A simple ranging system based on mutually coupled resonating circuits Marco Dionigi, Guido De Angelis, Antonio Moschitta, Mauro Mongiardo, Paolo Carbone Department of Electronic and Information Engineering University of Perugia Perugia, Italy {marco.dionigi, antonio.moschitta, paolo.carbone, mauro.mongiardo}@diei.unipg.it,
[email protected] Abstract—In this paper, a ranging technique based on inductive coupling between resonating coils is presented. The theoretical background is discussed, and a practical implementation is illustrated and experimentally validated. It is shown that the proposed technique, implemented using off the shelf components, features both a good range and a fair resilience to multipath, being suitable for indoor positioning applications. Keywords—indoor ranging; positioning; inductive coupling
I.
INTRODUCTION
Positioning techniques have recently witnessed a renewed research interest, connected to the possibilities offered by increased available processing capabilities, technological advancements in available electronic components, and the concurrent emergence of novel applications, such as domotics, health systems, and assisted navigation of buildings [1]-[4]. Various techniques have been proposed, coupled with advanced processing algorithms, all focused on the waveform propagation analysis . Well-known solutions are based on acoustic waves and, more recently, on various kinds of EM waves, ranging from low frequency waveforms to optical signals [5-9]. The most critical requirement in indoor positioning applications is multipath resilience, since such phenomenon may significantly affect measurement accuracy, especially when positioning is obtained from amplitude measurements. To this aim various solutions have been proposed, relying of diversity techniques to estimate channel paths or on the adoption of signals with suitable propagation properties [5-9]. For instance, Ultra Wideband (UWB) signals have been recently proposed and considered both in the literature and standards, because the increased bandwidth results in both good penetration properties and, coupled with the adoption of pulsed transmission and time based approaches, in the possibility of isolating the direct path, neglecting multipath contributions [7][8]. In this paper, an alternative measurement principle is considered, based on the transmission of very low frequency
signals [10][11]. In particular, two resonant mutually coupled circuits are considered, nominally tuned at the same frequency. Such a solution has been recently investigated in the wireless power transfer field [12] where the two resonators are used to exchange power, while mutual inductive coupling, combined with high resonator quality factor Q, helps increasing transfer efficiency and achievable transfer distance. In particular, two coils have been considered, inductively coupled and tuned to resonance by using lumped capacitors. In the present positioning case the main requirement is to obtain signals that are large enough at the receiver side to cope with system noise, allowing signal detection and accurate distance estimation. To this aim, mutual coupling may be profitably exploited, permitting both to extend the system achievable range, and a better resilience to noise, due to the filtering effect introduced by the resonant circuit transfer function. Moreover, a H-field based system is potentially insensitive to multipath, since the magnetic field typically propagates through most materials [11]. In the following, the developed system is presented, and the method potential is assessed throughout experimental verifications. II.
THEORETICAL BACKGROUND
A. Circuit and power transfer model We consider now a simple model of two coupled resonators, described in Fig. 1. While the element values may be different, we consider the case of synchronous resonators, i.e. with the same resonant frequency, described by the following Kirchhoff voltage equations:
1 V1 R1 jL1 I1 jMI 2 j C1 . 1 0 jMI 2 R2 jL2 jC I 2 2
(1)
M
C1
R1
C2 I2
I1
0.1
L1
L2
R2 Coupling K
V1
Fig. 1 Inductively Coupled Series Resonators.
Let us now assume to be at resonance condition; in this case the impedances are purely resistive. Let us also assume the coupling to be relatively small, so that we can neglect in the first equation the effect of the current I2. In this case, from the first equation, we have V (2) I1 1 , MI 2 R1I1 , R1 and we can solve the second equation for the current I2, obtaining jMI 1 jMV1 . (3) I2 R2 R1R2 Therefore the output power P2, i.e. the power dissipated on the resistance R2, is given by
0.01
1E-3
0
100
200
300
400
500
600
Center Distance (mm)
Fig. 2: Coupling coefficient k between 180 mm coils in coaxial configuration as a function of distance.
2
P2
2 M 2 V1 R2 2R1 R2 2
(4)
while the power P1, dissipated on the resistance R1 is
P1
V1
Fig. 3: Royer resonator with transmit and receive resonators [15]
2
. (5) 2R1 By considering the power ratio, and the expression of the resonator Q factor (Q=L/R), we obtain the following P2 2 M 2 2 k 2 L1L2 k 2Q1Q2 , P1 R1R2 R1R2
(6)
where k M / L1L2 is the coupling factor. B. Measurement model and performance considerations In absence of multipath, the voltage transmission coefficient may be obtained as
V2 V1 k Q1Q2 .
