Datasheet
SLOS209G − JANUARY 1998 − REVISED FEBRUARY 2004
37
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APPLICATION INFORMATION
gain calculation
Since the TLV2772 is capable of rail-to-rail output using a 3-V supply, V
O
= 0 (min) to 3 V (max). With no signal
from the sensor, nominal V
O
= reference voltage = 1.23 V. Therefore, the maximum negative swing from nominal
is 0 V − 1.23 V = −1.23 V and the maximum positive swing is 3 V − 1.23 V = 1.77 V. By modeling the shock sensor
as a low impedance voltage source with output of 2.25 mV/g (max) in the x and y axis and 1.70 mV/g (max) in
the z axis, the gain of the circuit is calculated by equation 1.
Gain +
Output Swing
Sensor Signal Acceleration
(1)
To avoid saturation of the operational amplifier, the gain calculations are based on the maximum negative swing
of −1.23 V and the maximum sensor output of 2.25 mV/g (x and y axis) and 1.70 mV/g (z axis).
Gain (x, y) +
* 1.23 V
2.25 mVńg *50 g
+ 10.9
(2)
Gain (z) +
–1.23 V
1.70 mVńg –50 g
+ 14.5
(3)
and
By selecting R3 = 10 kΩ and R4 = 100 kΩ, in the x and y channels, a gain of 11 is realized. By selecting
R3 = 7.5 kΩ and R4 = 100 kΩ, in the z channel, a gain of 14.3 is realized. The schematic shows the configuration
for either the x- or y-axis.
bandwidth calculation
To calculate the component values for the frequency shaping characteristics of the signal conditioning circuit,
1 Hz and 500 Hz are selected as the minimum required 3-dB bandwidth.
To minimize the value of the input capacitor (C1) required to set the lower cutoff frequency requires a large value
resistor for R2 is required. A 1-MΩ resistor is used in this example. To set the lower cutoff frequency, the required
capacitor value for C1 is:
C1 +
1
2p f
LOW
R
2
+ 0.159 µF
(4)
Using a value of 0.22 µF, a more common value of capacitor, the lower cutoff frequency is 0.724 Hz.
To minimize the phase shift in the feedback loop caused by the input capacitance of the TLV2772, it is best to
minimize the value of the feedback resistor R4. However, to reduce the required capacitance in the feedback
loop a large value for R4 is required. Therefore, a compromise for the value of R4 must be made. In this circuit,
a value of 100 kΩ has been selected. To set the upper cutoff frequency, the required capacitor value for C2 is:
C2 +
1
2p f
HIGH
R
4
+ 3.18 µF
(5)
Using a 2.2-nF capacitor, the upper cutoff frequency is 724 Hz.
R5 and C3 also cause the signal response to roll off. Therefore, it is beneficial to design this roll-off point to begin
at the upper cutoff frequency. Assuming a value of 1 kΩ for R5, the value for C3 is calculated to be
0.22 µF.