MPXM2102AS datasheet(466/670 Pages) MOTOROLA

466 / 670 page

AN1525

3–320

Motorola Sensor Device Data

www.motorola.com/semiconductors

First, the transfer function for VIN1 is determined by

grounding VREF and VIN2 at node 1:

VIN1

VO′ –VIN1

(1)

and at node 2:

VO′

= –

(2)

By solving Equations (1) and (2) for VO′ and equating the

results, Equation (3) is established:

) 1 VIN1 = –

VO(3)

Solving for VO yields

VO1 = –

) 1 VIN1

(4)

where VO1 represents the part of VO that VIN1 contributes.

To determine the transfer function for VIN2, VIN1 and VREF

are grounded, and a similar analysis is used, yielding

VO2 =

) 1 VIN2

(5)

where VO2 represents the part of VO that VIN2 contributes.

Finally, to calculate the transfer function between VO and

VREF, VIN1 and VIN2 are grounded to obtain the following

transfer function:

VOREF =

VREF

(6)

where VOREF represents the part of VO that VREF

contributes.

Using superposition for the contributions of VIN1, VIN2, and

VREF gives the overall transfer function for the signal–

conditioning stage.

VO = VO1 + VO2 + VOREF

VO = –

) 1 VIN1 +

) 1 VIN2

VREF

(7)

Equation (7) is the general transfer function for the

signal–conditioning stage. However, the general form is not

only cumbersome, but also if no care is taken to match certain

resistance ratios, poor common mode rejection results. A

simplified form of this equation that provides good common

mode rejection is shown in the next section.

APPLICATION TO PRESSURE

SENSOR CIRCUITS

The previous section showed the derivation of the general

transfer function for the two op–amp signal–conditioning

circuit. The simplified form of this transfer function, as applied

to a pressure sensor application, is derived in this section.

For pressure sensors, VIN1 and VIN2 are referred to as S–

and S+, respectively. The simplification is obtained by setting

Through this simplification, Equation (7) simplifies to

VO =

) 1 ( S+ – S–) + VREF

(8)

By examining Equation (8), the differential gain of the

signal– conditioning stage is:

G =

+ 1

(9)

Also, since the differential voltage between S+ and S– is the

pressure

sensor’s

actual

differential

output

voltage

(VSENSOR), the following equation is obtained for VO:

VO =

) 1 VSENSOR + VREF

(10)

Finally, the term VREF is the positive offset voltage added to

the amplified sensor output voltage. VREF can only be positive

when using a positive single–ended supply. This offset (dc

level shift) allows the user to adjust the absolute range that the

sensor voltage spans. For example, if the gain established by

R4 and R3 creates a span of four volts and this signal swing

is superimposed upon a dc level shift (offset) of 0.5 volts, then

a signal range from 0.5 V to 4.5 V results.

VREF is typically adjusted by a resistor divider as shown in

Figure 3. A few design constraints are required when

designing the resistor divider to set the voltage at VREF.

• To establish a stable positive dc level shift (VREF), VCC

should be regulated; otherwise, VREF will vary as VCC va-

ries.

• When “looking” into the resistor divider from R1, the effec-

tive resistance of the parallel combination of the resistors,

RREF1 and RREF2, should be at least an order of magni-

tude smaller than R1’s resistance. If the resistance of the

parallel combination is not small in comparison to R1, R1’s

value will be significantly affected by the parallel combina-

tion’s resistance. This effect on R1 will consequently affect

the amplifier’s gain and reduce the common mode rejec-

tion.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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