3–323
Motorola Sensor Device Data
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system performance. Adding a third op–amp to the circuit for
the negative dc level shifting capability (as shown in the next
section) is a solution that provides good common mode
rejection, but at the expense of adding an additional op–amp.
THE THREE OP–AMP GAIN STAGE
FOR NEGATIVE DC LEVEL SHIFTING
This circuit adds a third op–amp to the output of the two
op–amp gain block (see Figure 6). This op–amp has a dual
function in the overall amplifier circuit:
Its non–inverting configuration provides gain via the ratio
of R6 and R5.
It has negative dc voltage level shifting capability typically
created by a resistor divider at V–shift, as discussed in the
section on Application to Pressure Sensor Circuits. Al-
though this configuration requires a third op–amp for the
negative dc level shift, it has no intrinsic error nor low com-
mon
mode rejection
associated with the negative level shift
(as does the previous two op–amp stage). Depending on
the application’s accuracy requirement, this may be a more
desirable configuration for providing the negative dc level
shift.
First, use the same simplifications 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= 1
R6
R5
R4
R3
2R4
RG
1
VSENSOR
+ VREF –
R6
R5
V–shift
(20)
The gain is
G
= 1
R6
R5
R4
R3
2R4
RG
1
(21)
VREF is the positive dc level shift (offset), and V–shift is the
negative dc level shift.
Figure 6. Three Op–Amp Gain Stage with Variable Gain and Negative Dc Level Shift
VIN2
VIN1
VREF
R1
R2
R4
R3
VCC
U1
VO
′
U1
RG
VO
″
VO
V–SHIFT
R5
R6
U1
The transfer function for this stage will be similar to the
chosen two op–amp gain stage configuration (either the fixed
gain with positive dc level shift circuit or the variable gain with
positive dc level shift circuit) with additional terms for the
negative level shift and gain. As an example, the variable–gain
two op–amp gain circuit is used here. All of the design
considerations and explanations for the variable gain two
op–amp circuit apply.
The transfer function may be derived with nodal analysis
and superposition.
VO
= 1
R6
R5
R4
R3
R4
RG
R2R4
R3RG
1 VIN2
–
R4
R3
R4
RG
R2R4
R3RG
R2R4
R1R3
VIN1
+
R2R4
R1R3
VREF
–
R6
R5
V–shift
(19)
The preceding simplifications have been performed in the
previous sections, but by examining Equation 20, notice that
the third op–amp’s gain term also amplifies the positive and
negative dc voltage evel shifts, VREF and V–shift. If R6 and R5
are chosen to make an arbitrary contribution to the overall
system gain, designing an appropriate amount of positive and
negative dc level shift can be difficult. To simplify the transfer
function, set R5 = R6, and the following equation for VO results:
VO= 2
R4
R3
2R4
RG
1
VSENSOR
VREF
– V–shift
(22)
Now the third op–amp’s contribution to the overall system
gain is a factor of two. When designing the overall system gain
and the positive dc level shift, use the following guidelines:
F
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n
.