A digital Hall magnetometer with residual-voltage compensation and a sensitivity threshold of

4·10–4 Oe·Hz–1/2 for a PKhE602817 type sensor is described. An algorithm for compensating the residual

voltage by a factor of more than 300 is proposed.

Magnetic fields in the 10–3–103 Oe range are usually measured using a Hall transducer, which has high linearity,

small dimensions and inertia, and also a wide range of operating temperatures [1]. However, the accuracy with which a mag-

netic field can be measured with a Hall sensor is limited by its inherent residual voltage, which is due to the nonequipoten-

tial Hall contacts [1]. Hence, even in a zero magnetic field there will be a residual voltage Uo between the Hall contacts, pro-

portional to the current I flowing through the current contacts. For example, for the PKhE602817B sensor with a conversion

slope of 10 µV/Oe for a nominal current of 100 mA, the residual voltage amounts to 8 µV, which corresponds to a magnet-

ic-field strength of 0.8 Oe. The residual voltage in this case depends very much on the temperature, which considerably lim-

its the measurement range of the magnetometer in weak magnetic fields.

The error can be reduced by compensating the residual voltage of the Hall sensor [1]. The basic circuit of a magne-

tometer which uses this method is shown in Fig. 1. The measurement current I flows from the current source through the

switches S1–S4 into the Hall sensor HS. When there is no external magnetic field, the Hall sensor behaves as a passive linear

four-terminal network. By the reciprocity theorem [2], if a constant current I flows through the current contacts CC1 and CC2of the Hall sensor, corresponding to position 1 of switches S1 and S2, then a residual voltage Uo will be present on the Hall

(potential) contacts HC1 and HC2 of the Hall sensor. If now a current I flows through the contacts HC1 and HC2, corresponding

to position 2 of switches S1 and S2, exactly the same residual voltage Uo will be present on the contacts CC1 and CC2.

In a nonzero external magnetic field of induction B, the Hall sensor does not satisfy the conditions of the reciprocity

theorem. In the ideal case, when there is no residual voltage Uo, the voltage between the contacts HC1 and HC2 will be [1]

UH = KHBI,

where KH is the Hall coefficient. If a current I flows through the contacts HC1 and HC2, there will be a voltage UH of the

same modulus but of opposite sign between the contacts CC1 and CC2, since the Hall voltage is “antireciprocal” [1]. In gen-

eral, when both an external magnetic field and a residual voltage are present, because of the linearity of the Hall sensor we

can write

U1 = Uo + UH; U2 = Uo – UH, (1)

where U1 is the voltage corresponding to position 1 of switches S1–S4, while U2 corresponds to position 2. The Hall volt-

age is equal to half the difference between the voltages U1 and U2, while the residual voltage is equal to half the sum.

Measurement Techniques, Vol. 44, No. 7, 2001

A DIGITAL HALL MAGNETOMETER

ELECTROMAGNETIC MEASUREMENTS

V. K. Ignat’ev and A. G. Protopopov UDC 621.013 + 537.312

Translated from Izmeritel’naya Tekhnika, No. 7, pp. 46–49, July, 2001. Original article submitted December 25,

2000.

0543-1972/01/4407-0740$25.00 ©2001 Plenum Publishing Corporation740

This method of compensating for the residual voltage was used in [3],where the residual voltage was compensated by

using a synchronous integrator and constant switching of the current and potential contacts of the Hall sensor. However, this

method has two drawbacks. First, the synchronous integrator has an error of about 1%. Second, constant switching of the con-

tacts while measuring a magnetic field is the reason for pulsed interference. Since, at a constant current I and constant temper-

ature the residual voltage changes only slowly, these drawbacks can be eliminated if the residual voltage is determined immedi-

ately before measuring the magnetic field with a single switching of the current and potential contacts of the Hall sensor. For

further measurements of the magnetic field, this residual voltage must be calculated from the readings of the magnetometer, and

as a result the true value of the magnetic field strength will be obtained. The use of computer control enables the procedure for

such measurements to be simplified and increases its accuracy, and also enables uninterrupted measurements to be made.

