# A Compact C-Band Bandpass Filter with an Adjustable Dual-Band Suitable for Satellite Communication Systems

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## Abstract

**:**

## 1. Introduction

## 2. Design Procedure

#### 2.1. Proposed Coupling System

_{bend}) as illustrated in a simplified lumped-element circuit (LC) model shown in Figure 3a. In the LC circuit, C

_{1}, C

_{3}, C

_{4}and C

_{6}denote the gap capacitances. C

_{2}, C

_{5}, C

_{7}and C

_{11}describe the capacitances of the open-end stubs. The inductances of transmission lines are also modeled by L

_{1}, L

_{2}, L

_{3}, L

_{4}and L

_{5}, and the bending capacitances are denoted by C

_{8}, C

_{9}and C

_{10}. The values of the lumped elements are obtained using the procedure outlined in [53,54], and calculated as follows: C

_{1}= 0.107 pF, C

_{2}= 0.73 pF, C

_{3}= 0.3 pF, C

_{4}= 0.05 pF, C

_{5}= 1.289 pF, C

_{6}= 0.045 pF, C

_{7}= 7 pF, C

_{8}= 0.535 pF, C

_{9}= 7 pF, C

_{10}= 5 pF, C

_{11}= 0.65 pF, L

_{1}= 0.4 nH, L

_{2}= 0.34 nH, L

_{3}= 0.5 nH, L

_{4}= 0.435 nH and L

_{5}= 0.75 nH. It can be seen from Figure 3b that introducing the bending capacitors improves the passband response, reducing the passband insertion loss from 7.05 to 0.66 dB. The first and second resonant frequencies of the filter shown in Figure 3b can be calculated by equating the input impedance of the equivalent circuit model to zero as shown in (1). As a result, the equations of resonances are obtained as (2) and (3).

#### 2.2. Proposed Dual-Band BPF

_{H1}and L

_{H1}describe capacitance and inductance of the high impedance line. C

_{L1}and L

_{L1}are capacitance and inductance of the low impedance open-end stub. Additionally, capacitance and inductance of the open stub are presented by C

_{O}and L

_{O}, respectively. In order to calculate the lumped element values of this LC model, the method described in [6,56,61] can be used, in which the initial values are calculated [60] and then optimized to match the frequency responses of the LC model and the electromagnetic (EM) simulation.

_{H2}and L

_{H2}. C

_{L2}and L

_{L2}denote the capacitance and inductance of the low impedance open-end stub, respectively.

#### 2.3. Current Distribution Analysis

#### 2.4. Passbands Optimization and Tuning of the Filter

_{14}), where decreasing A

_{14}would decrease the capacitive effects, shifting the resonance frequency to higher frequencies, resulting in 600 MHz dynamic range (4.4 GHz to 5 GHz) as shown in Figure 8. The second passband can be adjusted by either varying the capacitive (A

_{21}) or inductive (A

_{18}) sections of the stepped-impedance resonators. Indeed, increasing A

_{21}or A

_{18}would have the same effect on the upper band, increasing the associated capacitor and inductor, respectively, shifting the upper band to lower frequencies. As shown in Figure 9 and Figure 10, the upper band has a large dynamic range of 1000 MHz (from 7 GHz to 8 GHz).

_{18}, A

_{21}and A

_{14}. As depicted in this figure, the Q. factor decreases by increasing A

_{18}, A

_{21}and A

_{14}.

## 3. Results and Discussions

_{1}= 4.42 GHz and f

_{2}= 7.2 GHz, and 3 dB bandwidths of 94 MHz and 83 MHz, respectively. Insertion and return losses at f

_{1}and f

_{2}are about 0.5/17.56 and 0.86/17.9 dB, respectively. The filter provides an excellent out-of-band response, showing a good rejection level of 30 dB in the lower stopband, and a 24 dB isolation level with a 25 dB rejection at upper stopband, which extends up to 14.5 GHz. The measured physical size of the filter is 11.4 mm × 5.8 mm corresponding to 0.23 λ

_{g}× 0.11 λ

_{g}, where λ

_{g}is the guided wavelength at 4.42 GHz. The fabricated filter shows a good selectivity in both bands with sharpness values of 106 dB/GHz and 212 dB/GHz, respectively, calculated using the filter sharpness formula in [61].

