**6. Simulation results of the complete sensor**

Series of free oscillation simulations (eigenmode) using the HFSSTM software, applied to the dielectric resonators, determine the diameter, thickness, permittivity of the dielectric resonator, as well as the distribution of the electromagnetic field necessary to define the caustic and the optimal coupling with the coplanar lines (see **Figure 7**). The determination of caustic makes it possible to establish the distribution of the electromagnetic field in the RD and leads to the definition of the position of the coplanar lines. In addition, the diameter of the resonator and the confinement of the electromagnetic field in it impose the distance between these two micro-machined lines.

In this study, we studied a dielectric resonator with a relative permittivity of 80 and no losses. The thickness and diameter of the dielectric resonator are used to determine the resonance modes and frequencies associated with them. Subsequently, we are interested in the modification of the physical properties of the PLZT material in the presence of a change in temperature, more precisely the variation of its dielectric permittivity. As shown in **Figure 8**, we observe the distribution of the electric field of the WGE8.0.0 mode in the dielectric resonator; it is thus isolated around 30 GHz.

We should also mention that the overall circuit of our detection system represents a directional filter consisting of two parts:


**165**

**Figure 9.**

*Optimal Temperature Sensor Based on a Sensitive Material*

From the coupling coefficient S12 between access 1 and 2 (simulated) given as a function of frequency, the gallery modes WGE and WGH were identified over a frequency range of 25–40 GHz. **Figure 9** shows the look of the transmission parameter

*The field distribution of the WGE8.0.0 to 30 GHz mode for eigenmode calculation (HFSS™).*

**Figure 10(a)** and **(b)** shows examples of simulation results corresponding to amplitudes of the magnetic field of the gallery modes at their resonant frequencies. Based on the results obtained as well as those in the literature, PLZT appears to be the right candidate for frequency temperature transduction. Indeed, it has been previously demonstrated that the dielectric permittivity of this material can be modified in the presence of a temperature variation. We therefore aim to analyze the impact of such a modification on the resonance frequency of a gallery mode. For this purpose, the dielectric constant εr was varied between 700 and 900 with a

*DOI: http://dx.doi.org/10.5772/intechopen.90733*

between access 1 and 2 in the Ka-band.

*Coupling coefficient S12 as a function of frequency for ɛPLZT = 760.*

**Figure 8.**

*Perovskite and Piezoelectric Materials*

these two micro-machined lines.

isolated around 30 GHz.

electromagnetic

sents a directional filter consisting of two parts:

material PLZT as an element of recognition

*The sensitive material and the resonator in the cavity with a holder.*

monitored and a direct relationship to be established between the temperature variation and the observed frequency offset. In this way, a temperature measure-

Series of free oscillation simulations (eigenmode) using the HFSSTM software, applied to the dielectric resonators, determine the diameter, thickness, permittivity of the dielectric resonator, as well as the distribution of the electromagnetic field necessary to define the caustic and the optimal coupling with the coplanar lines (see **Figure 7**). The determination of caustic makes it possible to establish the distribution of the electromagnetic field in the RD and leads to the definition of the position of the coplanar lines. In addition, the diameter of the resonator and the confinement of the electromagnetic field in it impose the distance between

In this study, we studied a dielectric resonator with a relative permittivity of 80 and no losses. The thickness and diameter of the dielectric resonator are used to determine the resonance modes and frequencies associated with them. Subsequently, we are interested in the modification of the physical properties of the PLZT material in the presence of a change in temperature, more precisely the variation of its dielectric permittivity. As shown in **Figure 8**, we observe the distribution of the electric field of the WGE8.0.0 mode in the dielectric resonator; it is thus

We should also mention that the overall circuit of our detection system repre-

• Coplanar lines (CPWs) used for RD excitation and field propagation

• Dielectric resonator used for coupling and excited in WGM as well as the

ment is carried out via an electromagnetic transduction.

**6. Simulation results of the complete sensor**

**164**

**Figure 7.**

#### **Figure 8.** *The field distribution of the WGE8.0.0 to 30 GHz mode for eigenmode calculation (HFSS™).*

From the coupling coefficient S12 between access 1 and 2 (simulated) given as a function of frequency, the gallery modes WGE and WGH were identified over a frequency range of 25–40 GHz. **Figure 9** shows the look of the transmission parameter between access 1 and 2 in the Ka-band.

**Figure 10(a)** and **(b)** shows examples of simulation results corresponding to amplitudes of the magnetic field of the gallery modes at their resonant frequencies.

Based on the results obtained as well as those in the literature, PLZT appears to be the right candidate for frequency temperature transduction. Indeed, it has been previously demonstrated that the dielectric permittivity of this material can be modified in the presence of a temperature variation. We therefore aim to analyze the impact of such a modification on the resonance frequency of a gallery mode. For this purpose, the dielectric constant εr was varied between 700 and 900 with a

**Figure 9.** *Coupling coefficient S12 as a function of frequency for ɛPLZT = 760.*

**Figure 10.** *Amplitude of the magnetic field of the gallery modes: (a) WGH6,0,0 and (b) WGE5,0,0.*

14% variation. As shown in **Figure 11**, the variation in PLZT permittivity produces measurable changes in resonance frequency, reflected in a shift to low frequencies of about 1 GHz, for example, in the case of WGE4.0.0 mode.

