Crystal Parameter Measurement Musings

In order to probe a crystal’s response with decent resolution, I need a gadget to step a decent-quality sine wave by 0.01 Hz across the 10-to-100 kHz range and a logarithmic front end with a decent dynamic range. That’s prompted by looking at crystal responses through the SA’s 30 Hz resolution bandwidth:

Quartz Resonator 32.765 kHz - 34.6 pF
Quartz Resonator 32.765 kHz – 34.6 pF

Mashing a cheap AD9850/AD9851 DDS board against an Arduino Pro Mini, adding a knob, and topping with a small display might be useful. A Raspberry Pi could dump the response data directly into a file via WiFi, which may be more complication that seems warranted.

The DDS boards come with absurdly high-speed clock generators of dubious stability; a slower clock might be better. A local 10 MHz oscillator, calibrated against the 10 MHz output of the HP 3801 GPS stabilized receiver would be useful. If the local oscillator is stable enough, a calibration adjustment might suffice: dial for 10 MHz out, then zero-beat with the GPS reference, so that the indicated frequency would be dead on to a fraction of 1 Hz.

The HP 8591 spectrum analyzer has a better-quality RF front end than I can possibly build (or imagine!), but, at these low frequencies, a simple RF peak detector and log amp based on the ADL5303 or ADL5306 should get close enough. One can get AD8302 / AD8310 chips on boards from the usual low-budget suppliers; a fully connectorized AD8310 board may be a good starting point, as it’s not much more than the single-connector version.

With frequencies from 10 kHz to 100 kHz coming from a local oscillator, one might argue for a synchronous detector, formerly known as a lock-in amplifier. A Tayloe Detector might be a quick-and-dirty way to sweep a tracking-filter-and-detector over the frequency range. Because it’s a tracking generator, the filter bandwidth need not be very tight.

At some point, of course, you just digitize the incoming signal and apply DSP, but the whole point of this is to poke around in the analog domain. This must not turn into an elaborate software project, too.


Quartz Resonator Test Fixture: 32 kHz Quartz Tuning Fork

Soldering a 32.768 kHz quartz tuning fork resonator into the test fixture:

Quartz crystal resonance test fixture
Quartz crystal resonance test fixture

The HP 8591 tracking generator doesn’t go below 100 kHz, so I used the FG085 DDS function generator as a source. I trust the 8591’s calibration more than the FG805’s, but right now I’m more interested in the differences between successive frequencies and the DDS can step in 1 Hz increments.

The output appears on the 8591, with a big hump comes from the analyzer’s 30 Hz IF filter response sweeping across what’s essentially a single-frequency input. The hump is not the crystal’s response spectrum!

With the jumper installed to short the 33 pF cap, the output peaks at 32.764:

Removing the jumper to put the cap in the circuit, the response peaks at 32.765 kHz:

The marker delta shows the difference between the two peaks, ignoring their 1 Hz difference:

Quartz Resonator 32.764-5 no-34.6 pF delta
Quartz Resonator 32.764-5 no-34.6 pF delta

So I’d say the cap really does change the resonator series resonance by just about exactly 1 Hz.

With the jumper installed to remove the cap from the circuit, setting the reference marker at the 32.764 kHz peak, and measuring the relative response at 32.765 kHz :

Quartz Resonator 32.764-5 no cap delta
Quartz Resonator 32.764-5 no cap delta

So the response peak is much much narrower than 1 Hz: being off-peak by 1 Hz knocks 13-ish dB from the response.

What’s painfully obvious: my instrumentation is totally inadequate for crystal measurements at these frequencies!

Quartz Resonator Test Fixture: 3.58 MHz Crystal Test

Just to see if the resonator test fixture produced meaningful results, I plugged a 3.57954 MHz color burst crystal into the socket:

Quartz test fixture - 3.57954 MHz crystal
Quartz test fixture – 3.57954 MHz crystal

This is a staged recreation based on actual events; pay no attention to the Colpitts oscillators growing in the background.

Attaching goesinta and goesouta cables to the HP 8591 spectrum analyzer & tracking generator showed it worked just fine:

Quartz 3.57954 MHz - no cap
Quartz 3.57954 MHz – no cap

The reference level is -40 dBm, not the usual 0 dBm, due to the loss in those resistive pads. Unsurprisingly, the parallel resonance valley looks pretty ragged at -120 dBm = 1 nW = 7 µV.

Remove the jumper to put the capacitor in series:

Quartz 3.57954 MHz - 36.4pF
Quartz 3.57954 MHz – 36.4pF

The marker delta resolution surely isn’t 1 Hz, but 750 Hz should get us in the right ballpark.

Substituting a 72 Ω resistor, found by binary search rather than twiddling a pot:

Quartz 3.57954 MHz - 72ohm
Quartz 3.57954 MHz – 72ohm

Which gives us all the measurements:

  • Fs = 3.57824 MHz
  • Fc = Fs + 750 Hz = 3.57899 MHz
  • Rm = 72 Ω
  • C0 = 3.83 pF
  • Cpar = 3.70 pF

Turn the crank and the crystal motional parameters pop out:

  • Lm = 117 mH
  • Cm = 17 fF
  • Rm = 72 Ω
  • Q = 36 k

Looks like a pretty good crystal to me!

