# Design and Optimization of Microwave Sensor for the Non-Contact Measurement of Pure Dielectric Materials

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## Abstract

**:**

_{r}= 3.5 and tanδ = 0.0018). The bridge-type differential inductor is introduced to obtain a maximum inductance value with high quality (Q) factor and low tunable resonant frequency. The central IDC structure is configured as a spur-line structure to create a high-intensity coupled electric field (e-field) zone, which significantly interacts with the materials under test (MUTs), resulting in an increased sensitivity. The proposed sensor prototype with optimized parameters generates a resonant frequency at 1.38 GHz for measuring the complex permittivity and material thickness. The experimental results indicated that the resonant frequency of the designed sensor revealed high sensitivities of 41 MHz/mm for thickness with a linear response (r

^{2}= 0.91567), and 53 MHz/Δε

_{r}for permittivity with a linear response (r

^{2}= 0.98903). The maximum error ratio for measuring MUTs with a high gap of 0.3 mm between the testing sample and resonator is 6.52%. The presented performance of the proposed sensor authenticates its application in the non-contact measurement of samples based on complex permittivity and thickness.

## 1. Introduction

## 2. Microwave Sensor Design and Operating Principle

#### 2.1. Microwave Sensor Design

_{C}) and parallel IDC structure (C

_{IDC}) affect the resonating frequency; thus, it is possible to employ it as an indicator. The total capacitance produced by the combination of C

_{IDC}and C

_{C}can be approximated as [29]:

_{e}is the length of the electrode, N

_{E}represents the number of fingers, and f

_{W}and f

_{g}define the finger width and gap, respectively. The analysis of interdigital capacitor type structure is essentially based on the sensing zone. The interdigital capacitor is performed like a traditional plate capacitor, but the main benefit lies between adjacent finger strips. The gaps between the fingers of such type of structure are enhancing the total e-field of the resonator. The fingers of interdigital structure and its gaps provide a high electrical potential at the surface of the designed sensor. Once the testing MUTs are loaded on the high field zone, it distracts the entire field, which indicates a variation in the resonance frequency and Q-factor.

_{EFF}determines the effective line width, L

_{MS}represents the length of the metal (copper) segment, H

_{MS}denotes the height of the metal segment. Similarly, n indicates the number of turns in the coil inductor, C

_{1}and C

_{2}are demonstrated the linearized parameters for the inductance and resistance, respectively. The mutual inductance of the designed sensor mainly depends on the gap between segments and can be defined as [31]:

#### 2.2. Operating Principle of the Design

_{0}and H

_{0}represent the e-field and m-field of the unloaded sample, E

_{1}and H

_{1}define the field distribution after loading an MUT on the resonator, and ${\mu}_{0}$ and ${\epsilon}_{0}$ represent the permeability and permittivity in free space. The designed sensor is decorated only to characterize the dielectric properties of materials; thus, the terms related to material permeability are neglected. All the tested samples are pure dielectric, and the modified equations can be expressed as [1]:

_{1}, h

_{2}, h

_{3}), where h

_{1}is the substrate thickness, h

_{2}denotes the air gap thickness, and the sample thickness is represented by h

_{3}. According to the definition of the capacitor, $C=\epsilon A/d=\epsilon \left(2h.\right)/\left(2{i}_{0}\right)$, the variable 2i

_{0}defines the d, and 2h represents the variable A in the capacitance expression, as shown in Figure 4b. The total capacitance of an MUT with an air gap on the proposed design can be represented as follows [27]:

## 3. Fabrication of the Proposed Design

## 4. Experimental Results and Discussion

#### 4.1. Analysis of Complex Permittivity with Air Gap Scenario

_{r}represents the alteration of the resonance frequency with different MUTs loaded on the resonator. The polypropylene strips are introduced between the testing MUT and resonator with varying thicknesses from 0.01–0.3 mm, as shown in Figure 7a–f. The designed sensor sensing accuracy is 97% for estimating the relative part of the permittivity with an excellent correlation coefficient (r

^{2}= 0.97765). The dielectric loss tangent of each testing MUTs is calculated from Equation (15).

^{2}= 0.92694).

_{21}| and simulation of the proposed microwave sensor is low, and it exhibits a small error ratio for measuring all the testing MUTs. The performance of the designed sensor based on the error ratio is represented in Table 3.

#### 4.2. Analysis of Thickness with Air Gap Scenario

_{r}) and frequency shifting (Δf

_{r}) against the variation in the gap between the designed sensor and mica thicknesses. The polynomial interpolation between the measured resonance frequency and frequency shifting of mica MUTs against the various gap variations is shown in Figure 8b,c, which can be defined as:

_{21}|). The frequency range is set to 1–2 GHz for the measurement setup, and the polypropylene strips are used for an air gap effect, as shown in Figure 9.

