3–320
Motorola Sensor Device Data
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First, the transfer function for VIN1 is determined by
grounding VREF and VIN2 at node 1:
VO
′
– VIN1
R2
and at node 2:
VIN1
R1
=
(1)
VO
′
R3
= –
VO
R4
(2)
By solving Equations (1) and (2) for VO
′
and equating the
results, Equation (3) is established:
R2
R1
1 VIN1 = –
R3
R4
VO3)
Solving for VO yields
VO1 = –
R4
R3
R2
R1
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 =
R4
R3
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 =
R4R2
R3R1
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 = –
R4
R3
R4R2
R3R1
R2
R1
1 VIN1 +
R4
R3
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
R4
R3
=
R1
R2
Through this simplification,
Equation (7)
simplifies to
VO =
R4
R3
1 ( S+ – S–) + VREF
(8)
By examining Equation (8), the differential gain of the
signal– conditioning stage is:
G =
R4
R3
+ 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 =
R4
R3
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 “l(fā)ooking” 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.
F
Freescale Semiconductor, Inc.
n
.