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International Journal of
eISSN: 2573-2838

Biosensors & Bioelectronics

Research Article Volume 4 Issue 4

A experimental method to the study of wireless passive LC sensors

Roberto Jacobe Rodrigues, Renan Melo De Freitas

Federal University of ABC, Brazil

Correspondence: Roberto Jacobe Rodrigues, Federal University of ABC, Avenida dos Estados, 5001-Bairro Santa Terezinha-Santo Andr, Tel +55-11-4996-0001

Received: June 25, 2018 | Published: July 11, 2018

Citation: Rodrigues RJ, Freitas RM. A experimental method to the study of wireless passive LC sensors. Int J Biosen Bioelectron. 2018;4(4):18510.15406/ijbsbe.2018.04.00121

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Abstract

This paper presents experiments related to the study of the operation of wireless passive LC resonant sensors that have important applications as the real-time implantable pressure sensor for monitoring of hypertension, pressure monitoring in eyes and in blood vessel. The presented experiments consisted of measurements of impedances, seen in an external module for different frequency values, to each capacitor used emulating a capacitive sensor placed in a blood vessel. The experimental results presented an excellent agreement with the analytical results and thus open the perspective of future studies as computational simulations perform and advanced experiments using capacitive sensors working along with better dimensioned coils.

Keywords: capacitive sensor, blood pressure, wireless measurements, resonant circuits

Introduction

The wireless passive resonant LC sensors studies and developments have had a significant growing in the last two decades because these sensors do not need for power supply, wiring connections and electronics circuits.1,2 These sensors represent great possibilities for monitoring of physiological parameters inside the human body.3 An implantable device has to operate under harsh environment as a blood vessel.2,3 Both development of an implantable intraocular pressure sensor for detection of glaucoma,1 and blood pressure sensor for monitoring blood vessel pressure are application examples.3‒6 The measuring, i.e. pressure in most cases, changes the capacitance of the LC circuit placed within the environment being monitored (Figure 1). Thus the LC resonant frequency is changed as a pressure function. This resonant frequency is detected by a coil, magnetically coupled and outside the sensor environment. A readout circuit is connected to this external coil.6 The coil L1 receives an AC signal from Signal Generator, which induces an electrical current in the coil L2 (Lei de Faraday-Lenz). The energy changes between L2 and the capacitor C induces an electrical current in the coil L1, which will be detected as coupled impedance, measured between (a) and (b) points marked in the Figure 1. The total impedance measured between (a) and (b) points is given by Equation 1.2,7

Z i ̇ = R 1 +jω L 1 + ( ωM ) 2 R 2 +jω L 2 j( 1 ωC ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaCbiaO qaaKqzGeaeaaaaaaaaa8qacaWGAbWcpaWaaSbaaeaajugWa8qacaWG Pbaal8aabeaaaeqabaqcLbsapeGaeS4bdycaaiabg2da9iaadkfaju aGpaWaaSbaaSqaaKqzadWdbiaaigdaaSWdaeqaaKqzGeWdbiabgUca RiaadQgacqaHjpWDcaWGmbqcfa4damaaBaaaleaajugWa8qacaaIXa aal8aabeaajugib8qacqGHRaWkjuaGdaWcaaGcpaqaaKqba+qadaqa daGcpaqaaKqzGeWdbiabeM8a3jaad2eaaOGaayjkaiaawMcaaKqba+ aadaahaaWcbeqaaKqzadWdbiaaikdaaaaak8aabaqcLbsapeGaamOu aSWdamaaBaaakeaajugWa8qacaaIYaaak8aabeaajugib8qacqGHRa WkcaWGQbGaeqyYdCNaamitaSWdamaaBaaabaqcLbmapeGaaGOmaaWc paqabaqcLbsapeGaeyOeI0IaamOAaKqbaoaabmaak8aabaqcfa4dbm aalaaak8aabaqcLbsapeGaaGymaaGcpaqaaKqzGeWdbiabeM8a3jaa doeaaaaakiaawIcacaGLPaaaaaaaaa@68CA@            (1)

where w is the angular frequency (rad/s), L1 and L2 are coils inductances (Henry), R1 and R2 are coils series resistors (Ohm), C will work as if it were the measuring dependent capacitance (Faraday) and M is the Mutual inductance (Henry).Therefore, this work presents an experimental method to confirm the impedance dependency,  (module and phase) with different capacitance values, C. In the future experiments, the capacitor will be replaced by a capacitive sensor and the coils will be designed to perform the best performance.

Figure 1 Wireless passive LC sensor.

