A Non-Invasive Thermal Drift Compensation Technique Applied to a Spin-Valve Magnetoresistive Current Sensor

A compensation method for the sensitivity drift of a magnetoresistive (MR) Wheatstone bridge current sensor is proposed. The technique was carried out by placing a ruthenium temperature sensor and the MR sensor to be compensated inside a generalized impedance converter circuit (GIC). No internal modification of the sensor bridge arms is required so that the circuit is capable of compensating practical industrial sensors. The method is based on the temperature modulation of the current supplied to the bridge, which improves previous solutions based on constant current compensation. Experimental results are shown using a microfabricated spin-valve MR current sensor. The temperature compensation has been solved in the interval from 0 °C to 70 °C measuring currents from −10 A to +10 A.


Introduction
Advances in the solid-state sensor manufacturing industries have allowed a significant improvement in the miniaturization, consumption and cost of instrumentation and measurement systems. The above benefits have been reached using semiconductors and transition metals as reference materials. However, the temperature dependence of their physical properties demands the use of specific compensation techniques, especially where the measurand of interest will not be the temperature (pressure, vibration, electrical current, etc.). In this way there are various and different efforts that have been dedicated to the reduction of the sensors temperature dependence. There are two main groups in which the temperature compensation techniques could be classified: hardware compensation and digital processing compensation methods. In [1] different hardware thermal compensation methods dedicated to a piezoresistive sensor are presented. Particularly, it is required to have complete accessibility to the sensor Wheatstone bridge terminals or the use of active components (like bipolar transistors). The temperature compensation of the fluid to be measured is of special relevance in a well-done flowmeter design. Following this goal, various solutions are proposed in [2,3] where some mathematical conditions must be satisfied or where two Wheatstone bridges were needed. In the power electronics field the techniques described in [4,5] are interesting. In [4], current sensing was done by temperature compensation of the inaccuracy caused by the inductor parasitic ohmic resistance temperature dependence. The compensation was successful but complex to satisfy in its mathematical requirements. The work described in [5] was based in a frequency domain compensation procedure and was used in a low voltage power supply situation.
Digital processing algorithms have been applied reducing the thermal dependence in piezoresistive sensors [6], load cells [7] or in pressure capacitive sensors [8]. These techniques require an additional processing hardware based in digital intelligence (computer, microcontroller or digital signal processor) and dedicated software. All of them are, in a large number of industrial situations, difficult to apply.
In this work the thermal drift of a microfabricated current sensor is reduced by the use of a simple hardware compensation method. This represents an improvement of a technique that was first developed in [9]. The sensor is a Wheatstone bridge implemented by four magnetoresistances of the spin-valve type [10]. The compensation is solved using a resistive temperature sensor by means of a simple procedure because no equilibrium Wheatstone bridge condition is needed, nor two bridge units or full access to the bridge terminals are required. The magnetoresistive current sensing technology has been successfully applied in power converters [11] or in instrumentation and measurement area (current probes design) [12]. In the present work the temperature compensation has been solved in the temperature interval from 0 °C to 70 °C measuring currents from −10 A to +10 A.

Compensation Method
A constant current driven Wheatstone bridge sensor is used to apply the compensation method ( Figure 1). The driving sensor current source was described in [13,14] and is based in a Generalized Impedance Converter circuit (GIC). The choice of a constant current source as the sensor bridge power supply was based on previous works that show a remarkable reduction in the temperature coefficient of the bridge sensitivity [15][16][17][18]. where R B is he GIC circ ref , [13,14].

Equation normalized before comp
The main compensate v o,c (t) will ha        or in is (12) and in a more compact form: (13) where TC denotes temperature coefficient of the quantity to be considered. In order to have TC(v o,c ) = 0, the value of the resistance R will be obtained from the equation: (14) Depending on the position of the temperature sensor R s (t) inside the GIC circuit two different expressions for resistance R could be obtained. If series association R s (t)+R plays the role of the resistances R1 or R3 [equations (6) or (7)] the equation (14) could be rewritten as: On the other hand, if the association R s (t)+R is placed in resistances R2 or R4 [equations (8) or (9)] equation (14) will give to: (16) From equations (15) and (16)  As a consequence of this and considering only passive resistances, the compensation method will be possible and effective if: The above expressions mean that │TC(R s )│>│TC(S)│ independently of the relationship between the sign of the temperature coefficients.

