Design of resonance based DC current sensor using BAW quartz resonators

Accepted Manuscript Title: Design of Resonance Based DC Current Sensor Using BAW Quartz Resonators Authors: Sameera Pisupati, Divija Kundukoori, Nithin Mekala, Suresh Kaluvan, Haifeng Zhang PII: DOI: Reference:

S0924-4247(17)31082-8 https://doi.org/10.1016/j.sna.2018.01.006 SNA 10561

To appear in:

Sensors and Actuators A

Received date: Revised date: Accepted date:

8-6-2017 28-11-2017 2-1-2018

Please cite this article as: Pisupati S, Kundukoori D, Mekala N, Kaluvan S, Zhang H, Design of Resonance Based DC Current Sensor Using BAW Quartz Resonators, Sensors and Actuators: A Physical (2010), https://doi.org/10.1016/j.sna.2018.01.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Design of Resonance Based DC Current Sensor Using BAW Quartz Resonators

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Sameera Pisupati, Divija Kundukoori, Nithin Mekala Suresh Kaluvan and Haifeng Zhang Smart Structures and Systems Laboratory, Department of Engineering Technology, University of North Texas, Denton, TX 76203.

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*Corresponding Author: [email protected]

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Highlight

 A novel DC-current sensor using quartz crystal is proposed in this paper.

) is unique and first of its kind.

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 The working principle of sensor (i.e Stiffening a BAW quartz crystal utilizing SMA Wire

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 The current flow in the SMA wire is tuning the resonance frequency of BAW quartz cryst

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al

 The proposed principle is very much useful for low electric current measurement applicat

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ion.

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Abstract

A novel approach is attempted to measure DC current in the range of 0 – 0.7A in this paper. The proposed current sensing system is designed using an AT-cut BAW quartz resonator sandwiched at the center of the rectangular beam. The SMA wire bonded over the rectangular beam changes its shape with the change in input current. The quartz crystal resonator is maintained at first mode resonance frequency using a closed loop resonator electronics. The electric current change in the

SMA wire contracts its length which bends the beam and produces an axial force on the quartz resonator which changes the resonance frequency of the BAW crystal placed in between the beam. The shift in quartz crystal resonant frequency is related to the input electrical current in the SMA wire. The analytical model of the entire current sensing system is derived, and the proposed concept is verified experimentally. It is observed that the experimentation results are highly linear,

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and it has the sensitivity of 350Hz/A DC current.

Keywords: DC Current sensor, SMA wire, Resonant sensor, Cantilever beam, and BAW Quartz crystal.

1. Introduction

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Infinitesimal fluctuation of electric current in an electronics circuit creates massive affect

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in the final output. The measurement of these small change in the electric current is very much necessary in the electronics research field and which motivates the researchers to invent various

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current measurement techniques. These current measurement techniques are categorized into

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three major principles, which are (a). Resistance based current measurement, (b). Inductance based current measurement, (c). Magnetic field based current measurement. This paper presents a

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completely novel Direct Current (DC) measurement technique using Bulk Acoustic Wave (BAW)

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Quartz crystal and Shape Memory Alloy (SMA) wire. The current measurement technique has very long literature history, a high frequency (MHz), high current (kA), and DC sensible of current measurement techniques using coaxial

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shunt resistive principle is discussed in [1, 2]. The copper trace current sensing technique is introduced [3] to avoid using of specific shunt resistance, in this technique, the intrinsic resistive

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property of copper trace materials used to sense the current flow. The Rogowski coil is another interesting current measurement technique which is working based on faraday’s law of induction

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[4], which has a high frequency bandwidth of current measurement, but it is not capable of DC current measurement. Hall-effect based electric current sensing technique is the one of accurate, very popular

and well commercialized current measurement technique, which is working based on the amount of Hall voltage generated when the current flows through thin materials. The Hall Effect current

sensor has the kilohertz frequency bandwidth current measurement, which is capable of measuring DC currents, but it has a heating issue for AC current measurements [5, 6]. The fiber optic current measurement technique is the one of the most popular technique to measure very high currents in the range of Kilo to Mega Ampere [7]. The rotational angle of linearly polarized light in the fiber optical cable is altered by the high current carried by cable.