Materials and methods

The Mutual inductance was determined by using the circuit showed in Figure 2. The nominal inductances values L1 e L2 are  22mH and the measured ones, by LCR Minipa MX-1010 equipment, were 21,38mH, equals for both coils. The adopted resistor was R = 1kW. The Mutual inductance value is given by:7

V 2 ̇ =jωM I ˙ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaCbiaO qaaKqzGeaeaaaaaaaaa8qacaWGwbqcfa4damaaBaaaleaajugWa8qa caaIYaaal8aabeaaaeqabaqcLbsapeGaeS4bdycaaiabg2da9iaadQ gacqaHjpWDcaWGnbGabmysa8aagaGaaaaa@420E@            (2)

The electrical current, I ˙ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiqadMeapaGbaiaaaaa@378B@ ;is the Ohm’s Law application of the difference of the measured signals read out from Oscilloscope (  V g ̇ V 1 ̇ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaGGOa aeaaaaaaaaa8qacaGGGcqcfa4damaaxacakeaajugib8qacaWGwbWc paWaaSbaaeaajugWa8qacaWGNbaal8aabeaaaeqabaqcLbsapeGaeS 4bdycaaiabgkHiTKqba+aadaWfGaGcbaqcLbsapeGaamOvaSWdamaa BaaabaqcLbmapeGaaGymaaWcpaqabaaabeqaaKqzGeWdbiablEWaMa aapaGaaiykaaaa@4669@ ;on R. The graph of the Mutual inductance vs coils distances is shown in Figure 3. The circuit, for experimental determination of the dependence between impedance (Module and Phase) and resonant frequency, is shown in Figure 4.

The circuit presented in Figure 4 is the same one presented in Figure 2, but adding R2=47W resistor and capacitor. The adopted capacitor nominal values were 10nF, 33nF and 68nF. The distance in between coils was 10x10-3m. Thus the Mutual inductance will be M » 2,2mH (Figure 3). For each adopted capacitance value, two curves were drawn: the impedance module vs frequency and the impedance phase vs frequency. These graphs were compared with analytical results from Equation 1. A 2V peak-to-peak sinusoidal signal was adjusted on signal generator. The impedance modules values were obtained from Vg/IR1 ratio, where IR1 is the VR1/R1 ratio (Figure 4). Already the impedance phase f (degree) is the phase difference measured between signals Vg and VR1 (Figure 6).

Figure 2 Mutual inductance determination.

Figure 3 Mutual inductance vs coils distances.

Figure 4 Circuit to measurement of the impedance dependence with the applied signal frequency and the capacitors.

Figure 5 Assembled circuit picture and a detail of the coil type used in tests.

Figure 6 Relation between signals as measured on oscilloscope to C = 33nF.

Results

The Figure 7 shows a excellent agreement between analytical and experimental to a 10nF capacitor. This agreement also occurred to 33nF and 68nF ones. Moreover, it was obtained a good qualitatively agreement with literature results.4,6 The resonant frequency values were determined in agreement with literature procedures,6 and showed arrowed on (Figure 7) (Figure 8). The resonant frequency value is given by Equation 3:4

f o = 1 2π L 2 C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsaqaaaaa aaaaWdbiaadAgal8aadaWgaaqaaKqzadWdbiaad+gaaSWdaeqaaKqz GeWdbiabg2da9Kqbaoaalaaak8aabaqcLbsapeGaaGymaaGcpaqaaK qzGeWdbiaaikdacqaHapaCjuaGdaGcaaGcpaqaaKqzGeWdbiaadYea juaGpaWaaSbaaSqaaKqzadWdbiaaikdaaSWdaeqaaKqzGeWdbiaado eaaSqabaaaaaaa@4775@            (3)

The resonant frequency is the frequency where the phase begin increase again.4,6 The resonant frequencies obtained were around 4kHz from 68nF capacitor, around 6kHz from 33nF and around 11kHz from 10nF.

The behavior of the spectrum with the resonant frequencies to each capacitor is shown by (Figure 9) (Figure 10),

Figure 7 Impedance x Frequency to C = 10nF.

Figure 8 Phase vs Frequency to C = 10nF.

Figure 9 Impedance module vs frequency and adopted capacitors./p>

Figure 10 Phase vs Frequency and adopted capacitors.

Discussion

The resonant frequency, pointed by arrows, from (Figure 7) (Figure 8) agree with literature procedure.4,6 The (Figure 9) (Figure 10) show that capacitance values below 10nF results a lower amplitude variation around resonant frequency. Therefore, new tests should be performed with lowers inductances values, mH rather than mH, as well as lower capacitances. Thus, the frequencies quite superior to adopted frequencies in this presented experiment, for example the frequencies presented in literature.2,8 In addition, longer distances will be tested.

Due to influence both coupling coefficient and quality factor, the calculated value of the resonant frequency, by Equation 3, do not agree with one obtained graphically by (Figure 7) (Figure 8).4 Thus, in future works, studies should be performed to analyze the influence of the quality factor on the performance of the system as well as on the experimental frequency. More precise procedures for the determination of the resonance frequency should be studied.

Conclusion

An experimental procedure using components available in the didactic laboratory was proposed for the study of a system similar to that used in applications such as the monitoring of blood pressure in real time from a blood vessel.3 The experimental results indicated a agreement with the analytical results obtained and thus open the perspective to new studies and new experiments, but using, instead of fixed capacitors, capacitive sensors immersed in environments being monitored, as well as with the use of better dimensioned coils. The purpose of this article was reached because it has been shown that a resonant LC circuit with variable capacitance values can communicate wirelessly with a distant coil.

Acknowledgements

The author would like to acknowledge Federal University of ABC (UFABC) for provided facilities and equipments.

Conflict of interest

Author declares that there is no conflict of interest.

References

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©2018 Rodrigues, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.