# Meander Microwave Bandpass Filter on a Flexible Textile Substrate

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Framework

_{r}= 1.2, and loss tangent tan δ = 0.0013. In order to determine the substrate dielectric constant and loss tangent of the felt substrate, the resonance method based on a split post dielectric resonator (SPDR) measurement was carried out.

_{1}and Z

_{2}, with the corresponding electrical length θ

_{1}and θ

_{2}, respectively [8], as shown in Figure 1. The resonant condition of the SIR depends on the values of θ

_{1}, θ

_{2}and R. Furthermore, the analytical models are used to compute the circuit parameters at 7.58 GHz central frequency. The total electrical length of the structural fundamental is given by [9], which is ${\mathsf{\theta}}_{\mathrm{t}}={\mathsf{\theta}}_{1}+{\mathsf{\theta}}_{2},K1$. The resonance condition of an SIR will occur when

_{1}= 50 Ω, Z

_{2}= 121 Ω and the electrical lengths of a line are θ

_{1}= 31°, θ

_{2}= 79°.

_{1}= 4 mm, which causes characteristic impedance Z

_{0}= 50 Ω on the substrate. The detailed dimensions were as follows: Ls

_{1}= 3.26 mm, Ls

_{2}= 18.5 mm, Ls

_{3}= 1.5 mm, and the spacing between two meander lines S = 1.5 mm. The width for microstrip quarter-wavelength resonators was set as W

_{2}= 0.5 mm.

_{1}) and inductances (L

_{1}, L

_{2}) corresponding to the equivalent circuit shown in Figure 2b. On the other hand, the proposed meander microstrip lines act as a resonant (L

_{2}C

_{2}) circuit. The vertical elements act as the inductor and horizontal elements act as the capacitor. The overall electrical equivalent circuit of the proposed filter structure, which is shown in Figure 2c, can be obtained by combining the equivalent circuits of symmetrical steps and meander microstrip lines. This circuit was simulated using an Advanced Design System (ADS) simulator and its frequency response was compared with full 3D electromagnetic CST (Computer Simulation Technology) Microwave Studio 2018 software.

_{1}and W

_{2}, respectively. ${Z}_{Ci}$ and ${\epsilon}_{rei}$ denote the characteristic impedance and effective dielectric constant corresponding to width W

_{i}and c is the light velocity in free space.

## 3. Filter Implementation and Results

^{2}, and the technique used was double-sided needle punching.

_{21}) and return losses (S

_{11}). The S

_{21}and S

_{11}were tested up to 10 GHz by means of a microwave analyser, N9916A FieldFox (Keysight, Santa Rosa, CA, USA), operating as a vector network analyser.

## 4. Bending Effects

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hong, J.S.; Lancaster, M.J. Development of new microstrip pseudo-interdigital. IEEE Microw. Guid. Wave Lett.
**1995**, 5, 261–263. [Google Scholar] [CrossRef] - Park, E.; Lim, D.; Lim, S. Dual-Band Band-Pass Filter with Fixed Low Band and Fluidically-Tunable High Band. Sensors
**2017**, 17, 1884. [Google Scholar] [CrossRef] [PubMed] - Makimoto, M.; Yamashita, S. Bandpass filters using parallel coupled stripline stepped impedance resonators. IEEE Trans. Microw. Theory Tech.
**1980**, 28, 1413–1417. [Google Scholar] [CrossRef] - Klemm, M.; Troester, T. Textile UWB Antennas for Wireless Body Area Networks. IEEE Trans. Antennas Propag.
**2006**, 54, 3192–3197. [Google Scholar] [CrossRef] [Green Version] - Elliot, P.E.; Rosario, E.N.; Rama Rao, B.; Davis, R.J.; Marcus, N.M. E-textile microstrip patch antennas for GPS. In Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium, Myrtle Beach, SC, USA, 23–26 April 2012; IEEE: Piscataway, NJ, USA, 2012. [Google Scholar]
- Paradiso, R.; Loriga, G.; Taccini, T. A wearable health care system based on knitted integrated sensors. IEEE Trans. Inf. Technol. Biomed.
**2005**, 9, 337–344. [Google Scholar] [CrossRef] - Moradi, B.; Fernandez-Garcia, R.; Gil, I. E-Textile Embroidered Metamaterial Transmission Line for Signal Propagation Control. Materials
**2018**, 11, 955. [Google Scholar] [CrossRef] [PubMed] - Hong, J.-S.; Lancaster, M.J. Microstrip Filters for RF/Microwave Applications; John Wiley&Sons: New York, NY, USA, 2001; ISBN 0-471-38877-7. [Google Scholar]
- Makimoto, M.; Yamashita, S. Compact bandpass filters using stepped impedance resonators. Proc. IEEE
**1979**, 67, 16–19. [Google Scholar] [CrossRef] - Pozar, D.M. Microwave Engineering, 4th ed.; John Wiley&Sons: New York, NY, USA, 2004; ISBN 978-0-470-63155-3. [Google Scholar]

**Figure 1.**Configuration of the basic structure of the stepped impedance resonator (SIR), where $K=\frac{{Z}_{1}}{{Z}_{2}}<1$.

**Figure 2.**(

**a**) Layout of the proposed e-textile meander microstrip line. (

**b**) Capacitance and inductances of the equivalent circuits for the subnetworks for symmetrical steps. (

**c**) Equivalent circuit model of network.

**Figure 4.**(

**a**) Return loss (

**b**) Insertion loss responses of the electromagnetically simulated, measured and equivalent circuit model of the bandpass filter.

**Table 1.**Comparison of the equivalent circuit model parameters for the simulation (ADS) and theoretical bandpass filter.

Comparison | L_{1} (nH) | L_{2} (nH) | C_{1} (pF) | C_{2} (pF) |
---|---|---|---|---|

Theoretical parameters | 0.96 | 2.32 | 1.7 × 10^{−6} | 1.1 |

Optimized Parameters | 0.03 | 6.4 | 0.05 × 10^{−6} | 0.13 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Moradi, B.; Fernández-García, R.; Gil, I.
Meander Microwave Bandpass Filter on a Flexible Textile Substrate. *Electronics* **2019**, *8*, 11.
https://doi.org/10.3390/electronics8010011

**AMA Style**

Moradi B, Fernández-García R, Gil I.
Meander Microwave Bandpass Filter on a Flexible Textile Substrate. *Electronics*. 2019; 8(1):11.
https://doi.org/10.3390/electronics8010011

**Chicago/Turabian Style**

Moradi, Bahareh, Raul Fernández-García, and Ignacio Gil.
2019. "Meander Microwave Bandpass Filter on a Flexible Textile Substrate" *Electronics* 8, no. 1: 11.
https://doi.org/10.3390/electronics8010011