INFICON PLO-10i Phase Lock Oscillator - Manual (Page 32)

PLO-10 PHASE LOCK OSCILLATOR
FREQUENCY ERRORS DUE TO IMPERFECT CAPACITANCE CANCELLATION 5-2
Effective Phase error = arctangent ((31.4e-6)/(100e-3)) = 0.018 degrees
In other words a one picofarad capacitance unbalance will result in an effective phase
error of 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 capacitance
imbalance
Freq. Error due to a
2 pfd capacitance
imbalance
Freq. Error due to a
1 pfd capacitance
imbalance
Figure 7 Frequency Error Due to Imperfect Capacitance Cancellation