[SI-LIST] Re: Crystal modelling parameters and parallel resonance frequency formula
- From: Ray Anderson <Raymond.Anderson@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx, Jean_Pierre.Bouthemy@xxxxxxxxxx
- Date: Fri, 25 Jul 2003 09:52:41 -0700 (PDT)
A data sheet for a common 32.768 KHz crystal can be found at the following URL:
http://www.hy-q.com.au/pdf/10120001.pdf
The data sheet provides the series resistance and motional capacitance
parameters for this particular crystal. (motional capacitance being
0.003pF in this particular case).
Refer to the following URL's for a several papers that pretty well
summarize quartz crystal modeling:
http://user276987.wx8.registeredsite.com/pdfs/xtaldesignnotes.pdf
http://www.ecsxtal.com/pdf/quar_des.pdf
http://www.hy-q.com.au/crystals/crystals-theory.htm
We find that the motional inductance L1 = 1/(4(pi^2)*(fs^2)*C1)
where fs is the series resonant freq. in hertz.
So for the fs of 32.768Khz and the C1 of 0.003pf given in the data sheet
you can calculate the motional inductance to be:
L1= 7863.6 Henries
(a real big number, but expected for a very low freq. xtal)
You can sanity check this value by calculating the resonant frequency
using C1 and L1 f=1/(2pi*sqrt(LC)). It does check out.....
Of course this calculation is based on the motional capacitance number
given in th edata sheet. If your part is very different you may want to
determine the motional inductance and capacitance numbers from lab
measurements of fs and fp (which will also provide delta f).
I haven't answered all your questions, but this should be enough to
get you started in the right direction.
Ray Anderson
Sun Microsystems Inc
>Hi SI experts,
>
>I would like to calculate the accurate parallel resonance frequency (also
>called ant-resonance) of my 32.768 kHz crystal, attached to the integrated
>oscillator of my Real Time Clock (RTC). The goal of this calculation is to
>know if my oscillator will run fast or slow and what could be the accuracy
>of the stability (error in minutes per month).
>It is not so easy because there are several parameters I just don't know.
>The crystal is FSM327 for 12.5 capacitive loading (CL). I need to know the
>following crystal characteristics:
>
>L1: motional inductance
>C1: motional capacitance
>C0: shunt capacitance
>
>None are given in the datasheet. Where can I find them? Has anybody already
>known these parameteres?
>
>To calculate my anti-resonance frequency, I have to calculate CL = (CL1 *
>CL2) / (CL1 + CL2) + Cstray. But what could I consider for Cstray?
>In my designs, I have CL = 11pF, here is why :
>You have to know that the design is a bit "strange": CL1 and CL2 are
>intetegrated in the RTC and I suppose they are equal to 12pF each (because
>the RTC is to be used with 6pF load crystal). But I also have external
>capacitors of 10pF, so that my total CL is : 22pF in parallel with 22pF +
>Cstray = 11pF + Cstray, where Cstray is parasitics capacitor of RTC device
>(DS1284) + parasitics capacitor of Crystal PCB connection (consider 0.5" of
>microstrip traces).
>Can I consider Cstray = 1pF ?
>
>The last question is relative to the parallel frequency formula. I have
>read so many different formula in the litterature that I am confused.
>Should I use C1 or not in the formula (note that it really change the
>result, since it is in the low fF range)? Is the following formula correct,
>or should I use an other one (which one?):
>
> Fp = 1 / ( 2*Pi*sqrt( L1 * (C1*CT) / (C1+CT) ) )
>
> Where CT = C0 + CL
>
>
>Thank you for your help.
>
>Jean-Pierre
>
>--------------------------------------------------------------------
>Jean-Pierre BOUTHEMY
>Hardware Design Engineer
>ALCATEL - Mobile Networking Division (MCG)
>Mobile Core R&D
>+33 (0)2 99 26 08 18
>mailto:jean_pierre.bouthemy@xxxxxxxxxx
>--------------------------------------------------------------------
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