Quartz Resonator Test Fixture

A recent QEX article (Jan/Feb 2017 2016; sorry ’bout that), Crystal Measurement Parameters Simplified, Chuck Adams K7QO) suggested a simplified version of the K8IQY crystal parameter test fixture would work just as well for low-frequency quartz resonators:

Quartz crystal resonance test fixture - schematic
Quartz crystal resonance test fixture – schematic

The resistive pads eliminate the fussy toroids and their frequency dependence.

Tossing a handful of parts on a small proto board:

Quartz crystal resonance test fixture
Quartz crystal resonance test fixture

I found two absurdly long hunks of RG-174 coax with BNC connectors, so that’s how it connects to the outside world; sacrificing a short SMA jumper would reduce the clutter, but that’s in the nature of fine tuning. At the frequencies this fixture will see, coax properties don’t matter.

I can’t think of a better way to mount those AT26 cans than by soldering the wire leads directly to a pin header; pushing them under spring clips seems fraught with peril, not to mention excessive stray capacitance.

Measure the actual in-circuit capacitance for the 33 pF cap (shown as 39 pF in the schematic, it’s not critical), which worked out to 34.6 pF.  That’s the external series capacitance Cx.

The overall procedure, slightly modified from the original:

  • Measure C0 with resonator in capacitance fixture
  • Solder resonator to pins
  • Remove jumper to put capacitor Cx in series
  • Find series-resonant peak = Fc
  • Install jumper to short Cx
  • Find series-resonant peak = Fs < Fc
  • Remember the peak amplitude
  • Unsolder crystal
  • Install suitable trimpot = Rm in socket
  • Adjust trimpot to produce same output amplitude

Crunch the numbers to get the crystal’s motional parameters:

Rm = trimpot resistance
Lm = 1 / [4 π2 (Fs + Fc) (Fs - Fc) (C0 + Cx)]
Cm = 1 / [(2 π Fs)2 Lm]
Q = [2 π Fs Lm] / Rm

Then you’re done!

AADE LC Meter: AT26 Crystal Capacitance Fixture

Crystals (or resonators) in AT26 packages have vanishingly small capacitances, so I conjured a little fixture for my AADE L/C Meter IIB (*) that holds them securely under little fingers snipped from an EMI shield:

AT26 crystal capacitance fixture - Cpar detail
AT26 crystal capacitance fixture – Cpar detail

The finger on the right sits atop a snippet of rectangular brass tube so it need not bend so far.

The base is a snippet of double-sided PCB with copper tape soldered around the edges. I drilled the holes slightly oversize and soldered copper tape there, giving the top foil a direct connection to the terminals. The raggedy slot looks like it came from a hacksaw; no false advertising there.

The meter reports 6.5 pF of stray capacitance and nulls it to zero as usual. Without the fixture, it shows 2.5 pF.

With the crystal in that position, the meter measures Cpar, the parasitic capacitance from both terminals to the can, which should be (roughly) twice the capacitance from either terminal to the can.

Two more clips measure C0, the plate-to-plate capacitance:

AT26 crystal capacitance fixture - C0 detail
AT26 crystal capacitance fixture – C0 detail

The meter drive is about 200 mV at 700 kHz, far away from resonance. Assuming the resonator’s effective series resistance is 25 kΩ (tuning forks aren’t crystals!), it’s dissipating 1.5 µW (and less as the ESR goes up). That may be slightly hot for some resonators, but it’s surely survivable.

Some preliminary data on five 32.768 kHz crystals shows Cpar = 0.4 pF and C0 = 0.9 pF. I don’t trust those numbers very much, but they’re reproducible within 0.1-ish pF.

(*) Almost All Digital Electronics and its website vanished after the owner died; the meter continues to work fine. The cheap knockoffs flooding eBay and Amazon may get you close to the goal.

Turkey on the Rail

We’ve often seen turkeys perched on horizontal tree branches and split-rail fences, but this is new:

Turkey on patio rail
Turkey on patio rail

Apparently she wanted to use the bird feeder atop the post festooned with plastic squirrel deterrence. Not being Elastigirl, she couldn’t quite stretch from rail to feeder, eventually gave up trying, and flapped to the driveway.

We’ve been turkey-watching for nearly two decades, it’s been eight years since we saw a turkey on the patio, and a few days after I set up the yard camerashazam, this bird shows off for my friend in Raleigh while I’m in the Basement Laboratory. I’m insane with jealousy.

In point of fact, turkeys seem perfectly aware of people inside the house, so it’s not surprising they avoid the patio. When we move close to a window, the flock decides it has business elsewhere and, generally without haste or confusion, flows over the hill and away.

Obviously, I must set up motion detection and capture some images …

Snowplow vs. Plastic Fence

We spotted this on our regular walk around the block:

Plastic fence vs snow
Plastic fence vs snow

The horizontal rails have a latching ramp that’s good enough in most circumstances:

Plastic fence - rail latch detail
Plastic fence – rail latch detail

Perhaps those latches released as designed under an overload. The snowplow would have been traveling toward us on that side of the road and pushed the snow against the fence panels hard enough to dislodge the rail latches from their sockets.

I suppose they can zip the fence panels back in place, one by one, without rebuilding the whole affair.