# Electromagnetic Differential Measuring Method: Application in Microstrip Sensors Developing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Differential Measurement Model

- If the wave-medium interaction is known, the link distance (emitter-receiver) can be estimated using differential measures in the receiver. This treatment is useful for location systems.
- If the distance emitter-receiver or some environment conditions are known, medium parameters can be estimated using differential measures in the receiver. This treatment is useful for medium detection systems.

#### Differences with Similar Methods

## 4. Advantages and Disadvantages Over the Conventional Scenarios

- A differential electric measurement is floating, meaning that it has no reference to ground. The measurement is taken as the voltage difference between two ports. The main benefit of a differential measurement is noise rejection, because the noise is added to both wires and can then be filtered out by the common mode rejection of the data acquisition system.
- The differential method proposed could use adapted TDT and TDR transmissions, expanding their capabilities on multi-frequency signals or multi-medium support.
- Conventional treatment must use a synchronized reference systems in the transmitter and receiver. In contrast to this conventional signal treatment a differential measure model is proposed and measured magnitude in the receiver (arrival time, signal amplitude, etc.) are relative. Differential measurements work with independent temporal references and enable the application of solutions with independent positional reference systems.

## 5. Simulation of wave Propagation in Dielectric Medium

## 6. Microstrip Sensor and Differential Measures

- Differential phase shift
- Differential electrical field
- Other differential measures (impedances, signal loss, etc.)

#### 6.1. Differential Measure Based in Phase Shift

#### 6.2. Differential Measure Based in Electrical Field

#### 6.3. Microstrip Sensors

#### 6.4. Simulation Platform and Other Electromagnetic Effects (Dielectric Losses and Materials)

## 7. Conclusions

- If unkown material permittivity ${\u03f5}_{m}$ is equal or similar to reference permittivity ${\u03f5}_{r}$, differential measures are minimum (Figure 13).
- Level detectors can be built using differential measures on microstrip configuration (Table 5).
- Multi reference materials can be used in substrate configuration to build levels detectors (Figure 15).
- Heuristic rules can be processed to detect levels exceeding limit values (Table 6).
- Materials permittivity could be characterized using microstrips configuration with reference substrate and adapted dimensions.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**EM waves treatment in remote sensing applications. Devices need to synchronize the reference systems. Reference systems have the same reference time.

**Figure 2.**Differential method with different frequencies. The differential measures in the receiver incorporate information. Time synchronization is not necessary. The differential method proposed can also use a single frequency inducing different medium conditions.

**Figure 3.**Multifrequency FDTD simulation in a dielectric medium. Transparent (${\u03f5}_{eff}=1$) for the first frequency at the top. Different interaction (propagation speed and energy absorption) for other frequencies with different ${\u03f5}_{eff}$. Time differences $\mathrm{\Delta}{t}_{1}$ and $\mathrm{\Delta}{t}_{2}$ can be measured to analyze dielectric medium.

**Figure 4.**Rectangular wave guide ($L=60$ mm, $a=7.894$ mm and $b=3.947$ mm) used in propagation simulation built with two differentiated transmission lines. One input signal is transmitted (1) to the waveguide and derived into the two transmission lines. Two output ports signals are obtained (2) and time difference of arrival between two waves are obtained (3). The difference measured (4) characterize medium ${\u03f5}_{r}$.

**Figure 5.**Three pictures with wave propagation simulation (in time domain) using waveguide shown in Figure 4; $m1$ is the input pulse, $m2$ is output line pulse with $\u03f5=1$, $m3$ is output line pulse with unknown ${\u03f5}_{r}$. One input signal is transmitted ($m1$) to the waveguide and derived into the two transmission lines. Two output ports signals are obtained ($m2$ and $m3$) and time difference of arrival between two waves are obtained (${\mathrm{\Delta}}_{t}=m3-m2$). The measured difference (4) characterizes ${\u03f5}_{m}$.

**Figure 7.**Frequency response in rectangular wave guide with different dielectric (${\u03f5}_{r}$) materials. Simulation using HFSS software is performed. Differences in cutoff frequencies (${m}_{i}-{m}_{j}=f{c}_{i}-f{c}_{j}={\mathrm{\Delta}}_{f}$) are obtained to calculate unknown ${\u03f5}_{r}$.

**Figure 10.**Sensitive analysis to determine how different values of dielectric medium (${\u03f5}_{m}$) and microstrip dimensions (h and w) impact on effective permittivity (${\u03f5}_{eff}$) shown in Equation (10).

