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I measured an 8.000 MHz crystal with the nanoVNA using my PHSNA notes and
Ignacio's suggestion of using a 2 kHz span and 12 segments. I did a
calibration on that basis with nanoVNA-saver and saved it.

I feel like I got a good measurement as it agrees within about 2% for Cm
and Lm of an earlier measurement of the same crystal with different
instruments a few years ago. The Q was within 1.5% and the Rs value was
dead-on.

I created an automatic crystal measurement function in PHSNA as Ignacio
noted. The key for me was in how to measure Rs, which is often done by
substitution or by using a pot. A formula from Wes Hayward showed me how to
calculate it from the crystal's attenuation at resonance and if you can do
that accurately, you can get a good reading of Rs. See below.

IIRC, I could do a crystal in 10 to 20 seconds or so if you don't count the
time I spent fumble-fingering the next crystal into the socket.

The process worked like this:

The user tells the software the resistance seen by the crystal in his
fixture, which is 12.5 ohms in my case. I've used both 4:1 transformers and
resistive pads but am settled on the latter now. They do give me ~ 23 dB of
loss, but there's still plenty of dynamic range.

The user must also do a one-time measurement of the fixture loss with a
short installed in place of the crystal. The difference between this value
and the loss at resonance with the crystal installed in the fixture is the
crystal's attenuation number needed to compute Rs.

The process starts with the user providing a frequency below the resonant
frequency with enough margin to be below the -3 dB point.

The software then begins scanning upward in 1 Hz steps and looking for the
resonant peak at minimum attenuation. The attenuation at that point is
recorded. Then the program scans down in 1 Hz steps until attenuation is 3
dB below the peak. It returns to resonance and scans upward in 1 Hz steps
until the upper -3 dB point is found. From these readings the 3 dB BW can
be calculated.

Next, the values for Cm, Lm, Rs and Q are calculated:

Rs = 2*Rg(10^(a/20) - 1)

Where Rg is the generator resistance or 12.5 ohms in most cases and a is
the attenuation of the crystal at resonance in dB, entered as a positive
number. Rs is the series loss resistance of the crystal.


Cm = BW / (2*PI*Fc^2*(2*Rg + Rs))

Lm = 1 / (39.48 * Fc^2*Cm) where (39.48 is 4*PI^2)

Q = (2*PI*Fc*Lm)/Rs

Where Fc is the series resonant frequency of the crystal.

In the above, C is in farads, L in Henry, and Fc is in Hertz.

In my measurement today, I got the BW and attenuation from nanoVNA and
cranked out the other stuff manually. But you can see how it could be
automated.

As for the parallel C or Co. No doubt it could be done with the nanoVNA or
with a low frequency instrument like the AADE or eBay versions of it.
Also, You can estimate Co as Co = 220 * Cm

73,

Nick, WA5BDU