The basic circuit of a digital magnetometer which implements this method is shown in Fig. 2. The instrument

consists of two functionally complete units:the Hall magnetometer and a digital control unit. The digital control unit is

741

Fig. 1. Basic circuit of the magnetometer:CSc) current source, HS) Hall sensor,

S1–S4) switches,A) amplifier, ADC) analog–digital converter, CS) control system,

and S) analog switch.

Fig. 2. Basic circuit of the digital Hall magnetometer:HS) Hall sensor, M1 and M4) K140UD708,M2) K157UD2A,

M3) K140UD26A,M5) K525PS2A,T1 and T2) KP301G, T3–T5) AOT110V, S1–S4) RES55A,L) miniature incan-

descent lamp,ADC) analog–digital converter, and CS) control system.

constructed in the form of a separate expansion plate for a type IBM PC/AT computer and consists of two parts: an ana-

log–digital converter ADC and a control system CS. The analog–digital converter selects the signal in a 16-digit port in

accordance with the address 304h. The control system is an eight-digit output port at the address 305h. The control sys-

tem triggers the analog–digital converter (digit 1 of port 305h),the K580VI53 timer (digits 5,6 and 7),changes the gain

in the analog–digital converter circuit (digits 4 and 3),and controls the analog switches T1 and T2 in the magnetometer

circuit (digit 2 of the same port).

In the Hall magnetometer, a four-terminal measurement circuit is used in order to eliminate the effect of the resis-

tance of the leads. The common source and the amplifier are supplied from separate transformer windings,and their com-

mon buses are dc decoupled. To eliminate the effect of the thermoelectric emf of the Hall sensor and the drift of microcir-

cuit M3, measurements are made at alternating current. The signal generator (at a frequency of 1 kHz) takes the form of

microcircuit M1 in a Wien–Robinson bridge circuit [4] and controls the current source, based on microcircuit M2 [5]. The

amplitude of the alternating current passing through the Hall sensor HS is regulated by resistor R1.

The voltage from the Hall sensor is amplified by preamplifier M3 and amplifier M4. The signal from the output of

M4 is applied to the X input of a synchronous detector, based on the analog premultiplier M5 [6]. The four-terminal alter-

nating current measurement circuit has an error, since there is a voltage between the common buses of the current source and

the amplifier produced by the alternating current I flowing through the current leads of the Hall sensor and the capacitance

C0 (see Fig. 1). The capacitance C0 is made up of the capacitance which occurs between the secondary windings of the trans-

former, supplying the amplifier and the current source, and the capacitance due to the fact that the voltage U, applied to the

input of the analog–digital converter, the signals Uk, controlling the electronic switch S (see Fig. 1),and the signals Up, con-

trolling switches S1–S4,have a common bus (the system bus of the computer). Hence, the capacitive current I0 begins to

flow through the capacitance C0 and the potential output of the Hall sensor, producing a voltage drop in it. This voltage is

added to the useful signal of the Hall sensor and is the reason for the occurrence of a systematic error at the output of the

magnetometer – a dc voltage unrelated to the measured magnetic field.

There are several methods of reducing this systematic error. The first method involves choosing the frequency of

the alternating current flowing through the Hall sensor. On the one hand, the frequency should be low so that the amplitude

of the capacitive current flowing through C0 is a minimum,while on the other the frequency of the alternating current should

be sufficiently high so that the high-pass filters (after the amplifiers M3 and M4) can cut off network interference. The sec-

ond method of reducing the systematic error involves minimizing the capacitance C0. To do this,the secondary windings of

the transformer of the current supply unit and the amplifier are arranged sectionally on the transformer core and a reference

signal on the Y input of the premultiplier M5 is applied from the master oscillator M1 through the optron T3. The working

point of the optron T3 is on the linear part of its characteristic and is established by the variable resistors R3 and R4. The

amplitude of the variable component at the output of optron T3 is regulated by the variable resistor R2. The analog switch-

es T1 and T2 and the relays S1–S4 are controlled by the control system CS through the optrons T4 and T5; the voltage Upand Uk are applied to the input of the optrons T4 and T5, which operate as switches. The capacitance between the light-emit-

ting diode and phototransistor in the optron in this case is not more than 2 pF [7].