**Figure 11.**General model of microstip sensor proposed ($L=25$ mm, $width=10$ mm, $height=2$ mm and patch $line=0.8$ mm). Numeric differential measures (${d}_{mr}$) can be obtained to characterize dielectric medium unknown (${\u03f5}_{m}$), knowing reference permittivity (${\u03f5}_{r}$) and microstrip substrate (${\u03f5}_{s}$).

**Figure 12.**Microstrip line simulation with reference and substrate permittivity ${\u03f5}_{r}=4$. Different permittivity medium ${\u03f5}_{m}$ are used to obtain phase shift on microstrip terminals.

**Figure 13.**Microstrip line simulation with reference and substrate permittivity ${\u03f5}_{r}=4$. Different permittivity medium ${\u03f5}_{m}$ are used to obtain differential electric field on microstrip terminals.

**Figure 14.**Microstrip line used as a sensor to detect permittivity levels of unknown material. Microstrip patch can have different dimensions and forms.

**Figure 15.**Configuration of a sensor microstrip that detect low, medium or high permittivity levels in applications where permittivity must be detected.

Medium is Represented by m Parameters in $\mathit{M}=\mathit{M}({\mathit{p}}_{1},\dots ,{\mathit{p}}_{\mathit{m}})$ Functions |
---|

IF $\mathrm{\Psi}$ is a measurable magnitude (speed propagation, time, amplitude, phase of arrival) which represents the interaction: wave (E) - medium (M), and the medium M has EM medium parameters (${p}_{1},\dots ,{p}_{m}$) |

THEN: measurable magnitude $\mathrm{\Psi}$ in the receiver is a function $\mathrm{\Psi}=\mathrm{\Psi}(E,M)$ |

IF differences (${\mathrm{\Psi}}_{i}-{\mathrm{\Psi}}_{j}$) are measured in the receiver THEN: different equations can be combined to calculate medium parameters (${p}_{1},\dots ,{p}_{m}$). |

1. IF different frequencies are used in the interaction THEN: the equations system formed is: |

${\mathrm{\Psi}}_{i}-{\mathrm{\Psi}}_{j}={\mathrm{\Delta}}_{\mathrm{\Psi}ij}={\mathrm{\Psi}}_{i}({E}_{i},{p}_{1},\dots ,{p}_{m})-{\mathrm{\Psi}}_{j}({E}_{j},{p}_{1},\dots ,{p}_{m})$ |

(${p}_{1},\dots ,{p}_{m}$) → are the unknown medium parameters |

${E}_{i}$ and ${E}_{j}$ → are EM waves at frequencies i and j |

${\mathrm{\Delta}}_{\mathrm{\Psi}ij}$ → are the differential measure obtained in receiver device |

For $n+1$ frequencies there are n differential measures ${\mathrm{\Delta}}_{\mathrm{\Psi}ij}$ in receiver device. |

2. IF only a frequency is used THEN: differential measures can be obtained with known medium parameters used as references. The same EM wave (E) is transmitted through a known reference medium ($E,{p}_{ref1},\dots ,{p}_{refm}$) and through the unknown medium ($E,{p}_{1},\dots ,{p}_{m}$). The equations are: ${\mathrm{\Psi}}_{i}-{\mathrm{\Psi}}_{j}={\mathrm{\Delta}}_{\mathrm{\Psi}ij}={\mathrm{\Psi}}_{i}(E,{p}_{ref1},\dots ,{p}_{refm})-{\mathrm{\Psi}}_{j}(E,{p}_{1},\dots ,{p}_{m})$ |

**Table 2.**Simulation measures (in time domain) obtained in three different materials. Simulated and theoretical results are compared. Time differences are obtained in waveguide transmission (shown in Figure 5).

${\mathit{m}}_{2}-{\mathit{m}}_{1}={\mathbf{\Delta}}_{\mathit{t}}$ | Simulated Result | Theoretical Result | Error % |
---|---|---|---|

$0.0778\phantom{\rule{4pt}{0ex}}ns$ | ${\u03f5}_{r}=3.16$ | ${\u03f5}_{r}=3$ | 5.3 |

$0.1493\phantom{\rule{4pt}{0ex}}ns$ | ${\u03f5}_{r}=6.2$ | ${\u03f5}_{r}=6$ | 3.3 |

$0.2053\phantom{\rule{4pt}{0ex}}ns$ | ${\u03f5}_{r}=9.32$ | ${\u03f5}_{r}=9$ | 3.5 |

**Table 3.**Simulation measures (in frequency domain) obtained in three different materials. Cutoff frequency differences are obtained in waveguide transmission (shown in Figure 7). Theoretical and simulated measures are compared.

