Hello builders -
I was reading some of W7ZOI¡¯s old website entries and found one on
determining a crystal¡¯s motional parameters by measuring the rate of change
of X (reactance) at the resonant frequency. I¡¯ve no doubt seen this before
but how to make that measurement wasn¡¯t readily apparent before the
nanoVNA. I¡¯d already done a crystal characterization using the 3 dB
bandwidth technique and had good results.
The formula used with this method is
Lm = delta_X/(delta_f * 4 * PI)
I pulled out an 8 MHz EVS HC-49/W crystal which I¡¯d previously measured
with my PHSNA system. I had done a 12 segment calibration close to 8 MHz
for my previous measurement so I applied it using nanaVNA Saver. I
connected the crystal to CH0 using a female SMA connector soldered to a
piece of PC board to which I soldered the crystal. No impedance
transformation jig required here.
I did a sweep of a few hundred Hz centered on the series resonant
frequency. The plot of X in the ¡°S11 R + jX¡± plot was pretty straight.
First I picked values 100 Hz apart yielding X values of ¨Cj1.69 and +j26 for
a delta_X of 27.69 ohms. The formula gave an L value of 22 mH. This
compared pretty well with my previous PSHNA measurement of 21.54 mH. That¡¯s
within 2%
If you know Lm, you also know Cm:
Cm = 1(4*f^2*PI^2*L) where f is the resonant frequency.
The nanoVNA will give the series resistance at resonance directly. In my
case it was 8.84 ohms versus 8.7 ohms with the PHSNA.
I thought I¡¯d try another look with a smaller delta_f. Taking readings only
10 Hz apart I came up with Lm = 21.7 mH. That¡¯s closer to my PHSNA value
but I won¡¯t say with certainty that the smaller delta_f made it better. I
do think a small delta_f close to the resonant frequency is probably best.
Next I wondered if the large number of calibration points close to the
crystal frequency is necessary. So I tried a 4.9152 MHz crystal I¡¯d
previously measured and this time used a 1.5 MHz to 10.5 MHz calibration
data set done in four segments.
I calculated an Lm value of 63.42 mH compared with 63.13 mH done previously
with PHSNA. Pretty close at 0.46%. My Rs value wasn¡¯t as close this time:
12.26 ohms versus 10.7 ohms with PHSNA. I¡¯m not sure of the reason for the
variation. The Rs measurement method in PHSNA is a little complicated.
So there¡¯s another method of measuring crystal parameters with the nanoVNA.
73,
Nick, WA5BDU
Nick Kennedy