# Accelerometer Power Calculation Example

Quote of the Day

I planned on having one husband and seven children, but it turned out the other way around.

Figure 1: Monolithic Accelerometer from Bosch. (Source)

I am working on a product that uses a Bosch BMA253 accelerometer as a motion sensor. This family of products has become a defacto standard for inexpensive motion detection. In this post, I will provide a simple power calculation example along with some empirical data that Bosch provided me. Normally, I would not consider a simple power calculation worth writing about, but the datasheet did not provide a worked example. I also provide an Excel workbook that parameterizes the critical variables.

Here are the critical formulas for low power mode 1. For low power mode 2, the formulas are the same with the 1 subscript changed to 2.

 Eq. 1 $\displaystyle {{t}_{{active}}}=\left| \begin{array}{l}{{t}_{{ut}}}+{{t}_{{w,up1}}}-0.9\text{ ms, }bw\ge 31.25\text{ Hz}\\4\cdot {{t}_{{ut}}}+{{t}_{{w,up1}}}-0.9\text{ ms, otherwise}\end{array} \right.$ Eq. 2 $\displaystyle {{I}_{{DDlp1}}}=\frac{{{{t}_{{sleep}}}\cdot {{I}_{{DDsum}}}+{{t}_{{active}}}\cdot {{I}_{{DD}}}}}{{{{t}_{{sleep}}}+{{t}_{{active}}}}}$ Eq. 3 $\displaystyle {{t}_{{ut}}}=\frac{1}{{2\cdot bw}}$ Eq. 4 $\displaystyle {{f}_{{Output}}}=\frac{1}{{{{t}_{{active}}}+{{t}_{{sleep}}}}}$

where

• bw is the bandwidth setting of the digital filter.
• tut is the updated time for the filter output data.
• tw,up1 is the data acquisition stabilization time.
• tsleep is the time during which the BMA253 is put in suspend mode ("sleep").
• tactive is the time during which the BMA253 is stabilizing and acquiring data.
• fOutput is the output data rate from the digital filter.
• IDD is the current draw of the BMA253 when it is performing data acquisition ("active").
• IDDsum is the current draw of the BMA253 when it is in suspend mode ("sleeping").

Figure 2 illustrates the data acquisition timing.

Figure 2: Data Acquisition Timing.

I can use Equations 1-4 to generate Table 1, which assumes that

• bw= 1000 Hz
• tw,up1 = 1.3 ms
• IDD = 130 μA
• IDDsum = 2.1 μA

Table 1: Estimated and Measured BMA253 Current Draws.

What I liked about the data I received from Bosch is that it allows me to determine the accuracy of the current draw formula relative to the measured data.

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