CAV424

C/V-converter for single and differential capacitive input signals

July 2014 – Rev. 3.0

Page 9/14

www.analogmicro.de

APPLICATION INFORMATION

1. Transfer Function

For the capacitive sensor system shown in Figure 2 the output voltage VOUT at pin 5, which is referenced to

GND, is given by:

REF

M

CM

R

CR

OSC

OSC

OSC

M

OUT

V

C

R

C

R

R

C

V

C

V

+













⋅

−

⋅

⋅













⋅

⋅

∆

⋅

=

1

1

8

3

)

(

(8)

with

CM = variable measurement capacitance

CR = reference capacitance

COSC = oscillator capacitance

RCM = measurement integrator current resistor

RCR = reference integrator current resistor

ROSC = oscillator current resistor

∆

VOSC = voltage amplitude at the oscillator (with ∆VOSC = 2.15 V @ VCC = 5 V)

VREF = reference voltage (VREF = 2.5 V @ VCC = 5 V)

Using equation (8) it is easy to see that the output voltage is a linear function of the reciprocal measurement

capacitance 1/CM. The following relationships can be used to reduce the number of parameters and to en-

sure that CAV424 works properly:

1

min

,

M

CM

R

CR

C

R

C

R

⋅

=

⋅

and

min

,

55

.

0

M

OSC

CM

OSC

C

R

R

C

⋅

⋅

=

(9)

wherein CM,min is the specific minimum measurement capacitance of the measurement setup.

Inserting (9) into (8) leads to the following easy transfer function,

REF

M

M

M

OUT

V

C

C

C

V

+













−

⋅

=

min

,

1

44

.

0

)

(

.

(10)

wherein VOUT only depends on CM,min and CM.

Equation (10) is illustrated in Figure 5 for the measurement range ∆CM = CM,max – CM,min, wherein CM,max is

the specific maximum measurement capacitance of the measurement setup. For CM = CM,min equation (10)

leads to VOUT(CM,min) = VREF.

1

For an optimal and easy dimensioning of the external passive components Analog Microelectronics has developed the

Excel-sheet, Kali_CAV424 (see section “Further Literature”).

Figure 5: Output signal VOUT as a function of the measurement capacitance CM