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The Fluxgate current sensing technique is the one most accurate method available commercially nowadays, which works based on the magnetic field sensing technique [8]. The fluxgate current sensor has vast sensing range, which is from mA to kA current. Other than the traditional current sensing techniques, there are few kinds of literatures reports the resonant sensor concepts for DC current

measurement,

which

are

designed

using

the

SMA

wire-cantilever

beam,

Magnetorheological fluid-cantilever beam, and electromagnetic coil –cantilever beam [9-11].

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Resonant based electric current measurement has the advantage of high accuracy and easy

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interface with any digital circuits. The basic of resonant sensor concepts and design of its closed loop resonator electronics are discussed in [12-14]. In the resonant sensor, the change in resonant

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frequency of the resonator is measured with the change in force, mass and structural shape

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change of the resonator. Few kinds of literatures report the BAW crystal resonator based temperature and pressure sensors [15, 16]. Most of the BAW sensor uses Quartz crystal as

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resonators because which are well commercialized, thoroughly studied materials, very high Q-

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factor, linear force frequency behavior, high acoustic quality and high frequency. In this paper, a new kind of resonant based DC current sensor using a rectangular beam with quartz crystal and

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SMA wire is proposed.

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2. Principle of current measurement system The schematic representation of proposed quartz crystal resonator based DC current measurement system is shown in Figure 1, which consists of a plastic flexible rectangular beam,

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Quartz crystal resonator, SMA wire and the closed loop resonator electronics. The proposed system is designed with the help of Creo software, and a 3-D model is printed. The dimensions of the rectangular beam are given in Table 1. In the 3D design, the rectangular shaped beam has a circle insertion in the middle. The circle dimensions projected into the rectangular beam are the dimensions of the quartz crystal. The 3D design of the rectangular beam and the crystal are shown in Figure 2.

The quartz crystal shown in Figure 2 has a top electrode and bottom electrode. The electrical contact for the crystal electrodes is carefully taken with the help of copper wires. The SMA wire is fixed between the two pillars of the rectangular beam, and a BAW quartz crystal is placed inside the groove, which forms a crystal-beam sandwich and two copper wires are taken out of the crystal and are connected to the closed loop resonator circuit. The DC current of very low

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magnitude i.e. the safe limit of the rectangular beam is applied to the SMA wire, thus making the wire to contract. The change in length of the SMA wire produces an axial force on the quartz crystal which shifts the resonant frequency of the BAW resonator. The closed loop resonant circuit [15] tracks the force induced resonance frequency shift and vibrates the quartz resonator with the new resonance frequency. The bottom electrode of quartz piezo and R2C2 low pass filter are connected in parallel to the non-inverting terminal of the operation amplifier. The

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voltage gain of the amplifier is maintained greater than 1 and the output of the op-amp is

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connected to top electrode of the quartz piezo crystal. When the system is switched ON the piezoelectric crystal responds to the noise and produces a small voltage which is used by the

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amplifier to built-up a steady state oscillating condition. The working principle of this proposed

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oscillator electronics is based on the principle of Wien bridge oscillator. By designing the value of the feedback resistance Rf, R1 and the value of R2C2 for providing the required gain and phase

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shift, the quartz piezo crystal is made to oscillate at its first harmonic vibration frequency and

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tracks the change in frequency with input current. The shift in resonant frequency quartz

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resonator is related to the input DC current I of SMA wire.

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2.1 Analytical modeling

The quartz crystal current measurement system is mathematically analyzed, and its

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corresponding lumped parameter model is shown in Figure 3. Due to the force FSMA generated by SMA wire on the rectangular beam at the eccentric distance ‘e’, a compressive axial force is produced between beam ends. This compressive force pulls the ends and buckling the rectangular beam inward direction with the same force, thus varying the length of the beam on both sides of the neutral axis i.e.