Experimental Results
In this section a MR electrical current sensor is compensated with a ruthenium based temperature sensor. Both sensors were fully microfabricated in the same substrate at the INESC-MN facilities (Lisbon). The temperature compensation sensor was integrated in the same microfabrication process as the spin-valve MR current sensor. This fact allows a close temperature matching between both sensors. Ruthenium is more useful than platinum as the material to implement the temperature sensor because its fabrication process is more compatible with spin-valve processes, as the material is often used in the spin-valve stack by several groups in synthetic antiferromagnetic layers, see for example [19]. The ruthenium target is included in the same deposition tool used for spin valve deposition and does not require the change of the deposition infrastructure configuration needed by the platinum. In spite of its lower sensitivity (0.16 %/°C) compared to platinum (0.36 %/°C) both materials belong to the same group of metals sharing good temperature linearity. Additionally ruthenium has lower fabrication costs than platinum.
The electrical current sensor is configured as a full Wheatstone bridge. Four active 3 µm × 100 µm spin-valve sensors were deposited by ion beam deposition [20]  Each single spin-valve sensor element was magnetically characterized providing a minimum resistance R min equal to 740.2 Ω ± 1.7 Ω and a maximum resistance R max equal to 801.1 Ω ± 2.1 Ω, this mean a MR effect of 8% according to R max -R min /R min .
The electrical current that generates the magnetic field to be measured circulated through an external copper conductor as it can be seen in Figure 3(a) (dimensions in mm). The chip layout could be shown in Figure 3(b) where the external conductor has been put on top.
Following the method described in Section 2, the MR Wheatstone sensor was biased by a constant current of 1 mA using the GIC circuit shown in Figure 2. A constant gain factor of n = 100 was designed for a reference input current of 100 µA given by the integrated circuit REF200. So the resistance values were: R1 = 2 kΩ, R2 = 1 kΩ, R3 = 5 kΩ, R4 = 1 kΩ. The MR current sensor was placed inside a climate chamber (model CH-600 from Angelantoni) that generated a controllable and stable temperature (with an accuracy of ±0.3 °C). The experimental sensitivity of the sensor was determined collecting the voltage output of the MR current sensor responding to steps of 1 A of the electrical input current that was selected within the range of ±10 A. An electrical current sweep was done at a temperature included in the interval from 0 °C to 70 °C and with increments of 10 °C. The results of these measurements corresponding to the extreme temperature values of the interval are shown in Figure 4, it could be noticed the decrease in the sensor sensitivity as the temperature increases. Taking the value 0 °C as temperature reference t o the thermal coefficient sensitivity was TC(S) = −0.152 %/°C. The equivalent resistance of the bridge was also measured, note that it is linear temperature dependent with opposite sign with respect to TC(S) ( Figure 5).
The sensitivity of the ruthenium thermoresistive sensor was obtained based on measurements taken with a Keithley K2700 digital multimeter. The results are depicted in Figure 6 showing the ruthenium resistance value as a function of the temperature. A linear least-squares fit was applied to the collected data in order to estimate the characteristic parameters of the Ru sensor. The main parameters obtained were a 0 °C reference resistor value of 904 Ω, a temperature sensitivity of 1.46 Ω/°C and a positive temperature coefficient TC(R s ) of 0.161 %/°C. The experimental correlation coefficient was 0.998 showing the good linearity offered by the ruthenium resistance temperature detector ( Figure 6).          for. This condition is easy to find when comparing the temperature coefficient of a resistance temperature sensor with the target sensor temperature drift.
The temperature compensation sensor was integrated in the same microfabrication process as the spin-valve MR current sensor. This fact allows a close temperature matching between both sensors. Ruthenium is more useful than platinum as the material used to implement the temperature sensor because its fabrication process is more compatible with existing spin-valves processes. Ruthenium is a material used in some spin-valves fabrication processes and does not require any changes to the deposition infrastructure configuration as needed by platinum.
The proposed technique has been applied to a magnetoresistive current sensor that finds application in industrial switched-mode power supplies, power converters or electrical drives. The current source designed by the GIC circuit improves the other classical constant current sources like the Howland circuit because it does not need good matching between resistances involved in the circuit and without requiring positive feedback in the GIC circuit as it occurs in the Howland current source.