Posts Tagged SDR
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.
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:
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:
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:
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.
And this about the measurement technique, using a fixture on my AADE LC meter:
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]
At least I can point to this and amend as needed.
With an LM75 atop the 125 MHz oscillator and the whole thing wrapped in foam:
Let it cool overnight in the Basement Laboratory, fire it up, record the temperature every 30 seconds, and get the slightly chunky blue curve:
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 the 36.125 °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:
|Time s||Temp °C||Exp App||Error²|
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:
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:
A day of jockeying the AD9850 DDS oscillator shows an interesting relation between the frequency offset and the oscillator temperature:
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:
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.
Obviously, you need Pretty Good Precision in your arithmetic to get those answers.
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:
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 original data:
While that’s happening, you compare the DDS output to a reference frequency on an oscilloscope:
The top trace (and scope trigger) is the GPS-locked 10 MHz reference, the lower trace is the AD9850 DDS output (not through the MAX4165 buffer amp, because bandwidth). If the frequencies aren’t identical, the DDS trace will crawl left or right with respect to the reference: leftward if the DDS frequency is too high, rightward if it’s too low. If the DDS frequency is way off, then the waveform may scamper or run, with the distinct possibility of aliasing on digital scopes; you have been warned.
The joystick acts as a bidirectional switch, rather than an analog input, with the loop determining the step increment and timing. The ad-hoc axis orientation lets you (well, me) push the joystick against the waveform crawl, which gradually slows down and stops when the offset value makes the DDS output match the reference.
The OLED displays the current status:
The lurid red glow along the bottom is lens flare from the amber LED showing the relay is turned on. The slightly dimmer characters across the middle of the display show how the refresh interacts with the camera shutter at 1/30 s exposure.
N.B.: Normally, you know the DDS clock oscillator frequency with some accuracy. Dividing that value into 232 (for the AD9850) gives you the delta-phase count / frequency ratio that converts a desired DDS output frequency into the delta-phase value telling the DDS to make it happen.
In this case, I want the output frequency to be exactly 10.000000 MHz, so I’m adjusting the oscillator frequency (nominal 125 MHz + offset), calculating the corresponding count-to-Hz ratio, multiplying the ratio by 10.000000 MHz, stuffing the ensuing count into the DDS, and eyeballing what happens. When the oscillator frequency variable matches the actual oscillator frequency, then the actual output will 10.000000 MHz and the ratio will be correct.
Got it? Took me a while.
Although the intent is to tune for best frequency match and move on, you (well, I) can use this to accumulate a table of frequency offset vs. temperature pairs, from which a (presumably simple) formula can be conjured to render this step unnecessary.
The Arduino source code as a GitHub Gist: