INFICON PLO-10i Phase Lock Oscillator - Manual (Page 56)

PLO-10 PHASE LOCK OSCILLATOR
THEORY OF OPERATION 8-8
L
η = Viscosity of the liquid in contact with the electrode in kg/m/sec
S
ω = Angular frequency at series resonance ( f π 2 )
For example, the decay length for a 5 Mhz crystal in water at 20°C is 2.5×10 -7 m = 0.25
microns.
8.5 DISSIPATION METHOD
The Dissipation Method is an alternate way of measuring the crystal to determine the
properties of the film and/or the liquid. In this method, the crystal is driven at its resonant
frequency by an oscillator then the crystal shorted and both the resonant frequency and
the oscillation decay time are measured. The crystal dissipation is related to Q and R as
follows:
Equation 10
L
R
Q
D
S
⋅
= =
ω
1
Where:
D = Dissipation
Q = Quality Factor
R = resistance in Ω
L = inductance in H
D can be determined from R if L is known. It has been shown that L will remain constant
unless there is an acoustic resonance in the film on the crystal. Independent studies 25
have shown that as long as the effect of the parasitic capacitance (C
S
) is properly
cancelled, the results provided by the PLO-10 System are in good agreement with those
obtained by the Dissipation Method.
8.6 ELECTRICAL DESCRIPTION OF THE QUARTZ CRYSTAL
Figure 18 shows the equivalent circuit of a quartz crystal. The circuit has two branches.
The motional branch, which contains the L, R & C, is the branch that is modified by mass
and viscous loading of the crystal. The shunt branch, which contains the lone Cs
element, represents the shunt capacitance of the crystal electrodes and any cable and
fixture capacitance.