lulu1113, 晶体的等效电路计算很简单,主要是他用错公式了.
下面是n2pk的mail,这个公式是正确的,没问题,但是简化了的.
你可以发给作者.
re: [n2pk-vna] using vna to measure crystal parameters
hi pete,
> does anyone have experience of measuring crystal motional parameters?
> i would be interested to hear from anyone who can recommend a
> procedure for doing this using the n2pk vna. i can see how to measure
> c0 and rs, but i am not sure of the best approach for measuring lm and
> cm.
i've measured many crystals with my vna. have built several filters based
on those measurements that performed as expected.
without going into a lot of detail here, there are several published works
by wes hayward, bill carver, doug demaw, ja hardcastle, and others that offer
crystal model values based on various measurements, as well as filter design
techniques.
generally i do my calcs in a 123 spreadsheet, based on reflection measurements
as follows:
1. measure co at a frequency sufficiently far from the crystal resonant
frequencies. if you vary the frequency and co stays the same, then you're
far enough away.
2. calibrate the vna near the expected series resonance. make sure you have
the vna frequency calibrated using a counter, wwv, wwvb, or whatever.
3. measure fs where z=r+jx=r+j0. this also determines rs=r.
4. measure the frequency, f1, where angle(z)=-45 deg. if f1 isn't less than
fs, then something's wrong.
6. most of the computations in the references determine lm and cm based on
transmission measurements.
instead, my reflection measurement uses:
cm = (fs-f1)/(rs*pi*fs^2)
and
lm = 1/(((2*pi*fs)^2)*cm)
and
q = fs/(2*(fs-f1))
most crystals are very sensitive to heating from your fingers, so handle them
only with tweezers or needlenose pliers.
i have also made pi holder capacitance model parameters using a transmission
at the frequency where co was determined to separate out lead to lead
capacitance from the two lead to case capacitances.
vna frequency calibration accuracy can be critical, especially for narrow
filters.
if you measure crystals on different days, re-check frequecny calibration and
try
tp maintain the same room temperature as well.
hope i translated my spreadsheet into the equations here correctly.
--
73,
paul, n2pk
see the n2pk vna at:
http://n2pk.com
