IEEE SENSORS JOURNAL, VOL. 14, NO. 6, JUNE 2014
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Piezoelectric Resonance Sensors of DC Magnetic Field Yuri K. Fetisov, Senior Member, IEEE
Abstract— The operational principle, methods of calculation, and designs of the dc magnetic field sensors using the combination of the Ampere force, the piezoelectricity, and the acoustic resonance have been described. The prototypes of the sensors based on a lead zirconate titanate ring and bimorph structures with radial or bending oscillations excited by the alternative current have been fabricated and investigated. The sensitivity of the sensors reached 245 V/(A·T) and the measured field range was from ∼10−5 T up to several Teslas. Index Terms— Acoustic resonance, Ampere force, magnetic field sensor, piezoelectricity.
I. I NTRODUCTION
T
HE magnetic field sensors widely used in science and engineering exploit various physical effects in order to convert the magnitude or direction of magnetic field into the output electrical signal [1]. During the sensors design one often uses a combination of two or more physical effects: the first one has to provide high sensitivity with respect to the field, and the second one has to provide electrical voltage at the sensor output. In the microelectromechanical magnetic field sensors the Ampere force affects the conductor carrying a current that results in a deformation of the sample. This deformation is then transferred into output electrical voltage using optical, capacitive, or piezoresistive sensing techniques [2]. In the magnetoelectric magnetic field sensors based on composite materials or laminated ferromagnetic-piezoelectric structures the magnetostriction results in a deformation of the sample, which is then converted into the voltage due to the piezoelectricity [3]. A possibility to use a combination of the Ampere force and the piezoelectricity to measure dc magnetic field has been demonstrated [4]–[6]. However, the sensitivity of such sensors fabricated using piezoelectric samples of disk or rectangular shape was rather low, less than ∼ 0.24 V/(A·T).
Manuscript received December 4, 2013; revised January 11, 2014; accepted January 11, 2014. Date of publication January 21, 2014; date of current version April 14, 2014. This work was supported in part by the Ministry of Education and Science of Russia and in part by the Russian Foundation for Basic Research under Project 13-02-12425 ofi_m2. The associate editor coordinating the review of this paper and approving it for publication was Dr. Kailash Thakur. The author is with the Moscow State Technical University of Radio Engineering, Electronics, and Automation, Moscow 119454, Russia (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2014.2301711
Fig. 1. Frequency response of dc field sensor based on PZT ring. Excitation current I = 0.3 A passes through external cut electrode.
The present paper describes the operational principle and designs of the dc magnetic field sensors using the combination of three effects: the Ampere force, the piezoelectricity, and the acoustic resonance. Due to the use of acoustic resonance, the sensitivity of the sensors has been considerably enhanced. The second part of the paper describes the theory, design, and measured characteristics of the sensor using radial acoustic oscillations in the piezoelectric ring. The third part describes the theory, designs, and measured characteristics of the sensors using bending acoustic resonance in the piezoelectric bimorph structure with various electromagnetic excitation systems. In conclusion the directions and prospects to improve parameters of the piezoelectric resonance magnetic field sensors are discussed. II. P IEZOELECTRIC R ING S ENSOR A. Theory for the Piezoelectric Ring Sensor Let us consider a sensor based on a piezoelectric ring [7], which is shown schematically in the inset to Fig. 1. The piezoelectric ring with medium radius r , thickness l, and width a is poled in the radial direction. Conducting electrodes of thickness δ are deposited onto the inner and outer surfaces of the ring. One of these electrodes is cut and carries ac current I (t) = I cos(2πft) with amplitude I and frequency f . The dc magnetic field B is applied perpendicularly to the plane of the ring. The generated voltage u is measured between the electrodes. Let us evaluate the amplitude of the generated voltage. Each segment of the electrode carrying current I in magnetic field B is under the action of the radial Ampere force.
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Fig. 2. Voltage u generated between PZT ring electrodes at resonance on measured field B for different currents I : 1-0.05 A, 2 -0.3 A, 3 -1 A.
Fig. 3. Frequency response of bimorph PZT sensor with excitation current passing through central electrode for B = 0.1 T and I = 24 mA.
