Figure 2-2 Acquisition Burst with Sync Signal
2.2 CS / CX Dependency
The signal value is a direct function of Cs and Cx, where Cs
is the fixed sample capacitor, and Cx is the unknown
capacitance. These two values influence device sensitivity,
resolution and response time, making them very important
parameters.
Sync Signal
Sensitivity and resolution are also a function of the size,
shape, and composition of the electrode, the composition
and thickness of any dielectric overlaying the electrode, the
composition and aspect of the object being sensed, and the
degree of mutual coupling between the electrode and the
object being sensed.
Acquisition
Burst
2.3 Burst Length
The burst length (and hence the signal level) is described by
the following formula:
Figure 2-3 Acquisition Burst: Sync Lost
k$CS
BL =
CX
Where ‘k’ is a constant, typically 0.51 (this may vary slightly
from device to device).
Sync Signal
Each doubling of Cs increases the signal level and
differential sensitivity by a factor of two. Likewise, doubling
Cx reduces the signal level and differential sensitivity by a
factor of two (Figures 6-1, 6-2, page 8).
Acquisition
Burst
The device has an internal Cx, Csns, which adds to the Cx in
the formula. This capacitance is about 11pF.
Because the QT301 has an 8-bit PWM output which spans
two calibration endpoints, the PWM output value is
expressed as:
100ms
Figure 2-4 Acquisition Burst: Sync Reacquired
k$C
k$C
S
S
−
−
C
C
C
X2$(CX1−CX)
X
X1
PWM = 255 $
= 255 $
;
k$C
k$C
CX$(CX1−CX2)
S
S
C
C
X1
X2
where:
Cx1 is the capacitance at the lower cal point
Cx2 is the capacitance at the upper cal point, and
Sync Signal
Cx is the measured capacitance between Cx1 and Cx2
Particularly noteworthy is that Cs is not part of this equation;
the PWM result is purely a function of the three Cx values.
Cs only needs to be large enough to prevent granularity
problems (i.e. coarseness or resolution).
Acquisition
Burst
In most cases the result is a nearly-linear response between
the endpoints. Only when the capacitance of the lower cal
point becomes comparable to delta Cx does the result
become substantially non-linear.
For a linear response, make sure that the lower cal point
capacitance is significantly larger than the delta capacitance
between the endpoints. If the delta Cx amounts to 5pF, the
response will be accurate to 2.4% of full scale if the lower cal
point is 50pF. But if the lower cal point is only 20pF and the
delta Cx is 10pF, the error rises to 10% at points. The largest
errors occur near the middle of the Cx span.
Figure 2-5 Sync Overclocked
Sync Signal
An example of the error can be seen in Figure 2-6.
Non-linear errors can be linearized using polynomials or a
piece-wise linear correction method in a microcontroller. A
spreadsheet with the calculations for this equation and the
error terms can be obtained on request.
Acquisition
Burst
LQ
3
QT301 R1.06 12/03
QUANTUM [ QUANTUM RESEARCH GROUP ]