The analog switches based on field-effect transistors T1 and T2 serve to eliminate switching interference, connect-

ed with the operation of the relays S1–S4. When the relay is switched, the current source and the amplifier are not connect-

ed to the Hall sensor, so that the preliminary amplifier M3 is driven to saturation. Hence, switching interference occurs in

the form of short pulses with a length of the order of 10 msec. In order to eliminate this,a high-level signal Uk from the con-

trol system is applied to the input of optron T5 before switching the relay. A voltage of –15 V appears on the gates of tran-

sistors T1 and T2 and hence they conduct and shunt the interference.

The contacts of HC1, HC2 and CC1 and CC2 are switched by the relay S1–S4,connected with the computer of the

control system via the optron T4. The optron, which is fed from a separate winding of the transformer, is controlled using

the logical levels of the voltage Up of zero digit of port 305h.

The purpose of resistor R5 is to balance the Hall sensor [1] and it enables the residual voltage to be reduced some-

what so that the chosen gain does not lead to saturation of the amplifier M4.

742

The voltage U from the output of the magnetometer is applied to the input of a ten-digit analog–digital converter,

based on a K1113PV1 microcircuit [8]. The algorithm for controlling the magnetometer computer is shown in the circuit in

Fig. 3 and has the following sequence:

1. Program control using the analog–digital converter is organized by selecting a signal of length 512 readouts in

the data matrix U1.

2. The application of a high level of voltage Uk from the control system CS (see Fig. 2) closes the switches T1

and T2, thereby preventing the occurrence of pulsed interference at the output of the magnetometer during the relay

switching time.

3. The control system establishes a high voltage level Up at the output,governed by the program,and the relays

S1–S4 switch.

4. The application of a low level of voltage Uk from the control system CS opens the switches T1 and T2.

5. Program control is organized by selecting a signal of length 512 readouts in the data matrix U2.

6. The mean value of the data matrices U1 and U2 is calculated.

7. The residual voltage Uo is calculated as the half-sum of the mean values of the data matrices U1 and U2.

8. If this voltage exceeds one tenth of the dynamic range of the magnetometer, i.e., the sensor is not balanced, bal-

ancing is carried out manually by changing the resistance of R5 so as to reduce the absolute value of the unbalance voltage.

After this, the control program returns to the start of the algorithm (paragraph 1).

743

Fig. 3. Sketch of the algorithm for controlling the magnetometer.

9. If the change in the resistance of R5 does not reduce the absolute value of the residual voltage, the process of

balancing the whole sensor is regarded as completed. The last value of the residual voltage Uo is stored. The Hall voltage

is then measured taking into account the residual voltage without switching the relay.

10. The selection of a signal of length 512 readouts in the data matrix U is organized by the control program using

the analog–digital converter.

11. The mean value of the data matrix U is found.

12. The Hall voltage is calculated by subtracting the residual voltage Uo from the mean value of the data matrix U.

The algorithm described enables one, if necessary, to track the change in the residual voltage and to take it into

account in measurements of the magnetic field.

The magnetometer was assembled in a container with dimensions of 400 × 200 × 200 mm,and the operational ampli-

fier M3,the switches S1–S4,the analog switch T1 and the optrons T4 and T5 were placed in a separate aluminum screen inside

the container. A type PkhE602817B Hall transducer is used; its conversion slope is 10.3 µV/Oe for a nominal current through

the sensor of 100 mA,and the residual voltage is 8 µV. The magnetometer was calibrated using a long solenoid placed in a

multilayer magnetic screen. The conversion slope of the instrument is set by the feedback resistor R6 (it is chosen as a regu-

lator) and is 1 V/Oe. The amplitude-frequency characteristic of the magnetometer was measured, the passband of the instru-

ment being 4 Hz. This is set by the low-pass filters,which are connected after the premultiplier M5, which forms part of the

analog-digital converter. The low cutoff frequency is due to the fact that the magnetometer is designed to measure constant

and slowly varying magnetic fields, in particular, for scanning the magnetic flux distribution in high-temperature supercon-

ductors,and enables the effective network interference to be reduced. If necessary, the bandwidth of the magnetometer can be

increased to half the sampling frequency. The nonlinearity of the instrument – the root mean square deviation of the points of

744

Fig. 4. Spectral density of the magnetic noise of the instrument (a), and the response

of the instrument to an external magnetic field (b).

the calibration graph from the “best” straight line – amounted to 0.2%. The magnetometer has two ranges – ±0.2 Oe and ±2 Oe,

which can be switched by program control of the voltage divider which forms part of the analog-digital converter.

