Crystal oscillators are one of the most widely used circuits, but are extremely difficult to analyze due to the high Q of the quartz resonator. This produces a long startup delay before the oscillator reaches steady-state and the waveforms can be observed. In some cases, the startup delay is too long to allow practical analysis, and the circuit must be simulated with a low-Q version of the crystal. This produces inevitable discrepancies between the simulated results and the actual circuit, which can be difficult to reconcile.
This paper describes a simple method of starting a high-Q crystal oscillator at full amplitude, where it quickly settles into steady-state operation.
It's easier to analyze a crystal oscillator in the frequency domain, open-loop. You can resolve the oscillation frequency to arbitrary precision and optimize the phase slope at resonance (0 degrees around the loop point) for low phase noise. You really can't tell much about crystal oscillator behavior from a time-domain analysis, except gross stuff like amplitudes. There's practical no way to measure the oscillation frequency to ppm precision from a time-domain analysis.
Just poking an initial condition won't "quickly settle to steady-state" ... not in 150 cycles, with a Q of 64K. It only looks steady-state because the Q is so high! Check it again every, say,
30,000 cycles to spot any trends.
Goosing an oscillator to get it going is hardly a new idea.
I really don't think frequency domain loop analysis will give the true oscillation frequency. The loop is not linear - the transistor is cut off most of the time. As the brief description shows, the voltages and currents injected into the crystal are not sinusoidal, but are highly distorted. So it's not possible to treat them as pure sine waves, which is needed to optimize the phase slope.
It makes little sense to calculate frequency to arbitrary precision when the crystal and circuit parameters are not known to that precision. That's what the trim capacitor is for. All you need to know is if it has the range needed to meet worst-case circuit and crystal parameters. You can get this information much better in the time domain.
You can get pretty accurate frequency information of the actual oscillation frequency in the time domain by counting over many cycles. But the oscillator has to be in steady-state.
Time domain gives information not available in frequency domain, such as collector waveform and phase relation to the tank current, and various waveforms, currents and time relationships everywhere in the circuit.
Frequency domain analysis doesn't tell you if the oscillator is clipping. This hurts phase noise.
Hajimiri and Lee have described the importance of timing the peak of the collector current pulse to coincide with the peak amplitude of the oscillator waveform. You cannot get this information in the frequency domain.
As the brief analysis shows, there are different phase shifts and distortions throughout the circuit, so you need time domain to tell where they are and how to deal with them.
Many crystals are destroyed by running at too high a power level. You cannot get this information in the frequency domain. You need the time domain to tell how much power is dissipated in the crystal, and how well the oscillator handles worst-case tolerances in crystal and circuit parameters.
Nope. MC8 allows you to go from one peak to the next with 6 digits or more of amplitude resolution. You can easily see from one cycle to the next if the amplitude is increasing or decreasing. If the amplitude is not changing, the oscillator is in steady-state operation.
The advantage of this method is it doesn't introduce serious transients into the oscillator that take a long time to die out. After a brief burble at the beginning, it quickly settles into steady-state operation.
Normally, "goosing" an oscillator means forcing a pulse or step somewhere in the tank. The amount of energy is difficult to control, and it usually does not bring the oscillator to full amplitude. You then have to wait many cycles for the oscillator to reach steady-state, which takes a long time in SPICE.
You can fiddle with the pulse amplitude to try to make it reach steady state sooner, but this usually introduces severe transients that take a long time to die out.
If you make any changes to the circuit parameters, the energy introduced into the tank changes, so you may have to fiddle with the step amplitude some more. This wastes a lot of valuable time.
The method described sets the initial condition by placing a predetermined current through the tank inductor. This is the normal peak current when the oscillator is running, so there are no large circuit transients such as those introduced by injecting a step or pulse into the tank.
The initial current causes the oscillation to start in a known phase with known amplitude. This sets the power level dissipated in the crystal to a known level, which is critical for some crystals. The brief transient at the start of Transient Analysis only takes a couple of cycles to die out and the circuit quickly settles into steady-state operation.
As described in the paper, the feedback capacitors and emitter resistor can be easily trimmed to maintain the desired power level.
Since you no longer have to wait hundreds or thousands of cycles to reach steady-state, you can quickly see the effect of changes in crystal and feedback parameters, and you can ensure the oscillator will operate satisfactorily with worst-case parameters. This is difficult or impossible to do in the frequency domain.
It's as old as TV sets, at least. A strategic blow onto the left bottom and the soccer game was back on. Of course, when Archie Bunker tried that a plume of smoke came out.
Mike, I assume you are the paper's author? I'd like to link the paper and usenet discussion on my website, and want to make sure I give proper credit. I enjoyed the discussion, and will pass it along to coworkers at my day job - they have to deal with similar issues all the time.
Thank you for the compliment. You have a very excellent site. Congratulations of a fine job!
Yes, I am the author of the method and the paper, and would be honored if you wanted to link to it. I update it fairly often, and am working with another colleague on a simple method of predicting the crystal dissipation that might go well with the analysis. I'll post the results here if we are successful. Regards,
Mike, thanks for posting the link to my paper, "SPICE Analysis of Crystal Oscillators", on your web site. That is an honor.
I have a favor to ask. My isp uses an "@" sign in the url, and some sites treat this as part of an email address and strip the address to foil spambots. For example, Yahoo does this to it:
formatting link
But the link no longer works.
I have a solution. Can you change the link on your site to
formatting link
to avoid this problem?
Also, I have made major revisions and updates to the article, including measurements of peak amplitude and frequency to the ppb level. Your colleagues may enjoy reading it if they have to deal with these issues. Regards,
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.