Lb   L

and

Lb   L

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Since the quartz crystal is placed middle of the beam, the neutral axis of the sandwiched beamcrystal setup is exactly passing through the middle of the crystal. The stress (σ) produced at Lb/2 due to compressive buckling force FSMA is given by [20],

 A b



 sec   I 

ec

FSM A



EI

Lb    2   

(1)

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 1

  FSM A 

where FSMA is the eccentric force from the SMA, e is the height of the pillar, Lb is the length of the beam and Ab is the cross-sectional area of beam, ‘c’ is the maximum bending stress point on beam, E is young’s modulus of the beam, I is the moment of inertia of the beam. The force

F SMA

produced by the SMA wire due to input current I is given as [9],   2 )   I (t ) R d t  C i  g 0  t

FSM A  a f ( K n

(2)

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/K p

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where af is the area of cross-section of the wire and n is the number of SMA wires used (n=1), Kp/Kg is a constant which depends on the system parameters like resistance, diameter, and current

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through the SMA wire, I is current through the SMA wire, R is resistance of the wire and Ci is the

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constant.

Differentiating the F SMA with respect to time, the change in SMA force ΔFSMA, d FSM A

 n K  a f  K 

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 FSM A 

g

 2  I R 

(3)

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dt

p

The known SMA parameters are, the unit resistance of the SMA wire is R = 1425 

/m

for the

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input current of I = 45 mA and diameter d = 0.24mm, the force Fs for the static system is 0.0873N. K

p

K

g

can be calculated as

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Hence the unknown parameter for static K

p

g

K

p

K

g

Fs

(4)

af  I R n

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K



2

 4 .4 5 7 3  1 0

6

(5)

From the equation (1), the force Fc acting on the quartz crystal can be calculated as follows, Fc    Ac

(6)

Where Ac is crystal surface area. Substituting equation (3) in (6), the change in the compressive force is given by

 FSM A



EI

Lb      Ac 2   

(7)

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 1  ec  Fc   F SM A   sec   I  A b 

The change in resonance frequency of the quartz crystal is given by  1  ec  f   FSM A   sec   A I   b

 FSM A



EI

Lb   Ac  K f  f 0  2   D 

2

(8)

The force-frequency effect of an AT-cut quartz crystal resonator as a function of azimuth angle could be calculated based on Tiersten’s perturbation integral [17-19], and its corresponding force

f

 30  10

15

mS

for AT-cut crystal,

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f0

is the natural frequency of the crystal.

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is K

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frequency result is shown in Figure 4. The maximum force frequency effect at 00 azimuth angle

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Therefore, the approximate overall change in natural frequency of the system is given by (9)

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f sys  f 0   f

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3. Evaluation of measurement system

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The quartz current measurement system is designed, developed and tested in the laboratory. The properties and dimensions of the proposed current sensor components are given in Table 1, 2 and

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3 respectively. The detailed analytical modeling of this system is derived, and the performance of the measurement system is confirmed through experimental verification. The commercially available BAW quartz crystal is used, and the rectangular beam is designed in the 3-D printer as

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per the requirement, and SMA is bonded on its top.

3.1 Experimental Evaluation: ABS Plastic beam A 3D design of the rectangular beam is designed with ABS plastic by using Creo software, and the 3D design is printed using 2X Makerbot 3D printer. The photograph of the experimental set up is shown in Figure 5. The crystal is placed in the slot of one of the designed rectangular beam so that the electrodes of the crystal are placed perpendicular to the length of the beam, and then,

the two beams are bonded tightly. The two copper wires from the quartz crystal electrodes are connected to the oscillator, which maintains the quartz crystal at its resonance frequency of 2.34290476 MHz. As shown in Figure 5, the SMA wire is fixed at both the ends of the rectangular beam and the output is taken at the ends of the SMA wire. The next step is to set the current input to the SMA wire from the DC Power Supply. For this work, the current input is

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varied from 0 to 0.7A with a step of 0.1A. The current should not cross 0.7A for safety reasons. Here, change in resonance frequency of the crystal is observed with respect to change in input current values. When we apply the current at the both ends of the SMA wire, it shrinks like about 5% of its length, and it returns to the original shape when the current supply is taken away. To validate the analytical model derived in section 2.1, the experimental change in resonance frequency with respect to input current is compared with the analytical result which is shown in

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Figure 6. From the Figure 6, the sensitivity of the quartz current sensor system is found to be

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20Hz/A. The difference in the experimental result is due to the non-inclusion of mass and

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stiffness of adhesive materials in the theoretical analysis.

