NanoVNA FaseShift Crystal calculator sheet

Calculations taken from : Crystal Motional Parameters A Comparison of Measurement Approaches By Jack R. Smith K8ZOA 11 June 2006

Requirements

NanoVNA setup

Stimulus : CENTER set near centerfrequency of crystal,
Stimulus : SPAN big enough to see +45 dgr and - 45 dgr phase shift.
Traces : CH1 LOGMAG and CH1 PHASE
Calibration : full (open, short, load, isoln, thru)"

Input

Ohm - Resistance of one side to the crystal (12.5 Ohm when using adapter)
pF - (not needed calculations)
Hz - Frequency at 0 dgr fase
Hz - Frequency at +45 dgr fase
Hz - Frequency at -45 dgr fase
dB - S21 LogMag at 0 dgr fase

Output

Hz - delta F = fH - fL
Q = fR / delta F
Ohm - Rm = 2 * RL ( 10 ^ ( -S21 / 20 ) - 1 )
Ohm - Reff = 2 * RL + Rm
pF - Cm = delta F / ( 2 * PI * fR ^ 2 * Reff)
mH - Lm = Reff / ( 2 * PI * delta F )

Usage

Step 1 :
Setup NanoVNA as mentioned above.

Step 2 :
Use marker to search for CH1 Phase close as possible to 0°
Register fR (frequency at 0°) in example screenshot below : 15996181 Hz
and S21 LogMag (dB at 0°) in example screenshot below : -2.09 dB

Step 4 :
Use marker to search for CH1 Phase close as possible to +45°
Register fL (frequency at +45°) in example screenshot below : 15995825 Hz

Step 5 :
Use marker to search for CH1 Phase close as possible to -45°
Register fH (frequency at -45°) in example screenshot below : 15995688 Hz