This force creates tangential tensile or compressive stress in the ring, the magnitude of which is given by the formula
homogenous field B up to 1.4 T oriented perpendicularly to the ring plane. The electrode was fed via a ferrite transformer with the voltage from a tunable oscillator within f = 1-180 kHz, which excited the current up to 1.5 A. The voltage generated by the structure was measured by digital oscilloscope with the impedance of 1 M. Fig. 1 shows the measured dependence of the voltage u generated by the ring at the current frequency f . At fr = 60.3 kHz the signal exhibits resonance with an amplitude of u r = 0.73 V and Q = 118, which corresponds to excitation of a lower radial acoustic mode in the ring. The estimated frequency of the mode is 60.0 kHz, being in good agreement with the measured value. The amplitude of the noise at f > 30 kHz remained constant and did not exceed 8 mV. Fig. 2 shows the dependence of u measured at resonance frequency on the magnetic field B at various currents passing through the ring electrode. The sensitivity of the sensor with respect to the field exhibited growth from 0.002 V/T to 0.3 V/T when the current was increased from 0.01 A to 1.5 A. The normalized sensitivity was u/(IB) ∼2 V/(A·T). Estimation using Eq.(4) for the parameters of the PZT ring and the measured Q value yields ∼2.6 V/(A·T), that is in good agreement with the measured value. As it was shown in [8], the ring sensor can be excited without a contact by using the ac magnetic field bcos(2πft) applied perpendicularly to the ring plane. The ac field, in accordance with the Faraday induction law, creates ac current I = 2π 2 f r 2 b in the electrode resulting in the above described effects. In this case the sensitivity of the sensor can be changed by adjusting magnitude of the field b.
T1 = I r B/(al).
(1)
The electric displacement D and mechanical deformation S in the piezoelectric ring are related to the mechanical stress T and the electric field E by the following equations D3 = d31 T1 + εε0 E 3 ,
(2)
S1 = s11 T1 + d31 E 3 .
(3)
In (1)-(3) ε0 is the dielectric constant, d31 is the piezoelectric modulus, s11 is the compliance, and ε is the permittivity of the dielectric. The subscripts “1” and “3’ refer to the tangential and radial components of the quantities, respectively. Using (2), we first determine a relation between the field strength in the piezoelectric and the mechanical stress for the open circuit (D3 = 0):E 3 = −d31 T1 /(εε0 ). Then, using (1), we obtain the following expression for the voltage: d31 r I B. (4) εε0 a As one can see, u depends on the electrical parameters of the piezoelectrics and both the radius and width of the ring as well. The voltage increases linearly with the current I and field B, but is independent on the current frequency f and the ring thickness l. When the current frequency f coincides with the frequency √ of the radial oscillations of the ring fr = (1/2πr ) Y/γ (where Y is the Young’s modulus and γ is the density of the dielectric), the magnitude of deformations in the ring exhibits resonant growth and the voltage increases by a factor of Q. u = E 3l =
III. P IEZOELECTRIC B IMORPH S ENSOR B. Ring Sensor Design and Characteristics
A. Theory for the Piezoelectric Bimorph Sensor
The measurements have been carried out on lead zirconate titanate Pb0.48 Zr0.52 TiO3 (PZT) ring with r = 8 mm, l = 1.3 mm, a = 4 mm, ε = 1750, and d31 = 175 pC/N. The thickness of Ag electrodes on the PZT surface was ∼2 μm. The ring was poled in the radial direction. The resistance of the outer cut electrode was ∼0.1 and the capacitance of the structure was about of 3 nF. The ring was placed between the poles of an electromagnet in the
Let us consider a sensor based on a bimorph piezoelectric structure, which is shown schematically in the inset to Fig. 3 [9]. It consists of two piezoelectric layers with metal electrodes. One electrode is between the layers and the two others are on the outer surfaces. The layers are poled in opposite directions perpendicularly to the sample plane. The structure has length L along the “x” axis, width a along the “y” axis, and total thickness l along the “z” axis. One end
FETISOV: PIEZOELECTRIC RESONANCE SENSORS OF DC MAGNETIC FIELD
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It is seen from (7), that the voltage depends on electrical and mechanical parameters of the piezoelectric, dimensions of the structure, and increases linearly with the current I and the measured magnetic field B. B. Bimorph Sensor Design and Characteristics
Fig. 4. Dependence of the sensor output voltage u at resonance frequency 170 Hz on dc field B for excitation current I = 24 mA.
of the structure (at x = 0) is free while the other (at x = L) is rigidly clamped. The ac electric current I ( f ) with frequency f passes through the middle electrode. The measured magnetic field B is applied along “y” axis. The Ampere force F is directed along “z” axis and results in bending of the sample causing the ac piezoelectric voltage u( f ) between the outer electrodes. The action of the uniformly distributed transverse force with linear density F1 = IB lead to the appearance of tangential stress in the sample which has non-uniform distribution across the structure’s length and thickness: T1 (x, z) = (F1 /2I )x 2 z.
