Ed Nisley's Blog: Shop notes, electronics, firmware, machinery, 3D printing, laser cuttery, and curiosities. Contents: 100% human thinking, 0% AI slop.
The bottom trace comes from the 100× = 40 dB MAX4255 amplifier boosting the crystal output to a useful level. The fuzz on the waveform is actually the desired (off resonance) 60 kHz signal at maybe 30 mVpp, so the input is 300 µVpp.
The worst part of the OLED noise looks like 100 mVpp, for about 1 mVpp at the crystal output, call it +10 dB over the desired signal. Some high-pass filtering would help, but it’s easier to just shut the display off while measuring the crystal.
The top trace is the log amp output at (allegedly) 24 mV/dBV. The input bandwidth obviously extends way too low, as it’s neatly demodulating the input signal: the peaks correspond to both the positive and negative signal levels, so reducing the 1 µF input coupling caps will be in order.
In between those 100 Hz groups, the input signal shines through to the log amp output at the V1 cursor. The peak noise rises 290 mV above that, so the log amp thinks it’s 12 dB higher. Pretty close to my guesstimated 10 dB, methinks.
So, turning off the OLED should help a lot, which is feasible in this situation. If you must run the display while caring deeply about signal quality, you must devote considerably more attention to circuit construction quality.
Came up from the Basement Laboratory to find my Dell Optiplex 980 PC had failed, with the power button and diagnostic 1 + 3 LEDs blinking amber. They built it back in June 2010, so section 3 of the Dell reference applies, the power supply status LED on the back panel was off, and, going straight to the heart of matter, I popped the top, disconnected the internal power supply cables, and poked the power supply test button:
Optiplex 980 Power Supply – rear panel test button
… and it’s dead.
Inside, the system board sports a Mini-ATX power supply connector:
Optiplex 980 – Mini-ATX power connector
I originally hoped to swap a supply from an Optiplex 755 (also in a Small Form Factor case) residing on the recycle heap, but it has an ordinary ATX connector:
Optiplex 755 – ATX power connector
So I moved the 980’s SSD and dual-Displayport video card into the 755, fired that devil up, and … it worked!
With my desktop back in action, albeit somewhat slower, I popped the dead supply’s case by violating the Warranty Void If This Label Removed sticker to unscrew the last screw:
The cluster of caps on the upper right have bulged pressure-relief lids, like this:
Optiplex 980 – Bulging capacitor 1
And this:
Optiplex 980 – Bulging capacitor 2
And this:
Optiplex 980 – Bulging capacitor 3
None had ruptured, but they’re obviously feeling a bit nauseous.
Given the 980’s mid-2010 manufacturing date, this probably isn’t capacitor plague, just simple overheating from operating in a dead-air zone amid all those heatsinks and wires. Some of the Usual Unnamed Sources suggest overheating the capacitors is how manufacturers ensure their hardware doesn’t last forever, without being obvious about planned obsolescence; I’m loathe to ascribe to malice what can be explained by design desperation.
A Genuine Dell replacement supply from eBay ($25 delivered) came from yet another “small form factor” Dell chassis, so it isn’t quite the same size, lacks a supply test button / LED status light, and doesn’t quite fit:
Optiplex 980 – replacement supply misfit
Nothing a sheet metal nibbling tool can’t fix, though, given I haven’t developed a deep emotional attachment to the chassis. I gnawed off the left side of the frame and squared up the rim around the lower screw, after which the opening fit the supply pretty well, although the latching tab bent up from the bottom of the chassis didn’t quite engage the far end of the supply. No big deal: it’s not in a high-vibration environment.
The new-to-me supply also carries an ATX connector, but the eBay seller included a Mini-ATX adapter. Jamming the adapter + wires into the space available required concerted muttering, assisted by tucking the SSD under the DVD-RW drive. No pictures, as it’s a classic seven pounds in a five pound box situation.
There’s not much room on an AT26 / TF26 can for a readable label, unless one owns a metal-marking laser, but a simple bar code should let me identify each one:
Quartz Resonators – binary marking
The empty “0” slot down at the bottom will hold the crash-test dummy resonator I’ve been using to get the tester working.
The red-and-blue stripes from plain old fine-point Sharpie pens will rub off under duress, which I hope to avoid. After finishing up, I’m still not sure blue makes a better zero than red; you can make a convincing argument either way:
Binary marked AT26 Quartz Resonators
The bag allegedly contained 25 resonators, although I’m willing to agree the last one escaped into the clutter on or under the Electronics Workbench.
A Circuit Cellar reader asked for a better explanation of the parasitic capacitors inside a quartz crystal can than I provided in my April 2017 Circuit Cellar column. Here’s the schematic, with values for a 32 kHz tuning fork resonator and the original caption:
Figure 1 – The mechanical properties of quartz resonators determine the values of the “motional” electrical components in the bottom branch of its circuit model. These values correspond to a 32.768 kHz quartz tuning fork resonator: the 10.4 kH inductor is not a misprint!