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3.2 Experimental Evaluation: Aluminum beam

Similarly, the sensitivity of the proposed concept is improved by designing the rectangular beam

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with metallic aluminum beam. The photograph of the experimental set up is shown in Figure 7

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(a) and (b). The crystal is placed in the slot of the aluminum pillar with height of 1cm. The electrodes of the crystal are placed perpendicular to the length of the beam and the electric connections are made with regular spring type quartz holder. The two copper wires from the

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quartz crystal holder are connected to the oscillator, which maintains the quartz crystal at its resonance frequency of 5.005016 MHz. The frequency response of the quartz crystal is shown in

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figure 8 at zero-amp input current to SMA wire. The next step is to set the current input to the SMA wire from the DC Power Supply. In this work, the current input is varied from 0 to 0.7A

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with a step of 0.1A. Here, change in resonance frequency of the crystal is observed with respect to change in input current values. Figure 9 shows the shift in resonant frequency for zero and 0.7-amp input current. The change in resonant frequency is with the input DC current is shown Figure 10. The aluminum beam with quartz crystal based current sensor system gives higher sensitivity than the plastic beam, which is found to be 350Hz/A.

4. Conclusion A different approach has been attempted to measure the DC current based on BAW quartz crystal, and SMA wire actuated rectangular beam in this work. The analytical model was

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derived, and the proposed technique was experimentally tested. The performance of this current sensing system was evaluated experimentally for the input current range of 0.1 to 0.7A. The resonant frequency alteration of the quartz crystal resonator with input current has been found to be piecewise linear. The sensitivity of the measurement system with plastic beam is ~20Hz/A and the aluminum beam is ~350Hz/A. The proposed quartz crystal current sensing method can be miniaturized in micro scale, and the sensitivity range can be improved kilohertz frequency shift. As a future work, SMA material is planned to coat over the quartz crystal electrodes, and

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the sensitivity range will be further improved.

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REFERENCES

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1. C.M. Johnson and P.R. Palmer, “Current measurement using compensated coaxial

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shunts,” IEE Proceedings - Science, Measurement and Technology, 141, 471–480, 1994 2. Silvio Ziegler, Robert C. Woodward, Herbert Ho-Ching Iu, and Lawrence J. Borle,

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Current sensing techniques: a review, IEEE Sensors Journal: 9 (4), 354– 376, 2009. 3. Silvio Ziegler, Robert C. Woodward, Herbert Ho-Ching Iu, and Lawrence J. Borle,

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“Investigation into static and dynamic performance of the copper trace current sense method,” IEEE Sensors Journal: 9(7), 782-792, 2009.

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4. W. F. Ray and C. R. Hewson, “High performance Rogowski current transducers,” IEEE Industry Applications Conference, Rome, Italy, 3083–3090, 2000.

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8. Pavel Ripka, “Review of fluxgate sensors,” Sensors and Actuators A: Physical, 33, 129– 141, 1992. 9. Suresh Kaluvan and Haifeng Zhang, “A Novel DC Current Sensor Using SMA Controlled Piezoelectric Bimorph Cantilever”, ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Paper No. SMASIS2016-9239,

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pp. V001T04A011, 2016.

10. Suresh Kaluvan and Seung-Bok Choi, “Design of current sensor using a magnetorheological fluid in shear mode” Smart Materials and Structures, 23, 127003, 2014.

11. B.V.M.P. Santhosh Kumar, K. Suresh, U. Varun Kumar, G. Uma and M.Umapathy, “Resonance based DC current sensor” Measurement, 45(3), 369-374, 2011. Stemme,

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Microengineering 1,113–125, 1991.

Journal

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12. Goran

13. Gehin, C., Teisseyre, Y. and Barthod, C., “Piezoelectric resonant sensor for static force

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measurement”, Sensor and Actuators A, 84(1-2), 65-69, 2000.

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14. K. Suresh, G. Uma, M. Umapathy, “A new resonance based method for the measurement of non magnetic conducting sheet thickness”, IEEE Transactions on Instrumentation and

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Measurement, 60(12), 3892 – 97, 2011.

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15. Suresh Kaluvan and Haifeng Zhang, “Design of an oscillator circuit for Langasite (LGS) based resonant pressure — Temperature sensor” Frequency Control Symposium (IFCS), 2016 IEEE International, New Orleans, LA, USA, 2016.