These modifications on the resonance frequency for variations in the permittivity of the PLZT material highlight the high sensitivity of this type of device. This sensitivity represents that of the electromagnetic transducer, which transforms a variation in permittivity into a variation in the resonance frequency of a WGM. In order to evaluate this sensitivity, we have shown in **Figure 12(a)** and **(b)** the resonance frequencies of the WGH7.0.0 and WGE9.0.0 modes, respectively, as a function of the permittivity of the PLZT when there is a temperature variation. The results obtained with a cylindrical dielectric resonator have shown that the resonance frequencies of the gallery modes are very sensitive to the change in the permittivity of the sensitive material. The relationship between permittivity and resonance frequencies is approximately linear.

The sensor sensitivity is the combination of the transducer sensitivity with the variation in PLZT permittivity as a function of temperature.

**167**

**Figure 11.**

*and 900).*

**Figure 12.**

dielectric resonator.

*Optimal Temperature Sensor Based on a Sensitive Material*

The gallery modes in the dielectric resonator and the PLZT material are evidently used here to measure the permittivity change and deduce the temperature change. From rigorous electromagnetic numerical simulations (HFSS™), we show here that a small change in the permittivity of the sensitive material induces a large variation in the resonance frequency of the dielectric resonator gallery modes.

*Resonance frequencies as a function of PLZT permittivity: (a) WGH7.0.0 mode and (b) WGE9.0.0 modes.*

*Transmission coefficient (S12) as a function of frequency for variations in PLZT permittivity (εr = 700, 800,* 

Based on the characteristics of the sensitive material used and the previous results, it is therefore possible to deduce the relationship between the resonance frequency of the detected gallery modes and the temperature. As a result, a linear dependence between frequency and temperature is clearly observed for all modes detected. In other words, the relatively linear dependence between temperature and dielectric constant of the sensitive material leads to a change in the coupling coefficient between the two coplanar waveguides, and this is subsequently reflected in a shift in the resonance frequency of the system. As a result, a temperature variation usually results in a shift in the resonance frequency of the excited mode in the

*DOI: http://dx.doi.org/10.5772/intechopen.90733*

#### **Figure 11.**

*Perovskite and Piezoelectric Materials*

14% variation. As shown in **Figure 11**, the variation in PLZT permittivity produces measurable changes in resonance frequency, reflected in a shift to low frequencies

These modifications on the resonance frequency for variations in the permittivity of the PLZT material highlight the high sensitivity of this type of device. This sensitivity represents that of the electromagnetic transducer, which transforms a variation in permittivity into a variation in the resonance frequency of a WGM. In order to evaluate this sensitivity, we have shown in **Figure 12(a)** and **(b)** the resonance frequencies of the WGH7.0.0 and WGE9.0.0 modes, respectively, as a function of the permittivity of the PLZT when there is a temperature variation. The results obtained with a cylindrical dielectric resonator have shown that the resonance frequencies of the gallery modes are very sensitive to the change in the permittivity of the sensitive material. The relationship between permittivity and resonance

The sensor sensitivity is the combination of the transducer sensitivity with the

of about 1 GHz, for example, in the case of WGE4.0.0 mode.

*Amplitude of the magnetic field of the gallery modes: (a) WGH6,0,0 and (b) WGE5,0,0.*

variation in PLZT permittivity as a function of temperature.

frequencies is approximately linear.

**166**

**Figure 10.**

*Transmission coefficient (S12) as a function of frequency for variations in PLZT permittivity (εr = 700, 800, and 900).*

**Figure 12.** *Resonance frequencies as a function of PLZT permittivity: (a) WGH7.0.0 mode and (b) WGE9.0.0 modes.*

The gallery modes in the dielectric resonator and the PLZT material are evidently used here to measure the permittivity change and deduce the temperature change. From rigorous electromagnetic numerical simulations (HFSS™), we show here that a small change in the permittivity of the sensitive material induces a large variation in the resonance frequency of the dielectric resonator gallery modes.

Based on the characteristics of the sensitive material used and the previous results, it is therefore possible to deduce the relationship between the resonance frequency of the detected gallery modes and the temperature. As a result, a linear dependence between frequency and temperature is clearly observed for all modes detected.

In other words, the relatively linear dependence between temperature and dielectric constant of the sensitive material leads to a change in the coupling coefficient between the two coplanar waveguides, and this is subsequently reflected in a shift in the resonance frequency of the system. As a result, a temperature variation usually results in a shift in the resonance frequency of the excited mode in the dielectric resonator.