(5)
The stress equals zero at x = 0, increases drastically while approaching x = L, and turns out to zero at the middle plane z = 0. At the bending of bimorph structure one layer elongates (T1 > 0) while the other layer contracts (T1 < 0) resulting in summation of electrical voltages generated by the layers. Using (2) and open circuit condition (D = 0), one gets a non-uniform distribution of electrical field in the structure: E z (x, z) = −d31 Tx (x, z)/ε0 ε.
(6)
Using equation for F1 and taking into account opposite directions of the poling, and integrating (6) over the structure volume, one obtains the expression for the charge generated at the outer surfaces of the piezoelectric layers: d31l L 3 I B , (7) 24 J where J = al3 /12 is the moment of inertia of cross-section with respect to the neutral axis of the structure. So as the surfaces of the layers are metalized, the requirement of constant potential results in a redistribution of free charges over the electrodes. The voltage may be estimated using the formula u = q/C, where C = εε0 a L/l is the capacitance of the structure. Finally, taking into account increase of mechanical stress by a quality factor at the resonance frequency, one gets the expression for electric voltage u generated by the piezoelectric bimorph structure with ac current placed in magnetic field B: q=
u=Q
d31 L 2 I B. εε0 al
The measurements have been carried out on bimorph structure made of PZT of the following dimensions L = 25 mm, a = 8 mm, l/2 = 0.1 mm, and parameters ε = 2000, and d31 = 190 pC/N. The PZT layers have been poled in opposite directions. The ac current with magnitude I = 0 - 120 mA and frequency f = 10 Hz-200 kHz was passed through the middle electrode of the structure. A bias field B = 0 - 1 T was applied with an electromagnet. Fig. 3 shows the measured f dependence of the voltage u generated by the sensor on I = 24 mA and B = 0.1 T. The resonance peak at fr = 153 Hz with magnitude u r = 0.38 V and quality factor Q = 43 which is due to excitation of the main bending mode of the sample. Fig. 4 shows the measured field B dependence of the voltage u r (B) at fr for I = 24 mA. The B-dependence of u r was found to be linear for the current I < 10 mA and field B < 0.05 T, and became essentially nonlinear for higher I and B. The nonlinearity of the u r (B) dependence is due to nonlinearity of bending oscillations, that was confirmed by a lowering in the resonance frequency from 153 Hz to 148 Hz with an increase in I or B. The normalized sensitivity of the piezoelectric bimorph sensor calculated using the initial part of the u r (B) curve in Fig. 4, was ∼165 V/(A·T). Estimation of the sensitivity using (8), given above parameters of the sample, and the measured Q = 43 gives ∼100 V/(A·T) which is in agreement with the measured value. This sensitivity is four orders of magnitude higher than for the piezoelectric disk sensor [5] and two orders of magnitude higher than for the piezoelectric ring sensor [7].
(8)
C. Piezoelectric Bimorph Sensor With a Coil Let us consider a sensor based on the same bimorph structure but with a coil, which is shown schematically in Fig. 5. The coil contains N turns of a wire carrying an ac current I ( f ) of the frequency f . The current produces ac magnetic moment M(t) which interacts with the field B and excites bending oscillations in the structure followed by generation of the voltage u. The distributed torque of linear density M1 = I /(N/L)al B affects the coil and creates nonuniform tangential stress in the structure Tx (x, z) = (M1 /J )x z.
