Selecting Crystal for oscillator

[ADWSystems]

I'm heading down the path to building the Hacker's Bench CD4060 based 1Hz oscillator. Part of the design includes a 32.768 crystal and 33pF capacitors. How were those values derived? The 32.768kHz crystal is obvious, but what of the 33pF capacitors? In looking for the 32768kHz crystal I found to available through Jameco. One with 12.5pF impedence and one with 10.5pF. What is the impact of the different impedences? Which one would be correct for this application?

 

[MrAl]

Hi,

When the crystal is made it is made based on some required capacitance values to be used with it. This means it is cut so that it resonates at the package stamped frequency WITH that capacitance included in the circuit. If the caps are not there, the crystal oscillates at a slightly different frequency. The caps also affect the temperature characteristic of the frequency and oscillator start up reliability. It may not matter that much though depending on your circuit and the required accuracy and temperature curve.
If you need a really really accurate and stable clock, you should look into some ready made oscillators that are made for more accurate applications. Stand alone crystals plus or minus caps do not make good real time clock oscillators for example for real time clocks that have to operate over a period of say 6 months or more.
So the question for you is what are you going to use this for. That makes a big difference in just how critical these cap values are and even if you should look for a different oscillator type altogether.

 

[Diver300]

You can just select the capacitors to give the right frequency. You will need to measure the frequency over a long period if you want good accuracy, unless you have a good frequency counter. However, you may not need to worry about the adjustment at all if you only want +/- 100 ppm accuracy (10 seconds per day)

The capacitors are usually around twice the load capacitance of the crystal.

The capacitors have very little effect on the temperature characteristic, only the initial adjustment. 32.768 kHz crystals are tuning-fork crystals and their temperature characteristics is -0.035 ppm/°C², centred around 25 °C

So at 40 °C, that is 15 °C from the centre, so the frequency will have changed by about -8 ppm (-0.035 * 15 * 15)

 

[ADWSystems]

You can just select the capacitors to give the right frequency.

That's one of the big questions. How? I've not been able to find a formula for it in the CD4060 datasheets I've seen.

You will need to measure the frequency over a long period if you want good accuracy, unless you have a good frequency counter. However, you may not need to worry about the adjustment at all if you only want +/- 100 ppm accuracy (10 seconds per day)

The capacitors are usually around twice the load capacitance of the crystal.

The capacitors have very little effect on the temperature characteristic, only the initial adjustment. 32.768 kHz crystals are tuning-fork crystals and their temperature characteristics is -0.035 ppm/°C², centred around 25 °C

So at 40 °C, that is 15 °C from the centre, so the frequency will have changed by about -8 ppm (-0.035 * 15 * 15)

10 seconds per day. I think that would be good. I don't think I have equipment accurate enough to get better than that anyway. And I'm certainly not worried about temperature.

The Hacker's Bench circuit is using 33pF caps and the crystals are spec'ed at 10.5pF or 12.5pF; almost 3X. Should I use smaller caps? Which I guess that goes back to question #1.

 

[Diver300]

What I meant by "select the capacitors to give the right frequency" was to put it together with the 33 pF capacitors, then measure the frequency, then increase the capacitors if the frequency it too high, reduce them if it is too low.

But at 10 seconds per day, it just doesn't matter. Either crystal will be fine and 33 pF will probably be fine as well.

The load capacitance seen by the crystal is approximately the series combination of the two capacitors, so that would be 16.5 pF, so you are certainly not 3x what it should be. 12.5 pF load crystals a very common, so that it probably what was intended. The difference is either caused by the effect on the crystal loading caused by the IC, or the original designer wasn't too worried about the frequency accuracy either.

The only difference between a 10.5 pF crystal and a 12.5 pf crystal is the frequency. In the same circuit, they would be about 30 ppm different, or about 3 seconds per day.

 

[mvs sarma]

you can salvage from any analog clock module, both crystal and capacitors.
the crystal making process necessitates the needed loading for the crystal. Perhaps, higher frequency ones need lower values. perhaps a datasheet of 32.768KHz from the manufacturer can better speak.

 

[RCinFLA]

Piezo resonators have a series resonance and a parallel anti-resonance. Most computer crystal operated as parallel mode (anti-resonance). The parallel resonance is higher in frequency then the series resonance and its frequency is dependent on the Co of the crystal plus holder along with external circuit loading capacitance.

Manufactures specs for parallel mode are based on a specified external extra load capacitance. 32.768 kHz crystals can be spec'd with load capacitance between about 7 pF to 20 pF but most common is 7 to 10 pF. The lower the spec parallel capacitance, the lower the power drain of the associated oscillator circuit so watch crystals are usually spec'd for 7 pF since battery life is very important.

Take a typical spec: https://www.electro-tech-online.com/custompdfs/2012/02/ABS07.pdf

The specified load capacitance is 12.5 pF (there are also 7 pF and 9 pF load capacitance option listed). With this load capacitance the crystal is spec'd to be within 32.768 kHz +/- 20 ppm. This is manufacturing make tolerance. You may put a trimmer cap as part of the load capacitance to tweek the frequency to exactly 32.768 kHz if you have an accurate frequency counter.

