Frequently Asked Questions
MEMS Sensor Terminology
BASICS
- What is a "g"?
- How do you calculate acceleration from the analog output of an accelerometer?
- How do you calculate acceleration from the digital output of an accelerometer?
- How do you determine that a +/-2g accelerometer will have a sensitivity of 660mV/g or 819counts/g?
- What happens if the product g-range is programmed higher than the specifications state?
TEMPERATURE RATIOMETRICITY SELF TEST NOISE MULTIPLEXING SHOCK ELECTRICAL
BASICS
What is a "g"?
In physics, the acceleration of an object caused by the force of gravity is called gravitational acceleration. On the surface of the Earth, all objects fall with an acceleration defined as one "g", which is approximately equal to 9.81 m/s² (32.17 ft/s²). Quite often, "g" is used as a unit of acceleration rather than expressing acceleration in m/s² or ft/s².
How do you calculate acceleration from the analog output of an accelerometer?
Kionix has several analog tri-axis accelerometer products. All of these products provide an output voltage proportional to the linear acceleration in each axis. Per standard convention, the zero acceleration (or zero-g offset) is usually defined as an output voltage equal to half the supply voltage (Vdd/2). For an accelerometer supplied using 3.3V, this would be a zero-g offset equal to 1.65V. Voltages above 1.65V indicate a positive acceleration. Voltages below 1.65V indicate a negative acceleration. The magnitude of the acceleration is typically expressed in units of g (1g = 9.8m/s2 = the Earth’s acceleration). It is calculated by finding the difference between the measured output and the zero-g offset then dividing by the accelerometer’s sensitivity (expressed in V/g or mV/g). For a 2g accelerometer operating at 3.3V, the sensitivity is 660mV/g or 0.660V/g. The acceleration would be equal to: a = (Vout - 1.65V)/(0.660V/g) in units of g.
How do you calculate acceleration from the digital output of an accelerometer?
Kionix has several digital tri-axis accelerometer products. All of these products provide digital outputs proportional to the linear acceleration in each axis. Per standard convention, the zero acceleration (or zero-g offset) is usually defined as an output equal to half the maximum output value (4096 for a 12-bit output, 1024 for a 10-bit output, etc.). For an accelerometer providing 12-bit output, this would be a zero-g offset equal to 2048. Outputs above 2048 indicate a positive acceleration. Outputs below 2048 indicate a negative acceleration. The magnitude of the acceleration is typically expressed in units of g (1g = 9.8m/s2 = the Earth’s acceleration). It is calculated by finding the difference between the measured output and the zero-g offset then dividing by the accelerometer’s sensitivity (expressed in counts/g or LSB/g). For a 2g accelerometer with 12-bit digital outputs, the sensitivity is 819 counts/g or 819 LSB/g. The acceleration would be equal to: a = (Aout - 2048)/(819 counts/g) in units of g.
How do you determine that a +/-2g accelerometer will have a sensitivity of 660mV/g or 819counts/g?
First, for an analog part, it is important to know what supply voltage the part will be operating at. For this example we'll use the very common supply voltage (Vdd) of 3.3V. The zero-g offset is most often Vdd/2 which in this case would be 1.65V. Output voltages above Vdd/2 indicate positive accelerations, and output voltages below Vdd/2 indicate negative accelerations. Obviously, one would assume that 0V would be equal to -2g and Vdd (3.3V, for example) would be equal to +2g. Therefore, a +/-2g part should have a sensitivity of (Vdd/2) / g-range, which in the example would be (3.3V/2) / (2g) = 0.825V/g = 825mV/g. There are a couple problems if you use this methodology to make a +/-2g part. First, the zero-g offset isn't always exactly Vdd/2. Because of offset trimming tolerances, misalignment errors, and temperature effects, the zero-g offset has a tolerance. The zero-g offset might be 1.65 +/- 0.10 V. If your part happens to have a zero-g offset of 1.70V, then at 825mV/g your part would measure a maximum of +1.94g and a minimum of -2.06g. You wouldn't be able to measure exactly +2g of acceleration and your part wouldn't truly be a +/-2g part. The second problem with using this methodology is that an output reading of 0V or Vdd (3.3V) would be indeterminate. Any acceleration of +2g or higher would give an output reading of Vdd, and any acceleration of -2g or lower would give an output reading of 0V. Thus, when the accelerometer gave an output reading of 3.3V, for example, you wouldn't know if that were +2g, +3g, or +5g. To prevent the problems described above, we choose to make 0.1*Vdd equal to -2g and 0.9*Vdd equal to +2g. This gives enough margin from 0V and Vdd to account for the zero-g offset tolerances and temperature variation. It also guarantees that +/-2g will always be measurable quantities. The sensitivity calculation in this methodology is: (0.9*Vdd - 0.1*Vdd) / (+g-range - -g-range). For our example, (0.9*3.3V - 0.1*3.3V) / (+2g - -2g) = (2.64V / 4g) = 0.66V/g = 660mV/g. For a digital part, the methodology is similar but dependent on the number of output bits. For example, a 12-bit digital part would give readings from 0 to 4095. We substitute the maximum output reading (4095) in place of Vdd in the above equations. Sensitivity is then: (0.9*4095 - 0.1*4095) / (+2g - -2g) = (3276 / 4g) = 819 counts/g.
