NanoVNA FaseShift Crystal calculator sheet

This is a copy taken from the website of ph2lb! For the original webpage, See: https://www.ph2lb.nl/blog/index.php?page=xtal-adapter-for-nanovna

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

Requirements

NanoVNA (non V2 version) or any other VNA

Crystal Testfixture (12.5 Ohm) like for example my Crystal adapter for NanoVNA (or any other VNA)

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

RL Ohm - Resistance of one side to the crystal (12.5 Ohm when using adapter)

C0 pF - (not needed calculations)

fR Hz - Frequency at 0 dgr fase

fL Hz - Frequency at +45 dgr fase

fH Hz - Frequency at -45 dgr fase

S21 LogMag dB - S21 LogMag at 0 dgr fase

Output

delta F Hz - delta F = fH - fL

Q Q = fR / delta F

Rm Ohm - Rm = 2 * RL ( 10 ^ ( -S21 / 20 ) - 1 )

Reff Ohm - Reff = 2 * RL + Rm

Cm pF - Cm = delta F / ( 2 * PI * fR ^ 2 * Reff)

Lm 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