${\mathit{m}}_{\mathit{i}}-{\mathit{m}}_{\mathit{j}}=\mathit{f}{\mathit{c}}_{\mathit{i}}-\mathit{f}{\mathit{c}}_{\mathit{j}}={\mathbf{\Delta}}_{\mathit{f}}$ | Simulated Result | Theoretical Result | Error % |
---|---|---|---|

2.8 GHz | ${\u03f5}_{r}=3.2$ | ${\u03f5}_{r}=3$ | 3.3 |

3.9 GHz | ${\u03f5}_{r}=6.2$ | ${\u03f5}_{r}=6$ | 3.3 |

4.4 GHz | ${\u03f5}_{r}=9.3$ | ${\u03f5}_{r}=9$ | 6.7 |

**Table 4.**Differential phase (rad) at the end of the line. Reference permittivity used is ${\u03f5}_{reff}=4$.

${\mathit{\u03f5}}_{\mathit{meff}}=1$ | ${\mathit{\u03f5}}_{\mathit{meff}}=2$ | ${\mathit{\u03f5}}_{\mathit{meff}}=3$ | ${\mathit{\u03f5}}_{\mathit{meff}}=4$ | ${\mathit{\u03f5}}_{\mathit{meff}}=5$ | ${\mathit{\u03f5}}_{\mathit{meff}}=6$ | ${\mathit{\u03f5}}_{\mathit{meff}}=7$ | ${\mathit{\u03f5}}_{\mathit{meff}}=8$ |
---|---|---|---|---|---|---|---|

0.523599 | 0.306717 | 0.140298 | 0 | −0.123605 | −0.235352 | −0.338115 | −0.433763 |

1.0472 | 0.613434 | 0.280596 | 0 | −0.24721 | −0.470705 | −0.676229 | −0.867527 |

1.5708 | 0.920151 | 0.420894 | 0 | −0.370815 | −0.706057 | −1.01434 | −1.30129 |

2.0944 | 1.22687 | 0.561191 | 0 | −0.49442 | −0.94140 | −1.35246 | −1.73505 |

2.61799 | 1.53359 | 0.701489 | 0 | −0.618025 | −1.17676 | −1.69057 | −2.16882 |

3.14159 | 1.8403 | 0.841787 | 0 | −0.741629 | −1.41211 | −2.02869 | −2.60258 |

3.66519 | 2.14702 | 0.982085 | 0 | −0.865234 | −1.64747 | −2.3668 | −3.03634 |

**Table 5.**Numeric results of simulation realized using configuration shown in Figure 15. ${d}_{mr}$ represents differential electric field in V obtained in terminals. $s{h}_{mr}$ represents the phase shift sign obtained on electric field in terminals and ${T}_{s{h}_{mr}}$ is time shift in $ns$. Sinusoidal signal with $f=1$ GHz is used in this simulation.

${\mathit{\u03f5}}_{\mathit{r}1}=4.4$ | ${\mathit{\u03f5}}_{\mathit{r}2}=10$ | ${\mathit{\u03f5}}_{\mathit{r}3}=20$ | ${\mathit{\u03f5}}_{\mathit{r}1}=4.4$ | ${\mathit{\u03f5}}_{\mathit{r}2}=10$ | ${\mathit{\u03f5}}_{\mathit{r}3}=20$ | ${\mathit{\u03f5}}_{\mathit{r}1}=4.4$ | ${\mathit{\u03f5}}_{\mathit{r}2}=10$ | ${\mathit{\u03f5}}_{\mathit{r}3}=20$ | |
---|---|---|---|---|---|---|---|---|---|

${\mathit{\u03f5}}_{\mathit{m}}$ | ${\mathit{d}}_{\mathit{mr}\mathbf{1}}$ | ${\mathit{d}}_{\mathit{mr}\mathbf{2}}$ | ${\mathit{d}}_{\mathit{mr}\mathbf{3}}$ | ${\mathit{sh}}_{\mathit{mr}\mathbf{1}}$ | ${\mathit{sh}}_{\mathit{mr}\mathbf{2}}$ | ${\mathit{sh}}_{\mathit{mr}\mathbf{3}}$ | ${\mathit{T}}_{{\mathit{sh}}_{\mathit{mr}\mathbf{1}}}$ | ${\mathit{T}}_{{\mathit{sh}}_{\mathit{mr}\mathbf{2}}}$ | ${\mathit{T}}_{{\mathit{sh}}_{\mathit{mr}\mathbf{3}}}$ |

