Electric/Magnetic

# A Case Study: MR vs. Hall Effect for Position Sensing

November 1, 2005 By: Joachim Quasdorf, iC-Haus GmbH Sensors

### How magnetoresistive sensors and integrated Hall sensors differ and what this means for designers of magnetic angle and linear position sensors.

While both magnetoresistive and integrated Hall sensors measure the strength of magnetic field components, they do so in different ways and this can directly affect their successful use in a position sensing application. Choosing which of the two is a better fit for your application may require you to consider sensor characteristics that don't show up on manufacturers' data sheets. This article is designed to help your decision process by reviewing two angle sensors—an anisotropic magnetoresistive (AMR) sensor and a Hall sensor—in a position-sensing application example.

## The Theoretical Basics

Figure 1 shows how the two sensor types react in the presence of an external magnetic field. A magnetoresistive (MR) sensor records axis or magnet angle information via the field vector in the chip plane. The AMR effect is a "resistor" effect based on the dependence of electrical resistance on the angle between the directions of the current flow and magnetization of a ferromagnetic material. An external magnetic field can switch the internal direction of magnetization of the AMR material and thus effect changes in resistance (ΔR/R) that are typically on the order of a few percent.

 Figure 1. Here we see the basic principles of operation for AMR and Hall effect sensors.

Several resistors connected in a Wheatstone bridge are used to measure angles. Each component resistor contributes to a change in the differential output voltage of the bridge, depending on the X,Y field direction in the sensor plane and on the direction of current flow in the resistors. This direction of current flow is either given by the alignment of the resistor paths or is forced in another direction by short-circuit contacts (barber poles).

For our sample AMR sensor (see its specifications in Figure 2), the bridge provides a differential sine voltage of 70 mV with a cyclic repetition every 180°. A field aligned in the opposite direction produces the same resistive effect.

 Figure 2. Selected electrical characteristics of the sensors from the manufacturers' data sheets.

To evaluate this bridge voltage we need a useful reference—preferably a reference voltage. Ideally, this is a second bridge set at a tilt to the first bridge and generating a differential cosine voltage. We can now determine the angle to be measured from the relationship between the two bridge voltages. Since any change in sensitivity (caused by temperature, for example) will affect both voltages in a similar way, these changes are not important for determining the angle.

For our sample Hall sensor, we're interested in the field component vertical to the chip. The Hall effect generates a directed voltage, typically of just a few millivolts, which is dependent on the strength of the Z component of a magnetic field. Consequently, a single Hall element sees only the distance between itself and the magnet. If several elements are used, each recording the Z field at various positions, then evaluating local gradients provides information on the angle. The arrangement of Hall elements on the chip determines which magnet to use since the sensor must be able to detect the bent near magnetic field. External homogenous stray fields, such as those from brushless DC motor assemblies, cannot cause interference.

Because the polarity of the Hall voltage follows the field direction, a magnetic north pole can be distinguished from a south pole. The range of angle measurement is extended to 360° but with half the sensitivity for angle changes within 180° in comparison to MR sensors.

To summarize, a designer can expect the following characteristics from the two types of sensors:
For the AMR sensor:

• 1. High sensitivity and a low-noise signal.
• 2. A large operating distance from the magnet is possible.
• 3. Angle of measurement is up to 180° but with higher angle sensitivity.
• 4. Possible disturbance from external stray fields.

For the Hall sensor:

• 1. Because of internal preamplification, sensitivity is comparable.
• 2. Sensor functions only in the near field of the magnet.
• 3. Angle of measurement is up to 360°.
• 4. Possible disturbance from external stray "dipole fields."

## Comparing Sensor Specifications

For our experiment, the two sample sensors are the KMZ43T MR angle sensor from Philips and the iC-MA Hall sensor from iC-Haus.

We shall exclude the various integrated evaluation functions of the Hall sensor from this study (for further discussion see sidebar "iC-MA Sensor Functions") and concentrate instead on the analog sensor signals which have been preconditioned on the chip. In the experiment these analog signals are linked to the evaluation circuitry.

Manufacturers' data sheets, as shown in Figure 2, don't usually specify the quality of the analog sine/cosine sensor signals with respect to harmonic-free waveform, amplitude synchronism, phase precision, and offset nor do they entirely specify changes in field strength dependency or temperature. The information provided is, however, sufficient to let us adapt the evaluation circuitry to the sensor and to correct first-order signal errors.

We want a reasonable signal level. The MR sensor's typical signal amplitude of 70 mV requires preamplification; in contrast, the Hall sensor provides preamplification on chip. Nonmatching amplitudes are not acceptable: a difference between the sine and cosine signal amplitude causes an angle error of ~0.2° (with respect to the signal period) at a difference in amplitudes of 0.7%. While the MR sensor does not suffer from nonmatching amplitudes, the Hall sensor will need to be calibrated due to the 5% signal-referenced specification.

Calibration of the offset is even more important because as little as a 1% error for both the sine and cosine signal leads to an angle error of ~0.8° (with respect to the signal period). The offset of the MR sensor is considerably higher than that of the Hall sensor, which is already conditioned on the chip. For more precise angle measurements both sensors will require additional offset calibration.

Change in offset voltage with temperature is also relevant to the angle error. With the MR sensor, an assessment based on drift values produces a signal-referenced change of 0.3% across 100 K, thus marking out error margins. Unless we compensate for the drift with the evaluation circuitry, the angle error must lie within these margins. With the Hall sensor, information on drift is not directly available. We narrow down the drift values based on the specifications governing system accuracy which include those for the on-chip interpolator. Since the sensor error is <0.5°, the provided interpolation resolution of 6 to 8 bits (1.4° angle error at 8-bit resolution) is too crude and exceeds the achievable resolution of the analog Hall signals.

Rather than study the electrical characteristics of the individual parts, it's more useful to assess the overall system, including the designated evaluation circuitry. Measuring the absolute angle error against a reference system should tell us how both sensor types behave in a magnetic field when assembled with typical mechanical tolerances. According to the data sheets the sensors should tolerate alignment variation of several tenths of a millimeter with respect to the center of the magnet axis.

## Angle Error Measuring Setup

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