I wrote this about the caps:
The value of C0 in the model’s middle branch corresponds to the capacitance between the electrodes plated onto the quartz. The 3.57954 MHz crystal in the title photo, with two silver electrodes deposited on a flat insulating disk, closely resembles an ordinary capacitor. You can measure a crystal’s C0 using a capacitance meter.
However, each of those electrodes also has a capacitance to the resonator’s metal case. The top branch of the model shows two capacitors in series, with Cpar representing half the total parasitic capacitance measured between both leads and the case. Grounding the case, represented by the conductor between the capacitors, by soldering it to the ground plane of an RF circuit eliminates any signal transfer through those capacitors. They will appear as shunt capacitors between the pins and ground; in critical applications, you must add their capacitance to the external load capacitors.
With the resonator case captured under the clip on the far right and both its leads held by the clip to the upper left, the meter measures Cpar, the lead-to-case parasitic capacitance. The meter will display twice the value of each parasitic capacitor, at least to a good approximation, because they are in parallel. The five resonators averaged 0.45 pF, with each lead having about 0.25 pF of capacitance to the case. Obviously, measuring half a picofarad requires careful zeroing and a stable fixture: a not-quite-tight banana jack nut caused baffling errors during my first few measurements.
With the resonator repositioned as shown in Photo 2, with one lead under each clip, the meter measures C0, the lead-to-lead capacitance. After careful zeroing, the resonators averaged 0.85 pF.
Although the parasitic lead-to-case capacitors are in parallel with C0, their equivalent capacitance is only Cpar/4 = 0.1 pF. That’s close enough to the measurement error for C0, so I ignored it by rounding C0 upward.
He quite correctly pointed out:
With both leads connected together on one side, then that essentially constitutes a single electrical element inside the case. And with the case being a single element, this configuration in the test fixture seems like a single capacitor with one lead being the case and the other lead being the pins, with a vacuum dielectric.
I would think the meter would display the total capacitance rather than twice the value … It makes sense to me to later say Cpar/2 when the leads are not connected together.
Here’s my second pass at the problem:
… the two-capacitor model comes from the common-case condition, where each lead displays a (nominally equal) parasitic capacitance to the case, because the crystal mounting is reasonably symmetric inside the can. It’s easiest to measure the total capacitance with the leads shorted together, because it’s in the low pF range, then divide by two to get the value of each lead-to-case cap.
[…]
For “real” RF circuits with larger (HC-49 -ish) crystals in parallel-resonance mode, you ground the case and subtract the parasitic capacitance at each lead from the external load capacitors. That’s the usual situation for microprocessor clock oscillators: the crystal sits across the clock amplifier pins, with two more-or-less equal caps from the pins to ground. You should subtract the internal parasitic caps from the clock’s specified load caps, but in practice the values are so small and the cap tolerance so large that it mostly doesn’t matter.
[…]
Un-grounding the case puts those two parasitic caps in series, just as with two discrete caps, so the lead-to-lead capacitance is (or should be!) half of each: 1/4 of the both-leads-to-case value.
Re-reading yet again says I glossed over the effect of having C0 in parallel with the Cpar/2 caps, but methinks dragging those complications into the model benefits only the theoreticians among us (or those working very close to the edge of the possible).
To make it worse, I also botched the QEX reference, which should be Jan/Feb 2016, not 2017. Verily, having a column go read-only makes the errors jump right off the page. [sigh]
With an LM75 atop the 125 MHz oscillator and the whole thing wrapped in foam:
LM75A Temperature Sensor – installed
Let it cool overnight in the Basement Laboratory, fire it up, record the temperature every 30 seconds, and get the slightly chunky blue curve:
125 MHz Oscillator – Heating Time Constant
Because we know this is one of those exponential-approach problems, the equation looks like:
Temp(t) = Tfinal + (Tinit - Tfinal) × e-t/τ
We can find the time constant by either going through the hassle of an RMS curve fit or just winging it by assuming:
The initial temperature, which is 22.5 °C = close to 22.7 °C ambient
The final temperature (call it 42 °C)
Any good data point will suffice
The point at 480 s is a nice, round 40 °C, so plug ’em in:
40.0 = 42.0 + (22.7 - 42.0) × e-480/τ
Turning the crank produces τ = 212 s, which looks about right.
Trying it again with the36.125 °C point at 240 s pops out 200.0 °C.
Time for a third opinion!
Because we live in the future, the ever-so-smooth red curve comes from unleashing LibreOffice Calc’s Goal Seek to find a time constant that minimizes the RMS Error. After a moment, it suggests 199.4 s, which I’ll accept as definitive.
