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I am trying to simulate a quartz crystal equivalent circuit.  The series LCR part simulates as expected, but when I add a parallel capacitor the simulation fails.  What am I doing wrong?


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Message 1 of 6



try that

good luck



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Message 2 of 6

It would help if you listed your value of lumped elements. Better yet show your schematic. Without seeing what you have, I suspect your parallel cap value is much too large.

Keep in mind, the parallel capacitance is the equivalent C of the holder and electrodes, so a value of around 4.5pf would be typical. The series L and C is the resonant frequency so, Fo= 1/2pi(SQR LC) the resistance is mechanical equivalent.

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Message 3 of 6

Hello, thanks for response.


Have you checked the second image?


the parralel Cap on schematic is too big.


but there is a problem -

according to books Cpar  and Cser should be close.


but try to simulate it and take a look on frequencies.


in real world in my field (which is ultrasonic welding) - these freqs are very close - f,e for 20Khz range it might be 19,800 and 20,000 or something like that.


in order to get these freqs  close in simulation I had to increase Cpar.


there are formulas -


there are 2 resonant freqs -


one for serial resonance( L, R, C_ser)


for Fo_ser= 1/(6.28(SQR(L* C_ser)))


and second one - for parallel resonance ( L, R, C_ser, C_par)-


for Fo_par= 1/(6.28 (  SQR  (  L*  (C_ser * C_par)  /  (C_ser + C_par)))


it means that C_par and C_ser are connected in serial for that matter.


BTW that why , serial  resonance freq is always higher  then parallel one.


in order to get these freqs close to each other -  the one of caps should be much bigger then other, and then  C_ser and Cpar in serial would be close to C_ser .


run the numbers your self and see. or run simulations , play with parameters and see the results.


and another question - what way \ technick do you use to measure these parameters - I mean - C+ser and C_par.???


thanks in advance for your opinion




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Message 4 of 6

If I understood the question right, the poster was trying to model a quartz crystal, I assume the type used in a crystal oscillator. I am not sure how close a Piezo transducer is to a quartz crystal used in a oscillator, but I am sure the values for the transducer are larger as the resonant frequency is much lower.


I found a App note that describes the quartz crystal model fairly well.


Note, this is a snippet from the App note concerning the parallel capacitance.


CL1 and CL2 are the loading capacitors. During the test, CL1 = CL2 and the value varies from 5pf to 59pf with the inverter supply voltage Vcc = 3.1V and Vcc = 2.3V. The crystal in the test has a nominal frequency of 27MHz at load capacitance of 14pF. It should be noted that the actual loading capacitance to the crystal equals CL1 || CL2 plus the parasitic capacitance of board and the terminals of the inverters.



The pdf for the app note.


Well, perhaps we are thinking Apples and oranges here, so I may just have misunderstood the original question.

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Message 5 of 6

hello, thanks for response.


I guess you are right, we talking apple and oranges here  indeed.


But common denominator of crystalls and transdusers  is - they both have the same model, but differt set of paramenters of coarse.


it seems to me the best solution - to read some good book aboutpiezzoelectric materials.


with hope it helps



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