1. Introduction

For some applications such as aerospace^[1], automotive^[2], and biomedical^[3] industries, a key unit of measure in a system is pressure. Instantaneous precise measurement of pressure has to be done at locations where it is almost impossible or impractical to connect the pressure sensitive element to the conditioning electronics or measurement circuit by using standard cables. Examples of these applications are the measurements of intraocular pressure^[4] or tire pressure^[5], and measurements under harsh environments, such as high loading^[6] or high temperature^[7]. Therefore, a complete passive sensor capable of measuring pressure in extreme environments is often desired. Passive pressure sensors based on an LC resonant circuit allow wireless operation using inductive coupling, and consist of an inductor in parallel with a pressure sensitive capacitor. The external pressure results in the variation of capacitor, so the sensor's resonant frequency changes. The pressure value can be obtained from the frequency which can be remotely detected by another inductively coupled coil that is connected to the measurement circuit. Because the LC passive pressure sensors do not require an internal power supply and a wire link, they have been widely used in some special applications^{[8, 9]}.

Due to the requirements for pressure measurement in extreme environments, realizing the precise measurement and real-time monitoring is particularly important. Various techniques for monitoring a sensor's resonant frequency exist. In some monitor systems, a voltage-controlled oscillator^[10] is used to sweep the frequency range and then the sweeping frequency signal is transmitted to the sensor. The reader antenna impedance changes greatly at resonance. The impedance variation is used to derive the sensor resonance frequency^[11]. In some applications, the sensor's resonant frequency is read out by measuring the phase shift of the antenna coil by using a network analyzer^[12] or impedance analyzer^[13]. However, with the techniques used for detecting the sensor resonance frequency, the recording of the sensor resonance frequency requires manual intervention. With a voltage-controlled oscillator, the control voltage value has to be manually input into the oscillator for the desired output frequency. The sensor resonance frequency displayed on the impedance analyzer has to be manually recorded.

In this paper, a readout system is proposed. The readout system consists of a reader antenna inductively coupled to the sensor, a measurement circuit, and a PC post processing unit. The system can detect the sensor's resonant frequency by monitoring a dc output voltage related to the reader antenna impedance, save the results and display them on the interface of post-processing software. The system is theoretically described and tested on a test platform. The experimental results show good agreement with the impedance analyzer's results. Although this paper emphasizes the measurement of pressure, a similar setup can be used to measure temperature, humidity, strain and so on. This system realizes sensor testing without using an impedance analyzer or a network analyzer. All could contribute to the promotion and integration of the passive sensors.

2. Sensor design and fabrication

The magnetic link between two adjacent inductance coils makes non-contact pressure measurement possible. As shown in Fig. 1, through the mutual inductance coupling of the reader antenna's and the sensor's inductors, the pressure information contained in the sensor's resonant frequency can be transmitted into the reader side. When the sensor is under pressure, the capacitance changes, and thus the sensor's resonant frequency also changes which can be read out by the reader antenna. The expression of the resonant frequency is given by:

$\begin{equation} \label{eq1} f_0 =\frac{1}{2\pi \sqrt {L_2 C_2}}. \end{equation}$

(1)

According to the mature fabrication technology on advance ceramic material, a pressure sensor prototype is designed and fabricated based on low temperature co-fired ceramic (LTCC). The sensor consists of a pressure deformable square cavity and a planar spiral inductor. The inductor windings shape is square, so we can obtain more turns compared with round shape windings^[14]. The design parameters of the inductor are illustrated in Table 1, according to Ref. [15], the calculated inductance is 2364 nH.

As shown in Fig. 2, the structure is stacked by 4 layers of LTCC tape, the inductor coil is on the surface of the first layer, the upper and the lower capacitor electrode are on the outer surface of the first and the third layer respectively, and they are connected to the inductor coil terminals through a via across the layers. The interconnection can form an LC circuit. An embedded cavity and an air channel are on the middle of the second layer. The upper ceramic membrane above the embedded cavity is pressure-deformable.

The sensor is fabricated through the mature LTCC technology which involves green tape shaping, circuit pattern screen-printing, stacking, laminating, and co-firing^[16]. The processing steps and the completed sensor sample are shown in Figs. 3 and 4 respectively. The sensor's initial capacitance is 13 pF, according to Eq. (1), the theoretical resonant frequency of sensor at zero pressure is 28.71 MHz.

3. Readout system

The readout system consists of a reader antenna, a measurement circuit, and a PC post processing unit. The measurement circuit drives the reader antenna with a sweep signal source and generates a dc output voltage. An analytical model of the measurement circuit with ideal components is shown in Fig. 5. $R_{1}$ and $R_{2}$ are the self-resistances of the reader antenna and the sensor circuit, $C_{1}$ is the capacitance of the reader circuit, $C_{2}$ is the sensor capacitance, and $M$ is the mutual inductance of the coupled coils. A reference voltage $U_{\rm ref}$ is generated using the resistance $R_{\rm ref}$, the sweep signal $U_{1}$ and $U_{\rm ref}$ are multiplied by using a mixer, and then a low-pass filter is used to filter the mixer's output signal $U_{\rm m}$, and pass a DC output voltage $U_{\rm out}$.