(7)
Since expression (7) relates the received rms signal to the transmitted one, by properly modeling M and k as a function of the distance d between the two coils, V2 can be related to the d. To this aim, various models have been published in literature for the computation of the magnetic coupling between coils in different positions [13]. An example of the wide variation of the coupling is given in Fig. 2, where two coils of diameter 180 mm and 30 mm length are considered. The position of the coils varies along their coaxial axis and the coils maintain their orientation. As expected, a large reduction of the coupling can be observed when the distance exceeds a few times the diameter of the loop. Observe however that (7) shows that the voltage transmission coefficient depends on the coupling coefficient multiplied by the geometric mean of the
quality factors of the resonators. Thus, while the inductive coupling coefficient decays abruptly as shown in Fig. 2, the effect on (6) and (7) may be mitigated by using high Q resonators, that, by increasing by Q times the H field, may provide a mean for extending the system range. Notice that Q1 and Q2 act like the antenna gains in the well-known Friis formula, used to describe the power balance in a conventional RF communication system. Notice that, even for low values of k, using high Q circuits may help achieving a good power transfer between the transmitter and the receiver devices. Moreover, the high penetration properties of the H field imply that the system may be more robust to multipath than conventional RF systems, providing signal strength measurement consistent with free space propagation distance model. Based on this reasoning, we have designed two twin resonators, used to experimentally validate the proposed approach, described in the following section. III.
EXPERIMENTAL VERIFICATIONS
A. Experimental setup The first resonator is part of a Royer oscillator [14]. The transmitter coil features a diameter of 180 mm and a length of 30 mm, while the second resonator is made with the same geometry and is used as a receiver without the Royer circuitry, leading to the overall system represented in Fig. 3. In order to
30 measured data linear fit 25
Computed Measured
rms
)
10
10log(V
H Field (A/m)
100
1
-5
0
5
10
15
20
25
30
35
40
20
15
10
Distance (cm)
Fig. 4: Measured H-field in the axial position of the resonator
investigate the effectiveness of the positioning principle the two coils have been arranged in a coaxial configuration. In particular, the Royer oscillator absorbs a current of 1A at 12 V dc, and oscillates at frequency f0=208 kHz. The H-field produced by the resonator has been estimated by measuring the induced voltage at the ends of a small loop in the axial position of the receiver coil, for increasing distances between the coils, leading to the results shown in Fig. 4. Notice that the H-field is noticeably high, exceeding the safety value for public exposure in the area within 400 mm from the coil center. This issue may cause safety concerns, requiring people to be prevented from getting too close to the signal source. Following such activity, one of the twin resonators has been further characterized using a HP4275A RLC meter at a frequency of 300 kHz, by separately measuring the coil inductance L and the related resistance RL, using the series impedance model and obtaining L1.54 H and RL 30 m. Then, the resonator capacitance C, and the corresponding resistance RC have been assessed using the parallel impedance model, obtaining C418 nF and RC130 m. Both C and L measurements have been repeated at different frequencies, in order to verify the stability of the obtained results. Then, by recalling that f0=208 kHz, the Q factor has been estimated as 2f 0 L Qˆ , (8) RL RC obtaining Q857. B. RSSI vs distance measurements Following the initial characterization, the system has been used in an indoor environment, by measuring the rms voltage at the receiver resonator output using an oscilloscope. The results have been plotted in Fig. 5 (blue curve) after being converted to a logarithmic scale, together with an interpolating straight line (in red), evaluated from the logarithms of both considered distances and measured rms voltages. It can be observed that, despite the fact that measurements have been taken in an indoor environment, the obtained curve has a regular behavior, showing that the system is potentially resilient to multipath. It should also be observed that the system
5 16
17
18
19
20 10log(d)
21
22
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24
Fig. 5: received rms voltage, expressed in mV, vs distance, expressed in cm, obtained for the developed two resonator system.
Fig. 6: received signal spectrum, obtained for a distance of about 8m between the transmitter and the receiver.
features a high SNR, possibly due the frequency response of the two resonating circuits, that implicitly act as a narrowband bandpass filter. In order to gain further insight, measurements have been repeated for increasing distances, showing that a range of 7 m can easily be exceeded. In particular, Fig. 6 shows the received signal spectrum obtained using an Agilent N9320B Spectrum Analyzer, at a distance of about 7m. A significant carrier at the resonant frequency can be observed. Notice that the prototype system features margins of improvements. In fact, since the adopted capacitors have a tolerance of about 5%, a better matching between the transmitter and receiver resonators’ frequencies may be achieved by introducing impedance fine-tuning capabilities in the adopted design. Following such results, further measurements have been carried out, in order to assess the achievable ranging accuracy. In particular, in order to assess the effects of misalignment between the two coils, the transmitter and the receiver have been placed at a distance of 100 cm, tuning the transmitter
120
2.45 2.4
100
2.35 2.3
received Vrms
80
2.25 2.2
60
2.15 2.1
40
2.05 2
20
1.95 0
10
20 30 40 50 60 70 angle btween wire-loops' axes [degrees]
80
1.6
1.8
2
2.2
2.4
2.6
90
Fig. 7: received signal Vrms, obtained by changing the angle between the two resonating coils, placed at a distance of about 100 cm.