What happens if the product g-range is programmed higher than the specifications state?
The sensitivity of the product will decrease, and it will exhibit non-linearity. Non-Linearity is where sensors do not demonstrate a perfectly linear relationship between input acceleration and output voltage.
TEMPERATURE
What is Zero-g Offset Variation from RT over Temp.?
Zero-g offset variation from RT over Temp. is the change in the zero-g offset from the room temperature zero-g offset as the temperature changes. The variation is measured at Kionix by placing the accelerometer in a thermal chamber. First, the zero-g offset voltage is measured at 25C. Then the chamber is heated to a high temperature (usually 85C), and the zero-g offset voltage is measured a second time. Finally, the chamber is cooled to a low temperature (usually -40C), and the zero-g offset voltage is measured a third time. After the testing is complete, the data is analyzed. The zero-g offset voltage at 25C is subtracted from each of the measurements. The resulting change in voltage is divided by the accelerometer's sensitivity to express the change in output in terms of acceleration (g or mg). The three data points (high temp., 25C, and low temp.) are plotted on a graph, and a least squares linear fit is done. The resulting slope (expressed in mg/C) gives the variation of the zero-g offset from room temperature (25C) over temperature.
What is Sensitivity Variation from RT over Temp.?
Sensitivity variation from RT over Temp. is the change in the sensitivity from the room temperature sensitivity as the temperature changes. The variation is measured at Kionix by placing the accelerometer in a thermal chamber. First, the sensitivity is measured at 25C. Then the chamber is heated to a high temperature (usually 85C), and the sensitivity is measured a second time. Finally, the chamber is cooled to a low temperature (usually -40C), and the sensitivity is measured a third time. After the testing is complete, the data is analyzed. The sensitivity at 25C is subtracted from each of the measurements. The resulting change in sensitivity is divided by the accelerometer's sensitivity at 25C to express the change in output in terms of percentage change. The three data points (high temp., 25C, and low temp.) are plotted on a graph, and a least squares linear fit is done. The resulting slope (expressed in %/C) gives the variation of the sensitivity from room temperature (25C) over temperature.
Does internal temp. compensation preclude an end user temperature calibration and compensation?
No. Any end user compensation or calibration can be done on top of the internal compensation. Cost saving can be realized by requesting a part specification with global compensation which does not require additional thermal testing on each part.
RATIOMETRICITY
Are Kionix accelerometers ratiometric?
Ideally, the sensor is ratiometric - the output scales by the same ratio that Vdd increases or decreases. For example, a 5% increase in Vdd results in a 5% increase in 0g offset.
What is ratiometric error?
Ratiometric Error is defined as the difference between the ratio that 0g offset or sensitivity changed and the ratio that Vdd changed, expressed as a percentage. For our specifications, ratiometric error is typically calculated for a +/- 5% change in Vdd from nominal. For example, the offset ratiometric error at Vdd = 3.3V +/- 5% is defined as the maximum absolute value of:
Similarly, the sensitivity ratiometric error at Vdd = 3.3V +/- 5% is defined as the maximum absolute value of:
SELF TEST
What does self test do?
