RE : calculating the output power of a Quartz oscillator

Why would you use PSS and then use the time-domain waveform? Wouldn't it make more sense to use the frequency-domain output - that's complex after all?

Also, for a crystal oscillator, you might also want to consider using harmonic balance (unless the output is very square).

Regards,

Andrew

I was using time-domain due to lack of experience and we were concerned about the output jitter. I will investigate further tomorrow.

Dear david j james,

david j james said:

I am designing a Crystal Oscillator ( which is a complex load) and trying to calculate Output power (to avoid over loading the crystal). I am using pss to simulate it and I get a tran waveform.

The power is complex so it is not easy to calculate. For example in a transient simulation phase information isn't readily available.

When I create calculations in calculator tool  get several different answers, and I am not sure which to trust

How should I calculate the output power?

What is the 'recommended' method?

I am not sure if you are aware of it, but computing the power dissipation of a quartz resonator contained in a quartz crystal unit is not straightforward as there are a number of subtleties. I apologize if I you are aware of these, but thought I should at least mention the topic.

You might consider the information in the article "Bulkwave Quartz Crystal Unit Power Dissipation in an Oscillator Environment" at URL:

www.electronicproducts.com/power-dissipation-of-bulkwave-quartz-xtal-units/

as you work on your simulation plan. The parasitic and actual load capacitances, the input capacitance of your sustaining amplifier (ad any package parasitics), and the Co/C1 ratio of your quartz crystal unit are needed to determine the power dissipation. There is an Microsoft Excel workbook that prompts for input parameters and plots the power dissipation of the quartz crystal unit as well as its real and imaginary input impedances if you are interested at URL:

www.dropbox.com/s/ao6vypu24nou8e3/xtal_z_pwr_072421v1p0.xlsx?dl=0

Shawn

In your excel it talks about 'Input Capacitance'. Is this from the amplifier only, or should it include the CL as defined in your paper?

More details : I am simulating the digital output of a Quartz oscillator, so it is very square. For pss When I calculate Pout using 'Shooting' method I get 75uW, but with pss/Harmonic Balance it is 86uW. When I use Harmonic Balance Tool, it gives 86uW.

Dear david j james,

david j james said:

In your excel it talks about 'Input Capacitance'. Is this from the amplifier only, or should it include the CL as defined in your paper?

The term "Input Capacitance" in the Microsoft Excel workbook includes both the sustaining amplifier's input capacitance and the combined value of the external capacitances (CL). Basically, it is the total effective capacitance seen by the terminals of the quartz crystal unit. It does not include the C0 of the quartz resonator within the quartz crystal unit nor any capacitances included within the quartz crystal unit as associated with its package.

Let me know if my explanation is not clear david j james!

Shawn

Dear david j james,

david j james said:

so it is very square. For pss When I calculate Pout using 'Shooting' method I get 75uW, but with pss/Harmonic Balance it is 86uW. When I use Harmonic Balance Tool, it gives 86uW.

I am guessing the difference is likely due to the difference between the steady-state (i..e., long term) frequency estimated by the two convergence algorithms. Did you compare the estimated steady-state frequencies of the shooting and Harmonic Balance simulations?

The estimated frequencies may be different as the final frequency is determined by the large signal impedance of your sustaining amplifier (including the external load capacitances). The frequency is determined by the imaginary part of this large signal impedance where its real part is equal in magnitude but opposite in sign to the real impedance of the quartz crystal unit. Since your sustaining amplifier is generating a waveform with a lot of harmonics, I would suspect the shooting algorithm will converge faster (fewer iterations) than a harmonic balance based algorithm. I would need to review your output log to provide any thoughts as to which frequency estimate might be most accurate. The accuracy with which it  estimates the large signal impedance will determine how accurate the estimated long term (steady-state) frequency.

Shawn

Question : why does increasing capacitance increase the Power Dissipation inside the crystal? It seems to me that larger caps will increase the load on the amplifier, but I do not see why it increases the power dissipated inside the crystal.

PSS simulation gives a Fundamental frequency of 10.0275 MHz, Harmonic balance gives Frequency= 1.0028e+07. That's a 0.0001% difference!

Dear david j james,

david j james said:

Question : why does increasing capacitance increase the Power Dissipation inside the crystal? 

A good question and one commonly asked an so I am glad mentioned it.! I am not sure of the quartz crystal unit parameters you are simulating with, but it is common for a 10 MHz  to roughly 100 MHz AT cut quartz crystal unit to exhibit that behavior. Intuitively, as the effective capacitance across the quart crystal unit becomes larger, its reactive impedance becomes smaller in magnitude (albeit a negative number). Since for steady-state oscillation, the sum of both the real and imaginary impedance of the sustaining amplifier and the real and imaginary impedance of the quartz crystal unit must be zero, this means its inductive impedance must also become smaller. This means the oscillation frequency will approach the series resonant frequency of the quartz crystal unit where its real impedance is a minimum. Therefore, the current flowing through the quartz crystal unit's real impedance is increased. With a real impedance of sometimes less than 10 ohms and any reasonable sustaining voltage across it of, say 0.50 Vpp, the power dissipation of the quartz crystal unit can be very significant. This is also why if an oscillator frequency is designed to operate close to its series resonant frequency its power dissipation is a factor that must be seriously considered.

In effect, at series resonance, the impedance of the quartz crystal unit is totally real and hence is a minimum. I've illustrated the operating point on a quart crystal unit for two cases -  an input capacitance of 5 pf  on page 1 and an input capacitance of 20 pf on page 2 of the attached Portable Document Formatted file. Note that as the input capacitance increases, the operating frequency moves closer to series resonance of the quart crystal unit and its power dissipation increases.

I hope my explanation makes some sense, but let me know if my words need any clarification david j james!

Shawn

xtal_z_pwr_cin_5pf_20pf_042723v1p0.pdf