The following equation can be derived using Kirchhoff's law:

$\begin{equation} \begin{cases} \left(R_1 +{\rm j}2\pi fL_1 +\dfrac{1}{{\rm j}2\pi fC_1 }+R_{\rm ref}\right)I_1 +{\rm j}2\pi fMI_2 =U_1, \\[4mm] {\rm j}2\pi fMI_1 +\left(R_2 +{\rm j}2\pi fL_2 +\dfrac{1}{{\rm j}2\pi fC_2}\right)I_2 =0, \end{cases} \end{equation}$

(2)

where $f$ is the frequency of sweep signal, using the substitutions

$\begin{equation} \label{eq3} Z_1 =R_1 +{\rm j}2\pi fL_1 +\frac{1}{{\rm j}2\pi fC_1 }+R_{\rm ref}, \end{equation}$

(3)

$\begin{equation} \label{eq4} Z_2 =R_2 +{\rm j}2\pi fL_2 +\frac{1}{{\rm j}2\pi fC_2 }, \end{equation}$

(4)

$\begin{equation} \label{eq5} Z_{\rm M} ={\rm j}2\pi fM. \end{equation}$

(5)

Equations (2) and (3) can be simplified as

$\begin{equation} \begin{cases} Z_1 I_1 +Z_M I_2 =U_1, \\[2mm] Z_M I_1 +Z_2 I_2 =0. \end{cases} \end{equation}$

(6)

The reference voltage $U_{\rm ref}$ can be derived by solving Eqs. (7) and (8) as

$\begin{equation} \label{eq6} U_{\rm ref} =\frac{R_{\rm ref} }{Z_1 +(2\pi fM)^2Y_2 }U_1. \end{equation}$

(7)

Then, the mixer's output signal $U_{\rm m}$ can be given by:

$\begin{equation} \label{eq7} U_{\rm m} =\frac{R_{\rm ref} }{Z_1 +(2\pi fM)^2Y_2 }U_1 U_1 . \end{equation}$

(8)

Using the substitution^[17]

$\begin{equation} \label{eq8} Z_{\rm i} =R_1 +{\rm j}\omega L_1 +\frac{1}{j\omega C_1 }+\frac{(\omega M)^2}{R_2 +j\omega L_2 +\dfrac{1}{j\omega C_2 }}, \end{equation}$

(9)

where $Z_{\rm i}$ is the input impedance seen from the reader side, Equation (10) can be rewritten by

$\begin{equation} \label{eq9} U_{\rm m} =\frac{R_{\rm ref} }{Z_{\rm i} +R_{\rm ref} }U_1 U_1. \end{equation}$

(10)

Using the substitutions: $L_{1}C_{1}$ $=$ 1/(4$\pi^{2}$$f_{1}^{2})$, $L_{2}C_{2}$ $=$ 1/(4$\pi^{2}f_{\rm o}^{2})$, $k^{2}$ $=$ $M^{2}/(L_{1}$$L_{2})$ and $R_{2}$ $=$ 2$\pi f_{\rm o}$$L_{2}$/Q^[18], where $f_{1}$ and $f_{0}$ are the resonant frequency of the antenna electronics and sensor respectively, k is the coupling coefficient, $Q$ is the sensor quality factor, and $Z_{\rm i}$ can be given by

$\begin{array}{l} {Z_{\rm{i}}} = {R_1} + {\rm{j}}2\pi f{L_1}\\ \times \left[ {1 - {{\left( {\frac{{{f_1}}}{f}} \right)}^2} + \frac{{{k^2}{{\left( {\frac{f}{{{f_0}}}} \right)}^2}}}{{1 + \frac{j}{Q}\left( {\frac{f}{{{f_0}}}} \right) - {{\left( {\frac{f}{{{f_0}}}} \right)}^2}}}} \right]. \end{array}$

(11)

Equations (12) and (13) show that the mixing signal $U_{\rm m}$ is related to the sensor's resonant frequency. The dc output voltage can be obtained by filtering the mixing signal using the LPF (the cut-off frequency of the LPF is 1 kHz), and the simulation results of it using the MATLAB are shown in Fig. 6. Figure 6(a) is the result of the reader antenna before being coupled by the sensor, and Figure 6(b) is after coupling. Due to the coupling effect, a sudden change in the shape of the DC output voltage response curve occurs; the corresponding frequency of the mutation point on the curve is the sensor's resonant frequency. The dc output voltage signal can be analyzed and processed by the signal acquisition module and the PC post processing unit to obtain the sensor's resonant frequency.

