I have a question on both the 32.768kHz XTAL and 32MHz XTAL specifications. In the CC2541/CC2540 specifications both XTALs are shown as requiring +/-40ppm. But there is also a footnote for both that states "Including aging and temperature dependency, as specified by [1]". The [1] reference seems to refer back to the BT Core spec for different PPM levels. This footnote seem reasonable for the way MHz crystals are specified, but not for the way 32.768kHz crystals are specified (due to parabolic coefficient). Please see my quick analysis below and confirm if my understanding is correct.
BT Core Spec requires +/-500ppm worst case on the sleep clock and +/-50ppm worst case on the active (MHz clock).
Looking at a 32.768kHz spec here is what I think:
Frequency Tolerance Options (32.768kHz) = 20ppm, 30ppm and 50ppm
Parabolic Coefficient = -0.04ppm / °C2
To convert from ppm to % -> x(%) = x(ppm) / 10000
Equation for parabolic coefficient use:
Freq = Freq0 * [1 – 0.04ppm * (T – T0)2]
So worst case:
Freq = 32.768kHz * [1 – 0.04ppm * (-40 – 25)2]
0.04ppm converts to 0.000004%
But you need to divide by 100 again in order to subtract from 1….therefore you now have:
32.768kHz * [1 – 0.00000004 * (-40 – 25)2] = ~32.7624kHz
A Seiko app note also shows for straight PPM just use (if analyzing at -40°C):
Ftemp = B * [T – T0]2
Ftemp = – 0.04ppm * (-40 – 25)2
Ftemp = -169ppm
Going hot will have the same negative effect on frequency because of the parabolic nature of the 32.768kHz XTAL but if you consider +105°C you will have a larger PPM:
Ftemp = -255ppm
These PPM rates even with the initial frequency tolerance added in are well within the specification for BLE of +/-500ppm. For the sleep clock you can just add the calculated PPM due to temp to the worst case ppm for the initial tolerance (in our case -30ppm for a device that meets the CC254x spec) for a total of -285ppm. This leaves quite a bit of margin for any additional ppm rate introduced by the CC254x internal clocking circuitry to stay within the +/-500ppm for BLE specification.
Therefore I believe the device specification is pointing out only the 40ppm initial tolerance rate for a 32.768kHz XTAL (even though it mentions temp I don’t think this includes the parabolic coefficient for the 32.768kHz XTAL).
Please confirm or correct my understanding.
For a 32 MHz oscillator I see options typically for 20ppm from -40°C to +85°C or 50ppm for -40°C to +125°C (which would not meet the CC254x requirements of 40ppm). I'm sure some companies offer a temp range in between with 40ppm as well. As mentioned above the active clock needs to be 50ppm worst case per BT Core spec for the MHz oscillator so I believe the spec calls out 40ppm on the MHz XTAL to give some buffer for the internal circuitry errors.
Please confirm or correct my understanding.
Kind Regards,
Marc