This test allows the user to verify the functionality at any point of both the mechanical structure, and the ASIC. When the self test feature is enabled, the ASIC electrostatically actuates (excites) the mechanical structure causing a shift and thus a resulting change in acceleration output. This shift is different for each accelerometer product that Kionix provides, and thus one will need to refer to its specification sheet to see what this change in acceleration is.
If I'm not using self test, can the pin be left as a no connect (floating)?
No, the pin should not be left as an open circuit. Depending on the surrounding conditions, the voltage on the pin may float high enough to inadvertently trigger a self test. Please connect the self test pin to GND for normal operation.
NOISE
How do I calculate noise from noise density?
Since the noise output of a sensor is highly dependent on the output filter settings, the noise is reported as a noise density (ND). The noise density is defined as the noise per unit of square root bandwidth (ug/sqrt(Hz)). To determine the expected noise for a given application first determine the equivalent noise bandwidth, B, of your output filter. The equivalent noise bandwidth of a filter is the -3 dB bandwidth (f-3dB) multiplied by a coefficient which is dependent on the order of the filter according to the following table.
B = 1.57 * f-3dB Hz for a 1st order filter
B = 1.11 * f-3dB Hz for a 2nd order filter
B = 1.05 * f-3dB Hz for a 3rd order filter
B = 1.025 * f-3dB Hz for a 4th order filter
So, if you apply a 50 Hz first order low pass filter to the outputs of a KXR94 accelerometer (ND = 40 ug/sqrt(Hz)) the expected noise would be (40 ug/sqrt(Hz)) * sqrt(1.57 *50 Hz) = 354 ug. This is the RMS sensor dependent noise expected on the outputs of the KXR94. The actual noise seen on the sensor outputs may be larger than this reported error due to environmental noise (thermal, Vdd regulation, mechanical accelerations) on the sensor.
What is resolution?
Resolution is the minimum detectible change in acceleration. To be detectible, the signal must be greater than the noise of the sensor. The resolution of our analog parts can be determined with the following equation: Resolution = sqrt((noise density ug/sqrt(Hz))*(noise bandwidth)).
The resolution of our digital parts can be determined using the following equation: Resolution digital = 1/(sensitivity)
MULTIPLEXING
Why is there a built-in multiplexer on some of your accelerometers?
The built-in multiplexer allows the user to measure X, Y, and Z axis acceleration with only one Analog to Digital (A/D) port and two digital output ports on their main microprocessor. This can be advantageous when the number of available A/D ports is limited. The KXPA4, KXPB5, KXP94, and KXR94 feature a built-in multiplexer.
How do I use the built-in multiplexer?
Connect the Vmux pin of the accelerometer to an Analog to Digital (A/D) input port of your microprocessor, and connect S0 and S1 of the accelerometer to digital outputs of your microprocessor. Select the desired multiplexer output by toggling S0 and S1 to the appropriate values. Once the desired multiplexer output has been selected, wait 5 microseconds then begin an Analog to Digital conversion. Refer to the product specification for an output select table that defines the S0 and S1 states that correspond to the Vmux output options. Application note AN003 also describes how to use the built-in multiplexer as well as an external multiplexer.
What do I do if I'm not using the built-in multiplexer?
When not using the built-in multiplexer, make the following connections: S0 and S1 - ground or Vdd. Vmux: leave floating.
SHOCK
What is mechanical shock?
Mechanical shock is a motion of the foundation or applied force of a mechanical system that is characterized by suddenness and severity that causes a big displacement in the system during the pulse.
ELECTRICAL
Is the center pad of Kionix's DFN package supposed to be grounded?
Yes, the center pad of Kionix's DFN package should be grounded. This will provide the lowest noise performance. Soldering the center pad to the printed circuit board (PCB) is recommended in general because it helps provide a strong mechanical coupling between the sensor and the PCB.
What is aliasing?
Aliasing is a distortion of the output due to sampling a continuous signal at too low a rate. To avoid aliasing you need to sample at a minimum rate of 2 times the low pass filter cutoff frequency. (Nyquist–Shannon sampling theorem)