The sensitivity threshold of the magnetometer is determined by the noise of the operational amplifier M3. The spec-

tral density of the noise voltage of microcircuit M3 does not exceed 3 nV·Hz–1/2 in the 800–1100 Hz band [9],which corre-

sponds to magnetic noise, reduced to the input,of Hn = 4·10–4 Oe·Hz–1/2.

In order to measure the noise of the instrument,the Hall sensor was placed in a thick-walled magnetic screen,and

the voltage U from the output of the instrument was applied to the input of the analog-digital converter. By means of a pro-

cessing program,ten time intervals were generated, inside which a signal was selected with a sampling frequency of 62.5 Hz

and a length of 1024 readouts. For each time interval, we calculated the spectrum using a fast Fourier transformation algo-

rithm with a Hann time window [10] and was averaged over ten samples of the spectrum using Bartlet’s method [10]. The

spectral density of the magnetic noise is shown in Fig. 4a, while in Fig. 4b we show the response of the instrument to mag-

netic field pulses of rectangular form (a meander wave form of frequency 0.2 Hz),produced in the calibration coil.

Since it is quite difficult to obtain a residual magnetic field with a strength of less than 1 mOe without using super-

conducting screens,the degree of compensation of the residual voltage was found indirectly. The Hall sensor was placed in

the thick-walled magnetic screen,assuming that the internal magnetic field in it Hi ≤ 10 mOe. The sensor was balanced as

described in paragraphs 1–9 of the above algorithm,and the Hall voltage UH = KH Hi was then measured as described in para-

graphs 10–12. The resistor R5 was then used to disturb the equilibrium of the sensor, corresponding to a magnetic field of

Ho = KH Uo ≈ 0.1 Oe. Then,after carrying out paragraph 1 of the algorithm, keeping the position of the slider of resistor R5

fixed, we measured the voltage U1 = UH + Uo (the mean value of the data matrix U1). When carrying out paragraphs 2–4 of

the algorithm the contacts of the sensor are switched. The voltage U2 = UH + Uo/Ks (the mean value of the data matrix U2)

was calculated when carrying out paragraphs 5 and 6. The degree of compensation (suppression) of the residual voltage was

found from the formula

Ks = (U1 – UH)/(U2 – UH)

and did not exceed 300.

This research was supported by the State Program “Present Problems in the Physics of the Condensed State,” sec-

tion “Superconductivity.”

REFERENCES

1. E. V. Kuchis, Methods of Investigating the Hall Effect [in Russian],Sovetskoe Radio,Moscow, (1974).

2. K. Shimoni, Theoretical Principles of Electrical Engineering [Russian translation], Mir, Moscow (1964),p. 339.

3. V. K. Ignat’ev and A. L. Yakimets, Prib. Tekh. Eksp., No. 5,104 (1997).

4. P. Horowitz and W. Hill, The Art of Circuit Design. Vol. 1 [Russian translation], Mir, Moscow (1983).

5. W. Titse and K. Shenk,Semiconductor Circuit Design [Russian translation], Mir, Moscow, (1982).

6. V. N. Timontseev,A. M. Velichko,and V. A. Tkachenko, Analog Signal Premultipliers inRadio-Electronic Apparatus

[in Russian],Radio i Svyaz’, Moscow (1982).

7. A. V. Bayukov et al., Semiconductor Devices: Diodes,Thyristors, and Optoelectronic Devices. A Handbook

[in Russian],Énergoatomizdat, Moscow (1985).

8. I. V. Novanchenko et al.,Microcircuits for Everyday Radio Apparatus. A Handbook[in Russian],KUbK-a,Moscow

(1996).

9. Integrated Microcircuits: Operational Amplifiers, Vol. 1 [in Russian],Nauka,Moscow (1993).

10. S. L. Marple Jr., Digital Spectral Analysis and Its Applications [Russian translation], Mir, Moscow (1990).

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