3–321
Motorola Sensor Device Data
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Figure 3. A Resistor Divider to Create VREF
R1
VREF
TO U1
VCC
RREF1
RREF2
THE TWO OP–AMP GAIN STAGE WITH
VARIABLE GAIN
Varying the gain of the two op–amp stage is desirable for
fine–tuning the sensor’s signal–conditioned output span.
However, to adjust the gain in the two op–amp gain circuit in
Figure 2 and to simultaneously preserve the common mode
rejection, two resistors must be adjusted. To adjust the gain,
it is more desirable to change one resistor. By adding an
additional feedback resistor, RG, the gain can be adjusted with
this one resistor while preserving the common mode rejection.
Figure 4 shows the two op–amp gain stage with the added
resistor, RG.
Figure 4. Two Operational–Amplifier Gain Stage with
Variable Gain
VIN2
VIN1
VREF
NODE 1
R1
R2
R4
R3
VCC
NODE 2
U1
VO
U1
RG
VO
′
As with the two op–amp gain stage, nodal analysis and
superposition are used to derive the general transfer function
for the variable gain stage.
VO
=
R4
R3
R4
R3
R2R4
R1R3
R4
RG
R4
RG
R2R4
R3RG
R2R4
R3RG
1 VIN2
–
R2R4
R1R3
VIN1
+
VREF
(11)
This general transfer function also is quite cumbersome
and is susceptible to producing poor common mode rejection
without additional constraints on the resistor values. To obtain
good common mode rejection, use a similar simplification as
before; that is, set
R1 = R4
and
R2 = R3
Defining the voltage differential between VIN2 and VIN1 as
VSENSOR, the simplified transfer function is
VO =
R4
R3
2R4
RG
1
(VSENSOR) + VREF(12)
Thus, the gain is
G =
R4
R3
+
2R4
RG
+ 1
(13)
and VREF is the positive dc level shift (offset).
Use the following guidelines when determining the value for
RG:
By examining the gain equation, RG’s resistance should
be comparable to R4’s resistance. This will allow fine tun-
ing of the gain established by R4 and R3. If RG is too large
(e.g., RG approaches
∞
), it will have a negligible effect on
the gain. If RG is too small (e.g., RG approaches zero), the
RG term will dominate the gain expression, thus prohibit-
ing fine adjustment of the gain established via the ratio of
R4 and R3.
Use a potentiometer for RG that has a resistance range on
the order of R4 (perhaps with a maximum resistance equal
to the value of R4). If a fixed resistor is preferable to a poten-
tiometer, use the potentiometer to adjust the gain, measure
the potentiometer’s resistance, and replace the potentiom-
eter with the closest 1% resistor value.
To maintain good common mode rejection while varying
the gain, RG should be the only resistor that is varied. RG
equally modifies both of the resistor ratios which need to be
well–matched for good common mode rejection, thus pre-
serving the common mode rejection.
THE TWO OP–AMP GAIN STAGE WITH VARIABLE
GAIN AND NEGATIVE DC LEVEL SHIFT
The last two op–amp circuits both incorporate positive dc
level shift capability. Recall that a positive dc level shift is
required to keep the operational amplifiers from saturating
near the low rail of the supply or to keep the zero pressure
offset above (or equal to) the low reference voltage of an A/D.
This two op–amp stage incorporates an additional resistor,
ROFF, to provide a negative dc level shift. A negative dc level
shift is useful when the zero pressure offset voltage of the
sensor is too high. In this case, the user may be required to
level shift the zero pressure offset voltage down (toward zero
volts). Now, for a specified amount of gain, the full–scale
pressure output voltage does not saturate the amplifier at the
high rail of the voltage supply, nor is it greater than the A/D’s
high reference voltage. Figure 5 shows the schematic for this
amplifier circuit.
F
Freescale Semiconductor, Inc.
n
.