(9)
Following the above described procedure, using (2)-(3), and taking into account an increase of the stress by a quality factor at resonance, one gets the expression for the voltage: u1 = Q
3d31 N I B. 2εε0
(10)
Fig. 5 shows measured voltage u vs. frequency f dependence for the bimorph PZT structure with dimensions of
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IEEE SENSORS JOURNAL, VOL. 14, NO. 6, JUNE 2014
equal to u/(IB) = 110 V/(A·T) at the resonance frequency fr = 0.67 kHz and for excitation current I = 10 - 100 mA. The power which is required to excite acoustic oscillations in the above described piezoelectric magnetic field sensors is of about 1-100 mW. One should note, that sensitivity of the magnetic field sensors can be increased: (i) by using the piezoelectric materials with higher ratio d31 /ε and higher acoustic quality factor Q, e.g. the langatate or quartz crystals [10]; (ii) by improving the design of the structures used; (iii) by lowering the air pressure in order to increase both the acoustic quality factor and output electrical voltage. Fig. 5. Frequency response of bimorph PZT sensor with excitation coil for B = 0.27 T and excitation current I = 17 mA.
IV. C ONCLUSION Thus, piezoelectric sensors of dc magnetic fields using combination of the Ampere force, the piezoelectricity, and the acoustic resonance have been proposed and fabricated. The sensor using radial acoustical oscillation of the piezoelectric ring showed the normalized sensitivity of 2 V/(A·T), while the sensors using bending acoustic oscillation of the piezoelectric bimorph structure had the sensitivity of 245 V/(A·T). The sensors allow measurement of permanent magnetic fields in the range from ∼10−5 T up to several Teslas. Due to rather high and electrically controlled sensitivity, wide range of measured magnetic fields, low power consumption, and simple design the piezoelectric sensors will find their applications in various fields of science and industry. R EFERENCES
Fig. 6. Dependences of the sensor output voltage u on dc field B at the resonance frequency for excitation current I = 17 mA.
L = 9.5 mm, a = 8 mm, and l/2 = 0.1 mm. The coil had resistance of 4.8 and contained N = 75 turns of the 80 μm copper wire. The resonance near the frequency fr = 1.14 kHz with magnitude of u r = 1.2 V and Q = 49 corresponds to excitation of bending oscillations of the structure. Estimation using (10) and experimental parameters gives the voltage u r ∼0.3 V, which coincides with the measured value by an order of magnitude. Fig. 6 demonstrates linear output voltage u r vs. magnetic field B dependence for the piezoelectric sensor at the excitation current I = 17 mA. The normalized sensitivity of the sensor was equal to u/(IB) = 245 V/(A·T), that is higher than for the bimorph sensor with linear current. There was no electric connection between the coil and the electrodes in this sensor that decreased the direct electrical leakage and reduced total noise level in the output signal up to ∼0.1 mV. By using the measured normalized sensitivity and the noise level, one gets the estimation for the minimal registered dc fields as small as Bmin ∼2·10−5 T. The same piezoelectric bimorph structure was used to fabricate a sensor with planar excitation coil. The coil on a 30 μm thick dielectric film had dimensions of 8 mm × 8 mm and contained 9 concentric turns of 50 μm width micro strip. The coil was glued to the electrode near the free end of the structure. The normalized sensitivity of the sensor was
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FETISOV: PIEZOELECTRIC RESONANCE SENSORS OF DC MAGNETIC FIELD
Yuri K. Fetisov (SM’96) received the Ph.D. degree in solid state physics from the Moscow Engineering Physics Institute, Russia, in 1981, and the D.Sc. degree in the physics of dielectrics and semiconductors from the Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Moscow, in 1993. He joined the Moscow State Technical University of Radio Engineering, Electronics and Automation (MIREA) as a Researcher in 1983. He was a Professor with the Physics Department in 1994, the Director of the Institute for Informatics of MIREA in 1998, and the Dean of the Faculty of Electronics of MIREA
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in 2007. He has held visiting appointments as a Visiting Researcher with Chiba University in 1995, Bochum University in 1999, as a Visiting Professor with Colorado State University in 1995, 1997, 1999, and 2001, Oakland University in 2005, 2006, 2010, and 2012, and University Paris-13 in 2007 and 2010. He is currently the Head of the Research-Educational Center Magnetoelectric Materials and Devices, MIREA, which is involved in research on ferromagnetic resonance, linear and nonlinear spin wave processes in thin magnetic films, the magnetoelectric effect in multilayer composite structures, and design of solid state magnetic and microwave devices. He is the co-author of more than 120 papers in peer-review journals and numerous presentations at international conferences. He has been a member of the Russian Academy of Natural Sciences since 2007.
