Quartz Crystal Spurious Modes - John Dunn, Consutant, Ambertec, P.E., P.C.

An equivalent circuit for a quartz crystal has two resonant frequencies, one at a parallel resonance and one at a series resonance, where the parallel resonant frequency is always slightly higher than the series resonant frequency.

Shamelessly setting the component values of this equivalent to yield the proper values of parallel resonance, series resonance and equivalent series resistance of a specific crystal, an impedance calculation versus frequency was performed and an actual crystal was tested with the following results:

 

The series resonance of the crystal was right on target at 16 MHz while the parallel resonance was about thirty kHz higher. However, the crystal also had some series and parallel resonances it was not supposed to have at other nearby frequencies.

When this crystal was used in this very commonplace clock oscillator, the oscillator would intermittently go into multi-moding and frequency hopping which was a very serious problem.

 
We read in specification MIL-PRF-3098K, 27 August 2010, PERFORMANCE SPECIFICATION, CRYSTAL UNITS, QUARTZ, GENERAL SPECIFICATION FOR as follows:

3.13 Unwanted modes (fundamental mode or overtone units). When tested as specified in 4.10.9, all unwanted modes shall have resistance that exceeds two times the main mode resistance.

4.10.9 Unwanted modes (fundamental mode or overtone units) (see 3.13). The resistance of any unwanted mode in the frequency range of ±20 percent around the main mode shall exceed two times the main mode resistance when measured at the test drive level.

In other words, believe it or not, crystals with spurious modes are permitted under this specification. Whether the crystal under discussion met the letter of that requirement or not isn't certain from such rudimentary test results, but that crystal certainly could not be trusted to work properly in the subject oscillator.

Since the crystal is the oscillator's only frequency determining component, if the crystal misbehaves, the oscillator will misbehave too. That's why I really distrust this kind of oscillator, even though it is very widely used.

This is also why I make my recommendation to clients that they use only a purchased oscillator from a trustworthy vendor and not try to follow the common practice of using a gate-based oscillator.

 

Comments

[Carl Schwab]

John, My experience with spurious responses with frequency controlling xtals is mainly with 3rd and 5th overtone, and an occasional fundamental. Two points from my experience. 1) Don’t overdrive the xtal—can cause heating and brings up the spurious if they are going to be a problem. 2)Any circuits I designed always had a gain setter (usually a strategic resistor) that was adjusted to optimize starting and stability.

FWIW the frequency pull ability varies as the square of the overtone ratio i.e. a third overtone is 9 times as hard to pull and a 5th overtone is 25 times as hard to pull.------Carl Schwab

[John D.]

Hi, Carl.

The oscillator as shown is typical of what is often rcommended and whatever drive level the gate devices provide, that's it and you really have no control.

You can trim the crystal's drive level of course, but I don't know by what criteria would one judge the optimization of that trimming given that the output is logic level stuff.

That's why I say, buy an oscillator from a compamy that is in-the-biz rather than let an FPGA or µP/µC or ASIC do its own oscillation.

John

[Eddy van Keulen]

Quartz crystals can have a substantial amount of unwanted modes that can bite you one way or another. Theoretically you can model all these resonances, spurious or overtones, with separate series branches.
These spurious modes are the result of a specific crystal design. I believe they are the result of reflections between edge of electrode and edge of quartz disc. The crystal manufacturer can change the design to move the spurious further from the main mode and/or increase the spurious resistance so your circuit can not accidentally get stuck on a spurious anymore.
I would place a resistor between the oscillator inverter output and the 22pF on the right. This improves (lowers) the drive and also improves (increases) the Q. You can try values in the range 100~1000 ohms.

Eddy

[Tom Christian]

I want to thank everyone for their comments
and John for his work.
This is the sort of useful stuff they should tell you
in school. I've run into this problem before
but just assumed it was a "bad" crystal.