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16. Franx, Cornelis, “Temperature sensor and method using a single rotated quartz crystal”, US Patent .4472656, 1984.

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17. H. Tiersten, “Perturbation theory for linear electroelastic equations for small fields superposed on a bias,” Journal of the Acoustical Society of America, 64, 832-837, 1978.

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18. Thanh Tuong Pham, Haifeng Zhang, Sujan Yenuganti, Suresh Kaluvan, John A Kosinski, Design, Modeling, and Experiment of a Piezoelectric Pressure Sensor Based on a Thickness-Shear-Mode Crystal Resonator, IEEE Transactions on Industrial Electronics, 64(11), page 8484-8491. 19. E. P. EerNisse, “Temperature dependence of the force frequency effect for the AT-, FC-, SC-, and rotated X-cuts,” in Proc. IEEE Ultrasonic Symposium 426–430, 1980.

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20. Weblink: http://www.continuummechanics.org/eccentriccolumnbuckling.html

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Dr. Hiafeng Zhang is an Associate Professor of the Department of Mechanical and Energy Engineering at the University of North Texas (Denton, TX). His research interests include advanced sensors, energy harvesters, structural health monitoring and ultrasonic nondestructive evaluation. He received his B.S. in Engineering Mechanics from Hunan University, China in 1997, his M.S. degree in Solid Mechanics from Northwestern Polytechnical University, Xian, China, in 2001, and his Ph.D. degree in Engineering Mechanics from University of Nebraska, Lincoln in 2007. He was a postdoctoral researcher in the Department of Material Science and Engineering in the Ohio State University before joining in University of North Texas in 2008. Dr. Zhang is the committee member of ASME energy harvesting technical committee.

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Suresh Kaluvan received his Bachelor’s degree in Physics from Arul Anandar College, Karumathur, Madurai, India in 2004, Master’s degree in Physics from the American College, Madurai, India in 2007, Ph.D degree in Instrumentation and Control Engineering from National Institute of Technology, Tiruchirappalli, India in 2012. He is currently working as a Post-doctoral fellow in Smart Materials Laboratory, University of North Texas, USA. His research interests include design and development of smart materials based resonant sensors, instrumentation systems and MEMS.

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Figure and Tables:

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Figure 1. Schematic representation of Quartz DC current measurement system

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Bottom Beam

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Top Beam

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D

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Quartz crystal

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Figure 2. 3D Printed model of proposed DC current measurement system

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Figure 3: Lumped parameter model of current sensor system

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3.5

x 10

-14

3

F

2.5

ψ

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2

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Kf

1.5

A

1

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0.5 0

0

50

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-1

D

-0.5

100  (Deg)

150

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Figure.4: The force-frequency effect of AT-cut resonator as a function of azimuth angle.

200

DC Current Source

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SMA Wire

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RF Counter

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Closed loop resonator electronics

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Quartz

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D

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Figure 5. Photograph of the experimental setup: ABS Plastic

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SMA

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Figure 6. Change in resonance frequency with input current

(a)

Quartz Crystal

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SMA

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Quartz

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(b)

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Figure 7. Photograph of the experimental setup: Aluminum beam

Figure 8. Frequency response of 5MHz crystal

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Figure 9. Frequency response at Zero and 0.7 Amp current

Figure 10. Change in resonance frequency with input current: Aluminum beam

Table.1 Dimensions and properties of the rectangular beam ABS Plastic 0.15m 0.003m 0.024m 0.02m ~2GPa

Aluminum 0.15m 0.003m 0.024m 0.03m ~71GPa

Table.2 Dimensions of BAW crystal used Plastic beam 0.024 m 0.56e-3 m 2.342902e6 Hz

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Table.3 Dimensions of SMA Wire

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Parameters

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Diameter of SMA wire (d) Length of SMA wire (LSMA)

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Aluminum beam 0.015 m 0.33e-3 m 5.005096e6 Hz

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Parameters Diameter of crystal (D) Thickness of crystal (tc) Resonant frequency(f0)

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Parameters Length of beam (L) Thickness of beam(tb) Width of beam (w) Eccentric distance(e) Young modulus(E)

Values for both the cases 0.24e-3 m 0.15m