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Subject: Re: (Quartz Crystal) Pspice template

Date: 08/05/02 at 10:28 AM
Posted by: Dale
E-mail: dchisholm@coinco.com
Message Posted:

In Reply to: Pspice template posted by napoleon on 06/24/02 at 6:36 AM:

The ARRL "Radio Amateur's Handbook" (most any edition from the last 30 or 40 years) has a page or two of discussion about quartz crystals, equivalent circuits, etc. I also recall coming across a handful of models on one of the crystal mfgr's sites several years ago - it may have been "Fox Crystals" but I can't say for sure.

The first-order equivalent circuit of a crystal in fundamental mode is fairly simple: an R-L-C series circuit, with an additional capacitance in parallel. So the model looks something like:

.subckt xtal 1 2
Lm1 1 10 10 ; Motional inductance - several henries
Cm1 10 11 1E-15 ; Material capacitance - femtofarads
Rs1 11 2 25 ; Piezo losses - few dozen ohms
Cp 1 2 10E-12 ; Holder & pin capacitance - 2 to 20 pF typical
.ends xtal

I believe the biggest shortcoming of this model is that it ignores overtone modes. These are modeled as additional R-L-C series circuits in parallel with Lm1-Cm1-Rs1:

Lm3 1 30 (3.33 ??)
Cm3 30 31 (.3E-15 ??)
Rs3 31 2 (50 ??)

Lm5 1 50 (2.00 ??)
Cm5 50 51 (.2E-15 ??)
Rs5 51 2 (100 ??)

. . . etc . . .

Each of these branches resonates at a higher frequency, with greater losses. People like to call these "odd harmonics" of the fundamental mode (3 times fund. freq; 5 times fund freq; 7 times fund freq; etc) but in fact I think they're related by the zeros of a Bessel function, which don't fall at exact integer multiples (the "third overtone" may actually be around 2.7 or 2.8 times the fundamental, if I recall correctly).

I think this model topology also applies fairly well to ceramic resonators and SAW devices, with proper adjustments to element values.


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