^{2}= 0.91567 for thickness and r

^{2}= 0.98903 for permittivity MUTs). It can be defined using the following regression equations (Equations (23) and (24)) for thickness and permittivity of the samples, as shown in Figure 10a,b.

_{mm}represents the thickness of the mica sample and ${\alpha}_{{\epsilon}_{r}^{\prime}}$ denotes the permittivity of loaded MUTs. Therefore, the f

_{r}of the designed sensor revealed high sensitivities (41 MHz/mm for thickness and 53 MHz/Δ${\epsilon}_{r}$ for permittivity sample) towards the measurement of thickness and permittivity of the specimen, simultaneously via a single sensor. The resolution and reproducibility of the proposed design are evaluated using a triplicate analysis of each sample. The designed sensor reveals a minute variation in the sample measurement, and it is estimated using the triplicate measurement analysis for permittivity (0.05734) and thickness (0.04618) of the samples. The high reproducibility is predictable, and it is due to the usage of a microwave analyzer (N9916A), which is calculated more precisely by the variation in the resonance frequency (down to 5 kHz). The linearity operation for the MUTs thickness concerning various gap variations is little degraded, as shown in Figure 10a. This is because the resonance frequency of the designed sensor is influenced by the MUTs thickness and different strips variations. The proposed sensor’s correlation coefficient for measuring the mica thickness linear response is r

^{2}= 0.91567. This effect can be minimized by decreasing the gap between the MUTs thickness and resonator. It depends on the measurement setup, and users can utilize it according to their terms and conditions.

## 5. Conclusions

_{r}(53 MHz/Δ${\epsilon}_{r}$ and 41 MHz/mm) for measuring the thickness and complex permittivity of MUTs with varying air gaps of 0.1 mm and 0.3 mm, respectively. The proposed microwave sensor exhibits an excellent sensing accuracy of 97% and 92% for the real and imaginary parts of the permittivity, respectively. Moreover, the curve fitting technique between the testing sample with varying thickness, permittivity, and air gap exhibited an excellent accuracy, authenticating its application in the non-contact measurement of material. The designed sensor performance affirms its application in the non-contact measurement of complex permittivity and thickness of different pure dielectric MUTs simultaneously.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The 3D geometry of the proposed non-contact optimized microwave sensor layout: (

**a**) front side of the proposed design; (

**b**) backside of the proposed design; (

**c**) simulation-based bridge-type structure; (

**d**) equivalent circuit of the designed sensor; (

**e**) strength of high intensity coupled e-field revealing a maximum field at the center of the developed sensor; and (

**f**) comparison of the resonating frequency of simulated and measured prototype for unloaded MUTs.

**Figure 2.**(

**a**) Traditional plate capacitor e-field lines and (

**b**) IDC structure capacitor e-field lines.

**Figure 3.**(

**a**) Lower tunable resonating frequency of optimized microwave sensor and (

**b**) different parameters of the developed sensor.

**Figure 4.**(

**a**) Designed sensor under testing with polypropylene strip between the testing specimen and resonator and (

**b**) dimension of the mapping air gap scenario between MUT and resonator.

**Figure 5.**Fabrication steps of the proposed prototype: (

**a**) RF-35 substrate with copper decoration on both sides; (

**b**) photoresist layer on the backside of the film; (

**c**) patterned mask on the film with UV light exposure for moving design on the substrate; (

**d**) the proposed microwave sensor with SMA connectors.

**Figure 6.**Proposed microwave sensor with e-field distribution at the lower tunable resonant frequency; (

**a**) designed sensor without a circular finger; (

**b**) with one circular finger; (

**c**) with two circular fingers and one bridge-type structure; (

**d**) with three circular fingers and two bridge-type structure; (

**e**) with four circular fingers and three bridge-type structure; (

**f**) with five circular fingers and four bridge-type structure; (

**g**) e-field at 1.74 GHz; (

**h**) 1.55 GHz; (

**i**) 1.52 GHz; (

**j**) 1.49 GHz; (

**k**) 1.46 GHz; and (

**l**) 1.38 GHz.

**Figure 7.**|S

_{21}|measured analysis of different permittivity MUTs loaded on the high e-field centralized IDC structure with varying air gaps ranging from 0.01–0.3 mm; (

**a**) FR4 MUT; (

**b**) rogers RO3003 (Rog) MUT; (

**c**) mica MUT curve fitting technique analysis with error bars for the triplicate measurement of testing MUTs with varying air gap scenario; (

**d**) FR4; (

**e**) rogers RO3003; and (

**f**) mica.

**Figure 8.**(

**a**) |S

_{21}|measured analysis of different thicknesses of mica MUT loaded on the high e-field centralized IDC structure with varying air gaps; (

**b**) resonance frequency; and (

**c**) frequency shifting (note: Equations (20) and (21) based on Figure 8b,c were arbitrarily proposed).

**Figure 9.**Measurement setup of the proposed design: (

**a**) designed sensor under testing; (

**b**) back view of the designed sensor; (

**c**) polypropylene strips between designed microwave sensor and MUT; (

**d**) fabricated bridge-type structure.

**Figure 10.**(

**a**) Linear regression graph as per change in MUTs thickness with error bar indicating an excellent linear response (r

^{2}= 0.91567); (

**b**) linear regression graph as per change in MUTs permittivity with error bar indicating an excellent linear response (r

^{2}= 0.98903).