The spreadsheet looks like this:
T_init
22.5
T_final
42.0
Tau
199.4
Time s
Temp °C
Exp App
Error²
0
22.250
22.500
0.063
30
25.500
25.224
0.076
60
28.000
27.567
0.187
90
30.125
29.583
0.294
120
31.750
31.317
0.187
150
33.250
32.810
0.194
180
34.375
34.093
0.079
210
35.375
35.198
0.031
240
36.125
36.148
0.001
270
36.813
36.965
0.023
300
37.500
37.668
0.028
330
38.125
38.273
0.022
360
38.500
38.794
0.086
390
39.000
39.242
0.058
420
39.500
39.627
0.016
450
39.750
39.959
0.043
480
40.000
40.244
0.059
510
40.250
40.489
0.057
540
40.500
40.700
0.040
570
40.750
40.882
0.017
600
41.000
41.038
0.001
RMS Error
0.273
The Exp App column is the exponential equation, assuming the three variables at the top, the Error² column is the squared error between the measurement and the equation, and the RMS Error cell contains the square root of the average of those squared errors.
The Goal Seeker couldn’t push RMS Error to zero and gave up with Tau = 199.4. That’s sensitive to the initial and final temperatures, but close enough to my back of the envelope to remind me not to screw around with extensive calculations when “two minutes” will suffice.
Basically, after five time constants = 1000 s = 15 minutes, the oscillator is stable enough to not worry about.
I let the DDS cool down overnight, turned it on, and recorded the frequency offset as a function of temperature as it heated up again:
125 MHz Osc Freq Offset vs Temp – Quadratic – 29 – 43 C
The reduced spacing between the points as the temperature increases shows how fast the oscillator heats up. I zero-beat the 10 MHz output, scribbled the temperature, noted the offset, and iterated as fast as I could. The clump of data over on the right end comes from the previous session with essentially stable temperatures.
I only had to throw out two data points to get such a beautiful fit; the gaps should be obvious.
The fit seems fine from room (well, basement) ambient up to hotter than you’d really like to treat the DDS, so using the quadratic equation should allow on-the-fly temperature compensation. Assuming, of course, the equation matches some version of reality close to the one prevailing in the Basement Laboratory, which remains to be seen.
In truth, it probably doesn’t, because the temperature was changing so rapidly the observations all run a bit behind reality. You’d want a temperature-controlled environment around the PCB to let the oscillator stabilize after each increment, then take the measurements. I am so not going to go there.
The original data:
125 MHz Osc Freq Offset vs Temp – 29 – 43 C – data
DDS Oscillator Frequency Offset vs. Temperature – complete
Now, as it turns out, the one lonely little dot off the line happened just after I lit the board up after a tweak, so the oscillator temperature hadn’t stabilized. Tossing it out produces a much nicer fit:
DDS Oscillator Frequency Offset vs. Temperature
Looks like I made it up, doesn’t it?
The first-order coefficient shows the frequency varies by -36 Hz/°C. The actual oscillator frequency decreases with increasing temperature, which means the compensating offset must become more negative to make the oscillator frequency variable match reality. In previous iterations, I’ve gotten this wrong.
For example, at 42.5 °C the oscillator runs at:
125.000000 MHz - 412 Hz = 124.999588 MHz
Dividing that into 232 = 34.35985169 count/Hz, which is the coefficient converting a desired frequency into the DDS delta phase register value. Then, to get 10.000000 MHz at the DDS output, you multiply: 10×106 × 34.35985169 = 343.598517×106
Stuff that into the DDS and away it goes.
Warmed half a degree to 43.0 °C, the oscillator runs at:
125.000000 MHz - 430 Hz = 124.999570 MHz
That’s 18 Hz lower, so the coefficient becomes 34.35985667, and the corresponding delta phase for a 10 MHz output is 343.598567×106.
After insulating the DDS module to reduce the effect of passing breezes, I thought the oscillator temperature would track the ambient temperature fairly closely, because of the more-or-less constant power dissipation inside the foam blanket. Which turned out to be the case:
DDS Oscillator Temperature vs. Ambient
The little dingle-dangle shows startup conditions, where the oscillator warms up at a constant room temperature. The outlier dot sits 0.125 °C to the right of the lowest pair of points, being really conspicuous, which was another hint it didn’t belong with the rest of the contestants.
So, given the ambient temperature, the oscillator temperature will stabilize at 0.97 × ambient + 20.24, which is close enough to a nice, even 20 °C hotter.
The insulation blanket reduces short-term variations due to breezes, which, given the -36 Hz/°C = 0.29 ppm temperature coefficient, makes good sense; you can watch the DDS output frequency blow in the breeze. It does, however, increase the oscillator temperature enough to drop the frequency by 720 Hz, so you probably shouldn’t use the DDS oscillator without compensating for at least its zero-th order offset at whatever temperature you expect.
Of course, that’s over a teeny-tiny temperature range, where nearly anything would be linear.
The Smell of Molten Projects in the Morning 