[time-nuts] overtone crystal question

[Bernd Neubig]

Sorry, I forgot the static capacitance C0, which is (without holder and strays)
C0 (pF) = 0.024*Ael^2*f/N with electrode area Ael in mm^2 and f in MHz
Best regards
Bernd

-----Ursprüngliche Nachricht-----
Von: Bernd Neubig [mailto:BNeubig at t-online.de] 
Gesendet: Samstag, 21. September 2019 08:42
An: 'Discussion of precise time and frequency measurement' <time-nuts at lists.febo.com>
Betreff: AW: [time-nuts] overtone crystal question

Hi,

There is nothing like a fixed  ratio between R1 at 3rd or 5th overtone the R1 at fundamental mode. The best approach through C1 and Q.
C1 reduces with the square of overtone N (for an infinite crystal plate). In reality C1(3rds about 85% of C1(fund/N^2. For the 5th and higher OT it is about 75 to 70% of C1(fund)/N^2..
Now Q comes into the game:
The Q of a crystal designed for 3rd overtone is approximately such that Q*f = 2E12 (f in Hz), for 5th OT is may be 3 to 5*E12 . Fundamental mode crystals have lower Q*f , around 1E12 This all is for a plano-plano AT-cut crystal plates and is only a rule of thumb. It finally depends on the crystal size and shape and some design details. Small crystals with convex shape will have better Q*f at fundamental, mode, crystals with well polished and plaon-parallel surfaces may be better at 3rd OT and have lower Q*f  at fundamental mode.
C1 at fundamental mode is given by the equation
C1(fF) = 0.15*Ael^2*f, with Ael = electrode are in mm^2 and frequency f in MHz With that and with the above estimated values for Q, the resistance can be calculated fundamentally from
R1 =1/(2*PI*freq*C1*Q)       - here is freq in Hz and C1 in F

Have fun

Best regards
Bernd
__________________
I wonder if anyone can shed any light on this question, since this forum is loaded with those who REALLY understand crystals.

I am modeling crystal filters (VHF)  in SPICE. There are some specific acoustic mode models for SPICE in some Post Doctorial papers, very interesting, they would be the best but rather painful to use.

However I using simplified Rm, Lm, Cm, Cs, Cp, Ccase etc

My question is, how does Rm vary with overtone number ?

My assumptions are Lm stays the same, Cm reduces proportionally to the square of the overtone number.  Those assumptions are close enough and canon.

I of course need the Rm number to acurately model loss.

73

glen english

VK1XX




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