Application Note Using MagAlpha in Off-Axis Mounting October 2014 Introduction The MagAlpha is an angle sensor that locally detects the direction of the magnetic vector. Therefore, only the strength and the direction of magnetic field at the sensor position (package center) matters. This leaves some freedom to the user to optimally adapt the magnet-sensor configuration to his application. In the present note, we consider cylinder magnets diametrically magnetized. Minimum field The MagAlpha can be placed at any position where the in-plane field strength remains above its operational limit, i.e. 20 mT or 60 mT depending on the MagAlpha version. In general, the magnetic field strength varies upon rotating the magnet. Thus, the smallest field value within one complete turn of the magnet must be considered. Non-linearity If the sensor is placed on the rotation axis, the magnetic field direction is proportional to the mechanical angle. Hence, the output of a sensor is linear (in ideal case). If the position of the sensor is eccentric, it probes a magnetic field out of the rotation axis. In this case, the magnetic field amplitude varies as a function of the angle. This variation comes along with an angle deviation with respect to a perfectly uniform magnetic field. When decomposing the magnetic field, it can be observed that its radial and tangential components behave as sine and cosine functions, with different amplitudes (see Figure 1). This is sometimes called an "elliptic" error. As a consequence the angle of the field vector does not move proportionally to the mechanical angle anymore. The sensor output is therefore nonlinear. We define the ellipticity ratio as: where and respectively. are the radial and tangential field amplitude 1 October 2014 Figure 1: Left: Example of Radial and Tangential Magnetic Field Off-Axis. Right: Resulting NonLinearity. The integral non-linearity (INL) is defined as the maxium deviation from the perfect straight-line response. For a given ellipticity , the INL is: If this non-linearity exceeds the user requirements, the MagAlpha can be configured to compensate this error. For this, the user needs to adjust the trimming parameters BCT, ETX and ETY (see MagAlpha datasheets and the guidelines below). Direction of rotation In the peripheral region, i.e. where the eccentricity is greater than the magnet radius, the direction of the radial field is reversed, while the tangential field keeps the same direction. The result is that the direction of rotation is reversed. Figure 2: The Direction of the Rotating Magnetic Field (Red Arrow) at the Sensor Position is Reversed when the Eccentricity is Greater than the Magnet Radius. 2 October 2014 Example Assume the magnet has the characteristics: Diameter Height Remanent field mm mm T 5 2.5 1 The sensitive region of the MagAlpha (which is in the package center) can be placed anywhere inside the surface limited by the color lines in Figure 3 left. For instance, if the lower limit is 20 mT the sensor must be somewhere within the violet line. The ellipticity is indicated in Figure 3, right. Note: the sign change reflects the change of sign of the radial field, and therefore the direction change. Figure 3: Left: The Minimum Field Amplitude over a Complete Turn. Right: The Ellipticity Ratio. For instance, if the user decides to position the Magalpha center at the position e = 2 mm and z = 4 mm, the minimum field within one rotation would be 20 mT. At this point, the ellipticty ratio is between 0.6 and 0.8. Note that along a curve in the e-z plane (light blue line) the ellipticity is -1. Along this curve , in other words, the sensor output is linear without any trimming. 3 October 2014 Guidelines for off-axis sensor positioning Whether a certain sensor position is suitable for MagAlpha and what is the optimal setting are determined from the values and . These values can be estimated from the graphs of Figure 4. Note that the parameters are normalized by the magnet height: for the magnet diameter, for the eccentricity and for the sensor vertical position. The field values are given for a remanent field 1 T. For different remanent field, multiply and by the ratio . Once and are known, go through the list below: 1. Check that the minimum field is above the lower limit of MagAlpha. The minimum field is the lower value between and : 20 mT 2. Determine the ellipticity ratio: and estimate the 3. If the without correction: is too large, determine the ellipticity correction: ETX ETY 1 0 0 1 BCT The BTX, BTY settings assumes that the sensor is positioned as displayed on the left. If rotated by 90°, the ETX - ETY settings are reversed. 4 October 2014 5 October 2014 Figure 4: Mapping of the Radial and Tangential Fields for a 1 T Remanent Field Magnet with Several aspects Ratios . Example Consider the magnet-sensor configuration. The chip is positionned as displayed on the left. Diameter Height Remanent field Eccentricity Height (mm) (mm) (T) (mm) (mm) 5 2.5 1.1 5 1.25 The normalized coordinates are: Normalized Parameter Value 2 2 0.5 6 October 2014 The sensor position is shown by the red dots in Figure 5. The table below indicates the values extracted from the graph. Note that the normalized values must be multiplied by 1.1 since T. Figure 5 : Sensor Position in the Magnetic Field of a Permanent Magnet. Normalized field Field Both and Unit mT Radial 55 60.5 Tangent 30 33 are more than 20 mT, therefore the position is OK. The ellipticity ratio is . Therefore without trimming, the would be 16.3°: Therefore to correct the non-linearity, the MagAlpha should be programmed with : Because the chip is rotated by 90 ° (see picture above) and trimming should occur along the Y axis: the ETX = 0 ETY = 1 7 October 2014