1 | 0.6 | 0.8 | >1 | - | - | - | 0.1 | 0.18 | 0.3 |

2 | 0.35 | 0.7 | >1 | - | - | - | 0.05 | 0.1 | 0.2 |

4.4 | 0.1 | 0.4 | 1 | + | - | - | 0.01 | 0.05 | 0.15 |

8 | 0.3 | 0.15 | 0.75 | + | - | - | 0.04 | 0.08 | 0.1 |

10 | 0.5 | 0.1 | 0.6 | + | + | - | 0.1 | 0.02 | 0.1 |

15 | 1.0 | 0.5 | 0.3 | + | + | - | 0.2 | 0.1 | 0.08 |

20 | >1 | >1 | 0.1 | + | + | + | 0.3 | 0.1 | 0.01 |

30 | >1 | >1 | >1 | + | + | + | >1 ns | 0.9 | 0.8 |

**Table 6.**Rules Configuration of a sensor microstrip that detect low, medium or high permittivity levels in applications where permittivity must be detected.

${\u03f5}_{m}$ | ($if\phantom{\rule{1.em}{0ex}}{sh}_{mr1}\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i}\ne \phantom{\rule{1.em}{0ex}}{sh}_{mr1}\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}\phantom{\rule{1.em}{0ex}})\phantom{\rule{1.em}{0ex}}then$ |

crosses | $if\phantom{\rule{1.em}{0ex}}{sh}_{mr{1}_{ti}}=-\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\in [{\u03f5}_{max},{\u03f5}_{max}]\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}$ |

minimum level | $if\phantom{\rule{1.em}{0ex}}{sh}_{mr{1}_{ti}}=+\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\notin [{\u03f5}_{max},{\u03f5}_{max}]\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}$ |

${\u03f5}_{m}$ | $(if\phantom{\rule{1.em}{0ex}}{sh}_{mr3}\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i}\ne \phantom{\rule{1.em}{0ex}}{sh}_{mr3}\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}\phantom{\rule{1.em}{0ex}})\phantom{\rule{1.em}{0ex}}then$ |

crosses | $if\phantom{\rule{1.em}{0ex}}{sh}_{mr{3}_{ti}}=+\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\in [{\u03f5}_{max},{\u03f5}_{max}]\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}$ |

maximum level | $if\phantom{\rule{1.em}{0ex}}{sh}_{mr{3}_{ti}}=-\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\notin [{\u03f5}_{max},{\u03f5}_{max}]\phantom{\rule{1.em}{0ex}}in\phantom{\rule{1.em}{0ex}}{time}_{i+1}$ |

$if\phantom{\rule{1.em}{0ex}}{d}_{mr1}\approx 0\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\to {\u03f5}_{r1}$ | |

${\u03f5}_{m}\in [{\u03f5}_{min},{\u03f5}_{max}]$ | $if\phantom{\rule{1.em}{0ex}}{d}_{mr2}\approx 0\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\to {\u03f5}_{r2}$ |

$if\phantom{\rule{1.em}{0ex}}{d}_{mr3}\approx 0\phantom{\rule{1.em}{0ex}}then\phantom{\rule{1.em}{0ex}}{\u03f5}_{m}\to {\u03f5}_{r3}$ |

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**MDPI and ACS Style**

Ferrández-Pastor, F.J.; García-Chamizo, J.M.; Nieto-Hidalgo, M.
Electromagnetic Differential Measuring Method: Application in Microstrip Sensors Developing. *Sensors* **2017**, *17*, 1650.
https://doi.org/10.3390/s17071650

**AMA Style**

Ferrández-Pastor FJ, García-Chamizo JM, Nieto-Hidalgo M.
Electromagnetic Differential Measuring Method: Application in Microstrip Sensors Developing. *Sensors*. 2017; 17(7):1650.
https://doi.org/10.3390/s17071650

**Chicago/Turabian Style**

Ferrández-Pastor, Francisco Javier, Juan Manuel García-Chamizo, and Mario Nieto-Hidalgo.
2017. "Electromagnetic Differential Measuring Method: Application in Microstrip Sensors Developing" *Sensors* 17, no. 7: 1650.
https://doi.org/10.3390/s17071650