INFICON RQCM - Quartz Crystal Microbalance Research System - Manual (Page 71)

RQCM – RESEARCH QUARTZ CRYSTAL MICROBALANCE
THEORY OF OPERATION 5-19
only 0.018 degrees when measuring a ten-ohm crystal. However, when measuring a one
thousand-ohm crystal the effective phase error will increase to 1.8 degrees and it will increase to
9 degrees when measuring a five thousand-ohm crystal.
Combining these two errors we can get an idea of the magnitude of the frequency error caused by
imperfect capacitance cancellation.
For a 10 Ω crystal a one picofarad capacitance imbalance results in a 0.018 degree phase error
and a 0.0067 Hz frequency error.
For a 100 Ω crystal, the phase error is 0.18 degrees and the frequency error is 0.67 Hz. For a
1000 Ω crystal, the phase error is 1.8 degrees and the frequency error is 67 Hz. For a 5000 Ω
crystal, the phase error is 9 degrees and the frequency error is 1,635 Hz.
A two picofarad capacitance imbalance will result in approximately twice the above error.
Frequency Error vs. Crystal Resistance
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
10000.000
100000.000
10 16 25 40 63
100 158 251 398 631
1,000 1,585 2,512 3,981 6,310 10,000
Crystal Resistance (ohm)
Frequency Error (Hz)
Freq. Error due
to a 5 pfd
Freq. Error due
to a 2 pfd
capacitance
Freq. Error due
to a 1 pfd
capacitance
Figure 26 Frequency Error Due to Imperfect Capacitance Cancellation
5.9 CALCULATING CRYSTAL POWER
Crystal power can be calculated as follows:
Crystal power, P
cry
= i 2 * R
cry
Crystal current, i = V
oc
/( R
s
+ R
cry
)
Hence, P
cry
= i 2 * R
cry
= [V
oc
/( R
s
+ R
cry
)] 2 * R
cry
Where: