RE : calculating the output power of a Quartz oscillator

1. I am looking at a range of crystals in the 10 -50MHz range. They all quote 10pF or more Shunt Caps values.

2. For Input Capacitance I made the following rough estimate : 

• External Shunt caps : 2 x 10pF
• Amplifier Input/output Capacitances : 2 x 2pF ( allowing for pads, PCB, ESD etc )
• Total : 24pF
• Does this sound right or silly?

3. Again you are right. I didn't read the excel carefully. The voltage on the pin is sinusoidal rail to rail.

The tool generates a spectrum with a single tone at 10MHz. I use the ymax function simply to get the magnitude of this tone. The rms calculator function doesn't work on this waveform.

The crystal Datasheets we have looked at, all quote 'Drive Level ( maximum)'. No mention of rms.

The oscillator is a Pierce type : like below but Ro is not used.

We strongly recommend using the hb interface.  It has all the "latest and greatest" features.   Two articles that I suggest you download and read from https://support.cadence.com are:

Getting the Most Out of Spectre® X-RF 21.1: Maximizing Performance 

How to simulate a high Q (LC or crystal) oscillator followed by strongly nonlinear circuitry (e.g. hard switching buffers) 

If you are a university student, please contact your professor (or Cadence contact at your university) and ask him to download these for you.

best regards,

Tawna

Dear david j james,

david j james said:

The tool generates a spectrum with a single tone at 10MHz. I use the ymax function simply to get the magnitude of this tone.

I would suggest you run a simple testcase where you apply a sinusoidal volatge across a resistor to determine if the peak value of the power represents an rms or peak power. If the spectruma relies on the Cadence dft(), it does not natively produce the rms value as its maximum. I have documented this and reported it.

david j james said:

The crystal Datasheets we have looked at, all quote 'Drive Level ( maximum)'. No mention of rms.

The maximum power dissipation is measured using the rms current. Please see, for example, the following two vendors suggestions for measuring power - both specify using the rms current. From a physics perspective, the peak power is not the important parameter but rather the rrns "heating" power. The latter impacts quartz resonator drive level effects and reliability (aging drift for example).

q-tech.com/wp-content/uploads/QTAN108-Crystal-Current-Measurement.pdf

www.renesas.com/us/en/document/apn/830-quartz-crystal-drive-level

david j james said:

The oscillator is a Pierce type : like below but Ro is not used.

I am sorry, but unless I am overlooking your Pierce schematic design, it does not show me how you voltage source is set up to measure power.

Shawn

When simulating high Q oscillators, set errpreset=conservative always.   hb accuracy depends more on harmonics.  pss accuracy depends more on errpreset.    These questions are answered in articles on https://support.cadence.com .  Do you have access?  

Dear david j james,

Thank you for the added and helpful information! A comment or two follow if I may  - and you have the patience with me!

david j james said:

1. I am looking at a range of crystals in the 10 -50MHz range. They all quote 10pF or more Shunt Caps values.

I understand. The shunt capacitance specified, 10 pf in your example, specifies the load capacitance where the oscillation frequency will be exactly the specified quartz crystal unit frequency at the specified temperature. Hence, if the accuracy of your output frequency is critical (less than say 50 - 100 ppm from the 10 - 50 MHz crystal unit's frequency), it is important that the total load capacitance the terminals of the crystal unit is the specified load capacitance - or 10 pf in the example you provided.

david j james said:

2. For Input Capacitance I made the following rough estimate : 

• External Shunt caps : 2 x 10pF
• Amplifier Input/output Capacitances : 2 x 2pF ( allowing for pads, PCB, ESD etc )
• Total : 24pF
• Does this sound right or silly?

The effective load capacitance in the Pierce topology is composed of the total capacitance consisting of the parallel combination of the values of C1 and C2 you show in a later Forum post plus your board stray capacitance(s) plus your amplifier input capacitance. I've put together a view of the relevant "equivalent" board and amplifier capacitances and the equivalent load capacitance seen by the terminals of the quartz crystal unit as Figure 1. I hope this helps!

Shawn

Figure 1

Sorry, I just looked at Figure 1 and realized I made an error! The corrected version is shown below.

Shawn

Firstly, sorry for the slow response cased by meetings at work. Thanks for your valuable support.

1. The testcase with a sinusoidal voltage (1V peak) across a 100 Ohm resistor gives hb = 5mW. Pout = V^2/R = 1^2/100 = 10mW. I have to think about where the x2 comes from, but I agree with you hb is giving MAXIMUM, not rms values.

2. the Quartz suppliers we looked at ( eg NDK), quote maximum drive. This has been confirmed with their rep.

3. the schematic I am using is this : bondwires, external caps with esr. the port and cds block are for stability sims. the 0V vdc used to measure power is called 'V_xosc'. The driver ( not shown ) is a simple Inverter.

OK, so using that calculation in my application : 

• External Shunt caps : 2 x 10pF
• Amplifier Input Capacitances : 2pF ( allowing for pads, ESD etc )
• PCB Capacitance : 3pF ( worst case)
• Total : 11pF
• so gives Operating Power Dissipation = 6.3uW.

Dear david j james,

david j james said:

1. The testcase with a sinusoidal voltage (1V peak) across a 100 Ohm resistor gives hb = 5mW. Pout = V^2/R = 1^2/100 = 10mW. I have to think about where the x2 comes from, but I agree with you hb is giving MAXIMUM, not rms values.

Please check your calculation, as I think the power of a 1 V amplitude sinusoid (2 Vpp) across a 100 ohm resistor is:

david j james said:

2. the Quartz suppliers we looked at ( eg NDK), quote maximum drive. This has been confirmed with their rep.

I'm not going to disagree, but the issue at hand is that the maximum drive refers to the rms power and not the peak power. From NDK's site:

reference:

Thank you for the schematic! I now understand that you are measuring the current through only the quartz crystal unit.

Shawn