MPR121

Sensors

Freescale Semiconductor

13

Any ADC counts outside of the range shown are invalid and settings must be adjusted to be within this range. If capacitance

variation is of importance for an application after the current output, charge time and supply voltage are determined then the fol-

lowing equations can be used. The valid range for capacitance is calculated by using the minimum and maximum ADC values in

the capacitance equation. Substituting the low and high ADC equations into the capacitance equation yields the equations for

the minimum and maximum capacitance values which are

and

.

Equation 5

SENSITIVITY

The sensitivity of the MPR121 is relative to the capacitance range being measured. Given the ADC value, current and time

and settings capacitance can be calculated,

.

Equation 6

For a given capacitance the sensitivity can be measured by taking the derivative of this equation. The result of this is the

following equation, representing the change in capacitance per one ADC count, where the ADC in the equation represents the

current value.

Equation 7

This relationship is shown in the following graph by taking the midpoints off all possible ranges by varying the current and time

settings. The midpoint is assumed to be 512 for ADC and the nominal supply voltage of 1.8 V is used.

Figure 6.

Smaller amounts of change indicate increased sensitivity for the capacitance sensor. Some sample values are shown in

Table 8.

In the previous cases, the capacitance is assumed to be in the middle of the range for specific settings. Within the capacitance

range the equation is nonlinear, thus the sensitivity is best with the lowest capacitance. This graph shows the sensitivity derivative

Table 8.

pF

Sensitivity (pF/ADC count)

10

-0.01953

100

-0.19531

C

low

IT

×

V

DD

0.7

–

--------------------------

=C

high

IT

×

0.7

-----------

=

C

IT

1024

×

×

V

DD

ADC

×

-------------------------------

=

dC

dADC

----------------

IT

×

1024

×

V

DD

ADC

2

×

-----------------------------------

=

Sensitivity vs. Midpoint Capacitance for VDD =1.8 V

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

500

1000

1500

2000

2500

Midpoint Capacitance (pF)

dC/dADC @cmid (pF/1 ADC Count)

0