Parameters | Abbreviation | Minimum Value | Optimized Value | Maximum Value |
---|---|---|---|---|

f_{w} | Finger width | 0.1 | 0.3 | 0.4 |

f_{g} | Finger gap | 0.2 | 0.325 | 0.5 |

l_{e} | Length of electrode | 7.0 | 12.5 | 14.0 |

w_{e} | Width of electrode | 0.1 | 0.3 | 0.5 |

f_{l} | Finger length | 2.0 | 4.0 | 6.0 |

w_{1} | Gap between electrode | 6.0 | 9.0 | 12.0 |

w_{3} | Width of circular finger | 0.1 | 0.31 | 0.5 |

g_{1} | Gap between circular finger | 0.1 | 0.31 | 0.5 |

g_{2} | Gap between bridge-type structure | 0.15 | 0.3 | 0.45 |

l | Length of the proposed design | -- | -- | 15 |

w | Width of the proposed design | -- | -- | 15 |

**Table 2.**Proposed microwave sensor comparison based on complex permittivity analysis with previously reported literature.

References | f_{r} (GHz) | ${\mathit{\epsilon}}_{\mathit{r}}^{\prime}\mathbf{Range}$ | S (%) | FDR (MHz) | Maximum Gap (mm) | Sensing Accuracy |
---|---|---|---|---|---|---|

[1] | 2.47 | 3.25–6.2 | 1.7 | 40 | 0 | -- |

[3] | 2.45 | 2.09–6.92 | 0.5 | 10 | 0 | -- |

[28] | 2.35 | 2.2–10.5 | 3.98 | 290 | 0 | 99.9% and 99.7% |

[32] | 2.0 | 2.2–10.2 | 3.3 | 225 | 0 | -- |

[33] | 5.79 | 1.6–6.15 | 4.3 | 373 | 0 | 99% and 97% |

[34] | 3.6 | 2.43–10.2 | 1.2 | 210 | 0 | -- |

[35] | 2.18 | 2.2–10.7 | 3.59 | 245 | 0 | -- |

[36] | 1.8 | 2.2–10.5 | 3.39 | 63 | 0 | 99% and 87% |

Proposed design | 1.38 | 3–6 | 0.51 | 7.2 | 0.3 | 97% and 92% |

**Table 3.**Measurement analysis of the designed sensor based on error ratio for the different permittivity MUTs.

Sample | $\mathbf{Reference}{\mathit{\epsilon}}_{\mathit{r}}^{\prime}$ | $\mathbf{Extracted}{\mathit{\epsilon}}_{\mathit{r}}^{\prime}$ | Reference tanδ | Extracted tanδ | Error (%) |
---|---|---|---|---|---|

FR4 | 3.0 ± 0.2 | 3.05 | 0.025 | 0.0237849 | 3.86 |

Rogers | 4.3 ± 0.15 | 4.25 | 0.001 | 0.0015649 | 4.49 |

Mica | 6.1 ± 0.2 | 6.15 | -- | -- | 6.52 |

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**MDPI and ACS Style**

Ali, L.; Wang, C.; Ullah, I.; Yousaf, A.; Khan, W.U.; Ullah, S.; Khan, R.; Alassery, F.; Hamam, H.; Shafiq, M.
Design and Optimization of Microwave Sensor for the Non-Contact Measurement of Pure Dielectric Materials. *Electronics* **2021**, *10*, 3057.
https://doi.org/10.3390/electronics10243057

**AMA Style**

Ali L, Wang C, Ullah I, Yousaf A, Khan WU, Ullah S, Khan R, Alassery F, Hamam H, Shafiq M.
Design and Optimization of Microwave Sensor for the Non-Contact Measurement of Pure Dielectric Materials. *Electronics*. 2021; 10(24):3057.
https://doi.org/10.3390/electronics10243057

**Chicago/Turabian Style**

Ali, Luqman, Cong Wang, Inam Ullah, Adnan Yousaf, Wali Ullah Khan, Shafi Ullah, Rahim Khan, Fawaz Alassery, Habib Hamam, and Muhammad Shafiq.
2021. "Design and Optimization of Microwave Sensor for the Non-Contact Measurement of Pure Dielectric Materials" *Electronics* 10, no. 24: 3057.
https://doi.org/10.3390/electronics10243057