Basically, it can be declared that it is sufficient to investigate the 1st, 2nd, 3rd and 4th order sampling spurs, higher order contents will not introduce such high power levels to fail the standard regulations.