Selecting a damping resistor for crystal oscillator circuit

I'm building a data acquisition board with an ADAR7251 ADC. I'm trying to figure out the crystal oscillator circuit, and am stuck on the damping resistor. The relevant datasheet is https://www.analog.com/media/en/technical-documentation/data-sheets/ADAR7251.pdf, page 21.

I'm planning on running the crystal at 19.2Mhz.

I understand how to determine the loading capacitors based on the load capacitance of the crystal, and know I should be selecting the resistor to achieve the desired drive level of the crystal. However, I have no clue how to go about determining the correct resistor value to achieve the desired power level. I've seen other examples (such as https://www.crystek.com/documents/appnotes/pierce-gateintroduction.pdf) of finding the resistance values when the feedback resistor is known, but I can't find it specified anywhere in the ADAR7251 datasheet.

How should I find the damping resistor value?

Here's the schematic from the ADC datasheet, it's pretty straightforward:

Thanks for the help!

-Seth

• You must spec Xtal f ! – Tony Stewart Sunnyskyguy EE75 Aug 21 '19 at 1:20
• Ah! thanks 19.2Mhz – sethgi Aug 21 '19 at 2:27
• 1k - 3.3k Ohm or 0.5 to 5k depending on loop gain need to start at high temp, low voltage. – Tony Stewart Sunnyskyguy EE75 Aug 21 '19 at 8:12
• There is an example for 20MHz in your link. Leakage capacitance is not exactly as written and depends on existence of ground plane under , near traces. And output. Capacitance effects are diminished by Rs. – Tony Stewart Sunnyskyguy EE75 Aug 21 '19 at 13:41

This applications note from IDT has you doing it by the simple expedient of using a current probe. I don't even want to think of the \$ involved in that.

I think this can be calculated. What matters is the crystal current. At resonance, a crystal has inductive reactance, at a frequency to resonate with the load impedance. So if you use the following circuit as a model, things should work.

Set C2 equal to your actual capacitor value choice (i.e., 27pF). Set C1 equal to the actual capacitor plus the expected input pin capacitance (5pF, for a total of 32pF). Set L1 to whatever resonates the series combination of C1 and C2 at your crystal frequency, and adjust it if it's not quite right in simulation. Just take a wild-ass guess at R1 (1k-ohm -- what could go wrong?)

Simulate the circuit as an AC model. Sweep the frequency around resonance. Find the frequency at which the phase shift from Xout to Xin is 180 degrees (this assumes that the amplifier in the chip has zero degrees phase shift). For that frequency, look at the current in L1 -- that's your guestimate of the crystal current.

Now adjust Rs, simulate, and repeat until you've got the crystal current that the manufacturer allows. The nice thing about this (for me) is that it should overestimate the crystal current -- so as long as your real circuit actually oscillates strongly, then your crystals should enjoy a long life.

In real life I'd build a test article and try it with my calculated Rs, then with successively larger values of Rs until I noted that it stopped oscillating. If it works at room temperature with an Rs of twice my calculated value, I'd feel comfortable in using my calculated value. If it works at room temperature with an Rs of 10 times my calculated value, I'd feel really comfortable in using my calculated value.

If it doesn't oscillate with Rs at my calculated value, I'd hit the boss up for the cost of renting an RF current probe...

simulate this circuit – Schematic created using CircuitLab

• Great, thanks! I'll definitely start with your simulation idea, that looks smart. If that doesn't get me close enough I'm a student and I'm sure some prof's lab has a current probe I could use if I really need to. – sethgi Aug 21 '19 at 2:34
• Is a single fixed inductance really an appropriate model for a reasonably broad band around resonance? The fact that the crystal has both a resoance and an antiresonance so close makes me question the validity of this approach. – polwel Feb 9 at 12:30
• Not for a broad band around resonance, no -- but for understanding how the thing oscillates at resonance, it works fine. Try searching on "circuit model for a crystal" -- the typical model is a series RLC that models the motational behavior of the quartz itself, in parallel with a capacitor that models the holder. That, in turn, ignores all of the overtones, but unless you're really going insane with your modeling you generally just model the one mode you're working at, and use common sense to make sure you don't oscillate at any other. – TimWescott Feb 9 at 19:56

The resistance is not straightforward to calculate because there is missing information (in particular the voltage across the crystal is not known, and depends to some degree on the design of the oscillator- less than the power supply voltage but it could be perhaps 600mV which would result in much less dissipation.

A rough starting point is the added resistance will probably be similar to the reactance of a load capacitor.

Crystal manufacturers typically either avoid the issue or tell you to measure the RMS current Irms directly through the crystal using an expensive oscilloscope current probe, and adjust the resistor to be sure that $$\I_{RMS} ^2 \cdot ESR \le DL_{MAX}\$$.

Here ESR is the maximum ESR of the crystal from the datasheet and DLmax is the maximum drive power, again from the crystal datasheet.

If you set the drive power too high, the resulting oscillator may be unreliable or the crystal may be damaged to the point where it fails entirely. If you set it too low, it may fail to start reliably, especially at temperature extremes.

• Thanks! Are you saying that the information is missing because I didn't add it, or because you also couldn't find it in the datasheet? I'd be happy to add any missing information. – sethgi Aug 21 '19 at 2:29
• It’s not provided, hence measurement. – Spehro Pefhany Aug 21 '19 at 2:30
• great, thanks for the help! – sethgi Aug 21 '19 at 2:31

The chosing of this resistor is complicated ----- because the resistor serves two purposes, not one purpose.

1) the adjustment of crystal-drive current level

2) the adjustment of loop phase-shift

In (2), different oscillator amplifiers will have different delay times. A 1 nanosecond delay at 10 MHz is 1% or 3.6 degrees. Barkhausen in a high-Q situation will likely not be satisfied, and you get no oscillation. The resistor is the major delay tweak.