32768 crystal oscillator
Hi Elone,
You can find a 32.768kHz crystal oscillator with CMOS inverters at **broken link removed** .
Regarding the electrical equivalent model of 32.768kHz crystal, there is info in an old MOTOROLA McMOS Data Book as follows: series resistance, Rs=25kohm; Q=50000 (typical); series motional capacitance,C1=0.0039pF; series motional inductance, L1=6000Henry (!); parallel capacitance, Co=3.9pF (these data are for Motorola MTQ 32 type crystal (NT-cut) but obviously many other 32kHz crystals have nearly the same equivalent motional L1 and C1, depending on their cut of course).
In the circuit on the above web site the 15Megohm resistor is important, because it adjusts the inverter into the linear part of the DC characteristic to get high gain, hence oscillation, do not use less then 10Mohm there! Also, it is very difficult to force a 32kHz crystal into oscillation with the usual circuits (Clapp, Colpitts etc) with bipolar transistor, so the easiest is to use the old CMOS (not TTL!) inverters. HCMOS/HCTMOS may be also good but I did not try them, only CMOS.
There is a paper on SPICE crystal oscillator simulation at **broken link removed** but it deals with a 12MHz oscillator.
See also the paper on crystal CMOS oscillators at **broken link removed** where there is series resistance in the feedback path with the given value --it may help oscillation.
I did not do crystal oscillator simulation in SPICE, only in Serenade with bipolar transistor and for a few MHz and higher frequencies.
Regards, unkarc