The designed measurement circuit has been built using analog integrated circuits on a PCB. It is shown in Fig. 7. The sweep signal and the reference voltage are multiplied using a Gilbert cell-based mixer AD831, and then a low-pass filter circuit is used to filter the mixer's output signal in a DC output voltage. The dc output voltage is amplified by using the output amplifier of the AD831. A fast 16-bit ADC (AD7667) is used to convert the dc output voltage into digital form.

The measurement circuit also contains a microcontroller unit (MCU) for communicating with the PC via a USB interface. The PC post-processing software processes the digital data, calculates and saves the resonant frequency of sensor.

4. Experiment and results

To complete the experiment, a test platform which mainly consists of a pressure controller, measurement circuit, a pressure vessel, a sweep signal generator (QA212D), and a computer has been made, it is illustrated in Fig. 8(a). The sensor and the reader antenna are placed together in a pressure vessel. The reader antenna inductor and the sensing inductor are designed identically, they are placed face to face as their central axes coincide using the position controllable platform which can be used to adjust the readout distance, as shown in Fig. 8(b). The reader antenna is connected to the measurement circuit through test ports of the pressure vessel, the pressure in the vessel is controlled by the PACE 6000 pressure controller.

With the designed sensor, a set of experimental tests on the test platform has been carried out by varying the pressure and also the readout distance. The pressure applied ranges from 0-3 bar, and the frequency of sweep signal ranges from 1-50 MHz. When the pressure and the readout distance are 0 bar and 6 mm respectively, the waveform displayed on the oscilloscope is shown in Fig. 9, the reference voltage signal and the DC output voltage signal are displayed on the second channel and the first channel of oscilloscope separately. As we can see from Fig. 9(b), when the sensor is coupled to the reader antenna, a sudden change of the waveform occurs. The tendency of the upper envelope curve displayed on the second channel is in good accordance with the simulation result. The measured output voltage of the measurement circuit versus frequency is shown in Fig. 10. The measured resonant frequency of the sensor is 31.286 MHz, which is 8.97% higher than theoretical value (28.71 MHz).

The discrepancy of frequency may be caused by the error of theoretical inductance value and measured inductance value, and the error of theoretical capacitance value and measured capacitance value. The measured inductance of the antenna reader is 1665 nH, which is 30% lower than the theoretical value (2364 nH), thus the measured capacitance is 15.54 pF, which is 19.5% higher than the theoretical value (13 pF). The slight collapse of the sensor's cavity structure will inevitably occur during the manufacture process, which shortens the distance between capacitor electrodes, then increases the capacitance. Figure 11 is the results obtained at various readout distances when the pressure is 0 bar, demonstrating that these measured values are almost insensitive to readout distance variation. The maximum readout distance of the system is about half of the inductance coil's outer diameter now.

Figure 12 shows the measured results of the measurement circuit and the impedance analyzer. As can be seen, the resonant frequencies measured with the measurement circuit are in good agreement with the impedance analyzer's results, and their error is less than 2.5%, which may be mainly attributed to the sampling precision of the circuit.

In addition, the testing experiments about the impact of the medium between sensor and reader antenna on the performance of the readout system have been carried out. When the medium is iron and aluminum materials, the experimental result is shown in Fig. 13(a). As we can see from the figure, there is no resonance point on the testing curve and the sensor's LC resonant circuit is not in resonance. The possible factor that leads to this phenomenon may be as follows: the iron and aluminum material makes the alternating magnetic field energy of the reader antenna not transmitted to the sensor's LC resonant circuit through the sensor's inductor, so there is no mutual inductance coupling between the sensor and the reader antenna, then the wireless signal transmission between the sensor and the measurement circuit cannot be realized effectively. When the medium is ceramic plastic material, the resonant frequency of sensor can be tested effectively and the experimental result is given in Fig. 13(b). In brief, the medium made of materials which cannot affect the mutual inductance coupling between the sensor and the reader antenna does not influence the performance of the readout system.

5. Conclusion

A readout system for an LC passive pressure sensor has been presented. The concept of a measurement circuit based on coherent demodulation for mapping the input impedance seen from the reader antenna side to a DC output voltage has also been introduced. It demonstrated that the resonant frequency of the sensor can be obtained from the dc output voltage signal. Based on the basic architecture of the measurement circuit, we have built its prototype.

A pressure sensor was designed and fabricated based on LTCC, and the readout system has been tested by using a test platform, the measured results with the measurement circuit are in good agreement with the impedance analyzer's results and almost insensitive to the readout distance variation. The readout system is practical, effective, and contributes to the promotion and integration of the passive sensors. Moreover, the readout system can be utilized in other applications, since the developed device can be used instead of the network or impedance analyzers as a readout device for inductively coupled resonance sensors.