oscillation frequency estimate using harmonic balance

Simulating that level of accuracy is difficult (I'd say it's really difficult with shooting), and harmonic balance is more likely to be better with a crystal oscillator. But I think it would be best to contact customer support so that we can take a look at your setup in more detail.

Kind Regards,

Andrew.

Dear fishbed,

I have experience designing quartz based designs and I would recommend that a different approach will provide the level of accuracy you desire and reduce the simulation accuracy requirements significantly. I will outline the methodology and hope it is both clear and useful to you.

For very high Q resonator based circuits such as a bulkwave quart crystal unit, the use of a "negative resistance" approach is one methodology that very efficiently and accurately will estimate the temperature dependence of the oscillating amplifier.

The methodology requires that one simulate the negative impedance of the oscillator sustaining amplifier by breaking the loop at the quartz resonator nodes. I've illustrated the concept in the attached figure. The input impedance of the parallel combination of the sustaining amplifier input node(s) with the C0 of the quartz crystal unit (including any board parasitics of the one or two quartz crystal unit node(s)) is simulated by applying a sinusoidal current source at or near the desired oscillation frequency in lieu of the series impedance arm of the quartz crystal unit model. A second, independent, current source is connected to the series arm of the quartz crystal unit model to simulate its impedance. The input impedance of the parallel combination of the oscillating amplifier input nodes with the C0 of the quartz crystal unit is determined by a transient simulation with the amplitude of the sinusoid set to a value that provides a negative real impedance that is equal and opposite in sign to the resistance of the series arm of the quartz crystal unit model. This is found by a series of iterative transient simulations of the sustaining amplifier where the amplitude of the current source is varied. This process can be automated. Note that since the high Q element is not in the sustaining amplifier simulation, the simulation time is minimal as the settling time of the sustaining amplifier will be orders of magnitude less than the time constant of the high Q element. The sustaining amplifier input impedance is found by taking the Fourier transform of the impedance at the applied sinusoidal input current frequency oscillation.

To determine the temperature coefficient of the sustaining amplifier, one needs to determine the imaginary part of the sustaining amplifier input impedance as the junction temperature is changed that produces a real part that is equal and opposite to the series resistance of the series arm of the quartz crystal unit model. In this fashion, if you know the temperature characteristics of the imaginary part of the quart crystal unit series arm, you can combine this with the temperature characteristics of the imaginary part of the sustaining amplifier to compute the resulting output frequency. This methodology is used to design temperature compensated oscillators.

I am sure this will take some thought to fully understand I will apologize if my explanation is either too brief or not clear. However, the process drastically reduces the simulation accuracy and simulation time for high Q resonator based circuits. I have responded to similar questions in the designer guide forums and these responses may be helpful.

Shawn

Thank you Shawn for such detailed reply.  This is what I am going to do following your suggestion.  

[1] run harminc balance sim and find the voltage swing across C0 and the frequency.

[2] Open the loop so that C0 is on amplifier side.

[3] Apply the same voltage swing and frequency to amplifier circuit plus C0.  Find out the complex input impedance.

[4] Apply the same voltage swing and frequency to RLC of XTAL.  Find out the complex input impedance.

[5] Real parts of the two impedances should sum up to zero.  Imaginary part may have small difference.

[6] Change the frequency slightly and run sim on RLC of XTAL until the imaginary parts sum up to zero.  This is the pulling result.

Am I correct?

Thank you!

fishbed

Thank you Andrew! I already gave up on shooting method. I run harmonic balance only. When I change C1 and C2 (caps on amp input and output) by 1pF , frequency changes 1.25ppm. So I guess if I change C1 and C2 by 8fF, I should see 0.01ppm pulling. I did see that with an 8fF change in C1 C2. I set # of harmonics to 1000 to force the time step down. I guess I can combine this and Shawn's method to find the pulling frequency accurately.

Dear fishbed,

> Am I correct?

Basically yes. 

I would recommend applying a sinusoidal current source whose current magnitude is set to provide the same magnitude but opposite sign as the series arm of the quartz crystal unit series arm - not a voltage source. The reason for this is that the current through the series arm of the quart crystal unit model will be essentially sinusoidal. The voltage across the series arm may not be free from harmonic distortion as some current in the sustaining amplifier and C0 may cause the voltage waveform to have distortion. However, the current through the series arm - which you are modeling with a current source will be essentially distortion free. I hope this makes sense to you.

Shawn