The equivalent series resistance is listed as 70 K ohms maximum. It is typically better, something like 40k to 50k ohms. Also note the Q spec of 30,000 typical and the crystal Co of 1.5 pF. You have all the necessary info to derive the equivalent electrical model of the crystal, specifically Lm (motiional series inductance), and Cm (motional series capacitance).

You need to pay attention to the maximum operating drive power of 0.5 uW for a 32.768 KHz crystal. In parallel mode the crystal can be easily overdriven to destruction. (like the "is it Memorex or is it real", audio driven wine glass breakage demonstration). For a standard CMOS inverter driver you need a series resistor from the CMOS output to reduce the drive power on the crystal.

The crystal temp coefficient plot for a typical watch crystal (BT cut quartz) is an inverted parabola. The freq goes lower at hot and cold side of 25 degs C.

 

[mvs sarma]

while thew wish to get most accurate is fine, it calls for very costly measuring equipment and / or takes long time. all said, the settings done wont remain for long time, as unless the crystal and other elements are kept in a temperature controlled chamber. this is where the OCXO and DCXOs ( digitally compensated XOs) have come to picture.
simple terms, you might use a quality trimmer cap and adjust the value. the whole job might take few days .

 

[Diver300]

For a standard CMOS inverter driver you need a series resistor from the CMOS output to reduce the drive power on the crystal.

The crystal temp coefficient plot for a typical watch crystal (BT cut quartz) is an inverted parabola. The freq goes lower at hot and cold side of 25 degs C.

The resistor also helps to prevent the crystal oscillating in the wrong mode, which would be a much higher frequency. With 32.768 kHz crystals, the CMOS inverter is always far faster than is needed, so often needs to be slowed down.

Watch crystals are tuning fork crystals, not BT-cut. BT-cut, like the more common AT-cut, oscillates in thickness shear mode. https://en.wikipedia.org/wiki/Crystal_oscillator

The temperature variation plot of a BT-cut is an inverted parabola, similar to a tuning fork crystal, but the coefficient is different. AT-cut crystals follow a cubic curve.

Also, in AT-cut and BT-cut crystals the frequency is mainly dependent on the thickness of the crystal. There can be maybe 1% adjustment by the amount of plating on the crystal, and then maybe 0.05 % adjustment by the circuit the crystal is in. So a 5 MHz BT cut crystal will be 2.536 / 5 = 0.506 mm thick. (https://www.nelfc.com/pdf/pdfapp/9113.pdf) A 32.768 kHz BT cut crystal would be 77 mm thick.

 

[ADWSystems]

Thank you for all the responses. I've learned a lot, but I think I'm headed off in the wrong direction. I'm trying to find the formula to calculate, with all things being equal, what size capacitors and resistors are required for the CD4060 oscillator with the 10.5 or 12.5 pF 32.768khz crystal.

 

[Diver300]

But at 10 seconds per day, it just doesn't matter. Either crystal will be fine and 33 pF will probably be fine as well.

That is my most basic advice.

 

[JimB]

I'm trying to find the formula to calculate, with all things being equal, what size capacitors and resistors are required for the CD4060 oscillator with the 10.5 or 12.5 pF 32.768khz crystal.

I can't help but think that you are over analysing this.

The crystal requires a certain amount of capacitance in parallel to operate on the exact frequency.
If the capacitance is not exact, the frequency will not be exact.

When building a circuit where the crystal requires (say) 30pF load capacitance, if we put a 30pF capacitor it will be too much because there is always stray capacitance of several pF depending on the circuit layout.
In such a situation we may put a 20pf fixed capacitor and a 20 or 30pF trimmer capacitor so that we can adjust the exact frequency.


In your situation where the crystal requires a load of 12pF and the circuit configuration requires a capacitor from each end of the crystal to circuit ground, if we put 22pF in each capacitor position, the two capacitors are effectively in series giving a crystal load capacitance of 11pF, add a few pF for circuit strays and we are in the ball park.
If we want to be able to set the exact frequency, make one of the capacitors a 30pF trimmer, and adjust as required for exact frequency.

Have a look here:
https://www.euroquartz.co.uk/technical_notes.aspx
Lots of good information about crystals and their applications.

JimB

 

[ADWSystems]

OK. The lights are on now. That's what I'm looking for. Something to get me in the ball park. I wasn't understanding what the 10.5 or 12.5 pF had to do to relate to the crystal and the circuit.

 

[RCinFLA]

see attached

 

[ADWSystems]

I saw that in the datasheet but doesn't match the Hacker's Bench circuit. Which was one of the drivers for me to start this thread. To understand why the difference and, in my mind, they're pretty big differences.

 

[RCinFLA]

Same basic circuit. Hacker circuit with two 33 pF plus I.C. and PCB strays must have a crystal that is cut for a high C load of 18-20 pF for a 32.768 kHz watch crystal. It will likely run low in freq for most available crystals.

You are going to get 5 to 6 pF of capacitance at input pin of CD4060 plus your PCB stray capacitance. Good guess would be total of about 7.5 pF in parallel with 33 pF at input side of CD4060, for a total of 40.5 pF. On crystal side with 330k resistor, the resistor pretty much isolates out the CD4060 output capacitance so you only have about 0.5 pF due to resistor plus PCB stray capacitance, guess about 1.5 pF to add to its side 33 pF for 34.5 pF.

40.5 pF in series with 34.5 pF = 18.6 pF C load on crystal.