# Crystal frequencies

the context is that I am working on project which uses a 32 768 Hz quartz oscillator used for a uC.

My questions are:

1. I have read that series resistance should be low (25 to 100 Ohm) otherwise it can lead to oscillator startup failure. But there is an exception for 32 768 Hz crystals. (link1). Why that ?
2. I have read that there is series and parallel resonance frequencies (link1 and link2), which can be really close. Is the fundamental frequency the series resonance frequency at it seems on link2?
3. On the quartz datasheets (datasheet example), the frequency specified is the series or parallel resonance frequency ? (I guess the parallel resonance frequency since there is a capacitve load specified )
4. On the same datasheet, it is specified the load capacitance. What happened if it is not exactly respected? (I guess the final frequency of the system will be not the one specified onto the datasheet)
5. On the link at source 2, it is written that the frequency of the oscillation will be between series and parallel resonnance frequency, is that correct ?

1. They are describing the equivalent series resistance of crystals, it's just a property of the material design for relatively low frequency crystals.

2. The fundamental frequency is commonly the series resonance (since that is the impedance minimum and it stays relatively constant as you add load capacitance), but it's probably better to explicitly specify which resonance you're speaking about when describing it since it can be ambiguous.

3. If it cites a load capacitance, it's the parallel resonance frequency. It will typically call out if it's designed to be a series resonant crystal (and at what frequency)

4. If you don't follow the load capacitance, it will be "pulled" to a different frequency. That's why it's important to include stray capacitance in the calculations, they will affect the frequency.

5. Yes, the frequency will be between the two. In that case, you are using the crystal in parallel resonance, and adding load capacitance in parallel will effectively increase Cshunt, which decreases the parallel resonance frequency.

• 3. Ok, so in the formula of equation 2 given in link3 , Fs is not the frequency given in the datasheet but Fl is the one. Am I correct ? 5. I do not understand. I think it's a semantic issue. I guess it should be: " Frequency could be between the 2", because the (parallel) frequency is "fixed" by the load capacitance, it will not "move" (except due to drift, such as temperatur, aging etc...) May 19, 2021 at 7:55
• Yes, FL is what's given on the data sheet. For number 5, yes it's a terminology thing. What I was calling the parallel resonance frequency is also called the loaded resonance frequency in the link. The loaded parallel resonance frequency (as measured in a circuit with load capacitance) changes with load, and will be between the unloaded parallel resonance frequency and the series resonance frequency. When people say "parallel resonance frequency," they typically mean "loaded parallel resonance frequency." May 19, 2021 at 12:50