Inductively coupled passive resonance sensors utilize magnetic fields for energy and data transmission. They provide a promising technology for implant applications due to their small size, battery-free wireless readout and simplicity. Such sensors may consist of only an inductor (L) and a capacitor (C) and are hence called LC circuit-based sensors, or LC resonator sensors. In addition, the inductor presents a parasitic resistance, due to which the devices are sometimes named RLC resonators in the literature. On the other hand, the RLC circuits may also contain a separate resistor (R) component. [5], [21]
Inductively coupled LC circuits can be wirelessly read using an external reader coil that is typically connected to an impedance analyzer [22]. A low frequency alternating current (AC) in the reader coil is used to generate an alternating magnetic field [23]. Bringing the inductor coil of the LC circuit close to the reader coil allows magnetic coupling of these two and thereby the induction of energy from the reader coil to the LC circuit [24]. When measuring the impedance of the reader coil, the inductively coupled circuit can be detected from a deviant resonance curve [18]. The curve is usually in the form of a peak or dip, depending if the real part of the
impedance (Re (Z)) or its phase is measured, respectively. The resonance frequency (f0) of the LC circuit can be estimated from the maximum value of the peak, or the minimum value of the phase-dip. A simplified illustration of the measurement setup as well as the two measurement options maximum Re (Z) and minimum phase-dip are presented in Figure 1.
Figure 1. (a) A schematic illustration of typical physical components used for the LC circuit-based measurements. The sensor resistance (Rs) often consists of parasitic resistances alone, but the circuit may contain a separate resistor component as well. (b) A characteristic graph of the Re (Z) measurement, indicating the estimated sensor resonance frequency fmax(Re). (c) A corresponding phase measurement graph, showing the estimated sensor resonance frequency fphase-dip.
The sensing principle of the RLC circuit-based sensors is related to a shift in their resonance frequency in response to a certain stimulus. The resonance frequency f0
of the sensors is characterized with respect to their capacitance, inductance, and resistance and can be estimated according to the following equation [18]:
𝑓0= 1
2𝜋√ 1
𝐿𝑠𝐶𝑠−𝑅𝑠2
𝐿2𝑠 (1)
where Ls, Cs and Rs are the inductance, capacitance and resistance of the sensor, respectively. The effect of parasitic resistance is often neglected, which leads to a simplified estimation in the absence of a resistor component [21]:
𝑓0 = 1
2𝜋√𝐿𝑠𝐶𝑠 (2)
Each of the circuit components (capacitor, inductor, or resistor) may respond to a parameter of interest, but in a typical case the capacitor is used as the sensing element. For example, a parallel plate capacitor with an air cavity or an elastomeric dielectric material between the capacitor plates can be used to monitor pressure or force. The measurement is based on capacitance changes as the distance between the capacitor plates is altered. Another example of capacitive measurements involves complex permittivity changes near the interface between the sensor and its environment, which influence the capacitance of the sensor. The method has been proposed e.g. for characterizing different tissues based on their distinct complex permittivity values. In certain cases even parasitic capacitors can be considered as sensing elements, if no external capacitor is connected to the inductor coil. [16], [21], [22], [25], [26]
The most common inductors used in LC circuits can be divided into two main categories, namely planar and solenoidal inductor coils. Inductive sensing applications are often based on alterations of relative permeability, which may be designed to cause a linear inductance change. In addition, alterations in the dimensional parameters of the coil affect the inductance value of the LC circuit. [21]
This can be utilized for example in a strain sensor, where the inductance of a solenoidal coil is consistently altered by dimensional changes in the coil [27].
Measurements where resistance variation is used as a means for sensing can be applied for example in temperature monitoring if the conductor material is temperature-sensitive, or in strain sensing using a resistive strain gauge [28], [29].
However, measurements founded upon resistance changes are relatively uncommon, as they involve a change in the quality factor of the sensors, which is often defined using the resistance value [18], [21]:
𝑄 = 2𝜋𝑓0𝐿𝑠
𝑅𝑠 = 1
𝑅𝑠√𝐿𝐶𝑠
𝑠 (3)
The higher the Q-factor, the narrower is the measured Re (Z) or phase curve, thus allowing better discrimination between different resonance frequencies. In addition
to a narrower bandwidth, a higher peak amplitude is found at resonance for high-Q resonators. In other words, a device with an increased Q-factor can acquire more energy via inductive coupling as well as transmit data more effectively. This interpretation means that LC circuits with higher Q-factors have also longer reading distances compared to their lower Q-factor counterparts. Another definition for Q can be formulated as:
𝑄 = 𝑓0
𝐵𝑊 (4)
where BW is the -3 dB bandwidth at resonance. However, these definitions for Q are only valid for high-Q (Q>>1) resonators. [21], [30]–[32]
The distance between the reader coil and the LC circuit, or the reading distance, may affect the resonance frequency of the sensor due to parasitic capacitances in parallel to the reader coil. The coupling distance can be even used as a sensing method for monitoring sensor displacement. However, in many applications this feature is undesirable and should be compensated. [21], [33], [34] This includes many implant applications, where the reading distance might be difficult to control precisely.
Certain environmental factors may affect the characteristics of LC circuit-based sensors. For example, temperature fluctuations in the sensor environment might influence the inductance, capacitance or Q-factor of the device. Thus, temperature changes are a possible error source that may affect the sensitivity of the sensor or its baseline resonance frequency f0. For instance, changes in the Young’s Modulus due to increased temperature of the substrate can cause sensitivity drifts in pressure sensors. Furthermore, the resonance frequency of a capacitive sensor may change if the dielectric material has a temperature-dependent dielectric constant. Separate temperature-sensing compensation structures can be used to eliminate the influence of temperature on other measurements if necessary. [9], [35]–[41]
The conductivity of the environment inside the human body causes losses for implantable LC circuits, resulting in an attenuated resonance curve. In addition, proximity of metallic implants or other objects may interfere with the measurement.
Thus, implantable inductively coupled sensors should be ideally located remotely from any metallic implants. [26], [42]–[44]