power so that the measured Vrms at the output of the receiver’s coil equaled 100 mV, with the two coils perfectly aligned. Then, the angle between the axis of the transmitting coil and that of the receiving coil has been progressively changed, measuring the Vrms at the output of the receiving coil and leading to the results of Fig. 7. It can be observed that a misalignment of up to 10 degrees can be tolerated, since it does not introduce significant variations in the received signal power. Moreover, the effect of misalignment is fairly regular, and As such it may be modeled and included in the estimation algorithms of a positioning system. C. Ranging accuracy In order to assess and improve the achievable accuracy, the system has been observed over extended times up to two hours, repeating measurements in fixed positions and using an Agilent Infinium MSO8104A Digital Oscilloscope (DSO), a HP 3441A Digital Multimeter (DMM), and a HP 53131A Universal Counter to simultaneously monitor the stability of the signal amplitude and frequency, both at the transmitter and at the receiver’s end. The analysis has shown a frequency drift of the Royer oscillator, due to thermal transients, of about 1 Hz/s. In order to characterize the effect of such phenomenon, on the ranging accuracy, simultaneous Vrms measurements have been taken, recording the ratio between the transmitter Vrms,tx and the receiver Vrms,rx for various distances, using the Infinium DSO. This procedure removes inaccuracies due to frequency drifts occurring in the time interval between the transmitter side measurement and the receiver side one. The residual uncertainty is then mostly due to gain variations in both coils, due to the fact that drift moves the sinewave frequency away from both coils’ resonant frequencies. To gain further insight, the bi-logarithmic plot of Fig. 8 has been obtained, that shows as blue crosses the decimal logarithm of the Vrms,tx/Vrms,rx ratio as a function of the decimal logarithm of the distance, expressed in cm . Then, linear fitting has been applied to the
Fig. 8: bi-logarithmic plot of transmitted to received Vrms ratio, as a function of the distance between the two resonant coils (blue crosses), fitting line (green), and fitting tolerance interval (red lines)
1
10
0
10 Vrms,rx [V]
0
-1
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-2
10
1
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2
10 d [cm]
3
10
Fig. 9: bi-logarithmic plot of received Vrms, as a function of the distance between the two resonant coils, using the upgraded system with a INA at the output of the receiver’s resonant coil. The blue curve as been obtained without activating the INA, while the red curve has been obtained by switching on the INA and normalizing the measurement results to the INA’s gain.
logarithmic data, using Matlab tools. In particular, Fig. 8 shows both the fitting line, in green, and the fitting tolerance interval, marked by the red dashed lines. Using the coefficients of the fitting line and performing additional Vrms,tx and Vrms,rx measurements, the distance have been estimated in a set of known positions, and compared to the true one. The obtained results show that the position can be estimated with an extended uncertainty of about 2 cm, in a range of 2m. Notice that such uncertainty corresponds to an expanded uncertainty not exceeding 2% over the measurement range, and is compatible with the DSO measurement uncertainty.
D. Range extension Since the developed system consents accurate distance measurements in a range of about 2m, an extension has been developed, by including a Burr Brown INA114 Instrumentation Amplifier (INA) in the receiver, at the output of the resonant coil. Such an approach has been proven effective in range extension, as shown by Fig. 9, that plots the received Vrms as a function of the distance. In particular, the blue curve has been obtained without activating the INA, while the red curve shows measurements in an extended range, obtained by switching on the INA and compensating the Vrms reading by the INA gain. The behavior of the red curve is very similar to that obtained in absence of amplification, and suggests that the proposed strategy may be effectively applied to extend the range of the developed system, without jeopardizing the achievable accuracy. IV.
CONCLUSIONS AND FUTURE WORKS
A ranging system has been presented, based on inductive coupling between resonating coils; the system is, potentially capable of robust performance in presence of multipath and achieves high SNR due to its very narrowband characteristics. An expanded uncertainty of about 2 cm has been obtained in a range of 2m, and a technique to extend the system’s range as been presented. The activity is still in progress, and the proposed system will be extended by including automatic gain control in the receiver’s INA and by considering alternate solutions for the sinewave generation, in order to guarantee higher frequency stability.
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