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Bended coupling system: (

**a**) Layout, A

_{1}= 5.3, A

_{2}= 4.8, A

_{3}= 5.6, A

_{4}= 5.1, A

_{5}= 4.8, A

_{6}= 0.1 (all in mm), (

**b**) EM simulation.

**Figure 5.**Integration of flag-shaped resonators with the bended coupled system. (

**a**) Layout, (

**b**) EM simulation, (

**c**) LC model of flag-shaped resonator. The dimensions of the introduced flag-shaped resonators are as follows: A

_{7}= 2.7, A

_{8}= 1.9, A

_{9}= 0.2, A

_{10}= 4.3, A

_{11}= 2.2, A

_{12}= 0.2, A

_{13}= 0.2, A

_{14}= 1.32, A

_{15}= 3.2 (all in mm).

**Figure 6.**Completed dual-band bandpass filter (BPF): (

**a**) Layout, A

_{16}= 2.6, A

_{17}= 0.8, A

_{18}= 1.4, A

_{19}= 0.8, A

_{20}= 0.3, A

_{21}= 1.3 (all in mm), (

**b**) EM simulation, (

**c**) LC model of stepped-impedance resonator.

**Figure 8.**Adjustability of the lower band of the proposed BPF by varying A

_{14}: (

**a**) |S

_{21}|, (

**b**) |S

_{11}|.

**Figure 9.**Adjustability of the upper band of the proposed BPF by varying A

_{21}: (

**a**) |S

_{21}|, (

**b**) |S

_{11}|.

**Figure 10.**Adjustability of the upper band of the proposed BPF by varying A

_{18}: (

**a**) |S

_{21}|, (

**b**) |S

_{11}|.

**Figure 11.**(

**a**) Variations of bandwidth as a function of A

_{18}, A

_{21}and A

_{14}, (

**b**) Variations of fractional bandwidth (FBW) as a function of A

_{18}, A

_{21}and A

_{14}.

**Figure 12.**(

**a**) Variations of Q. factor versus physical parameters: (

**a**) A

_{14}, (

**b**) A

_{18}and A

_{21}.

**Figure 13.**Proposed BPF: (

**a**) A photo of the fabricated filter: (

**b**) Simulation and measurement results.

Refs. | f_{1}/f_{2} (GHz) | IL_{1}/IL_{2} (dB) | RL_{1}/RL_{2} (dB) | SL_{1}/SL_{2} (dB) | USB | USB (GHz) | TR_{1}/TR_{2} (MHz) | $\mathbf{NCS}\text{}\left({\mathsf{\lambda}}_{\mathit{g}}^{2}\right)$ |
---|---|---|---|---|---|---|---|---|

This work | 4.42/7.2 | 0.5/0.86 | 17.56/17.9 | 30/25 | 3 f1 | 7.4–15 | 600/1000 | 0.0253 |

[30] | 0.9/2.2 | 0.5/1 | 20/20 | 20/20 | 3 f_{1} | 2.4–3 | 200/200 | 0.0391 |

[32] | 3.8/4.8 | 1.38/1.82 | 14/17 | 20/20 | 2 f_{1} | 5.6–8 | 500/200 | 0.0496 |

[33] | 2.35/5.8 | 1.1/1.6 | 20/18 | 30/20 | 3 f_{1} | 6.5–8 | -/- | 0.0288 |

[35] | 2.55/3.6 | 1.22/2.13 | 20/18 | 20/20 | 1 f_{1} | 3.7–5 | -/- | 0.1189 |

[36] | 2.45/5.2 | 0.6/0.9 | 20/19 | 20/20 | 3 f_{1} | 6–7.5 | -/- | 0.0253 |

[37] | 2.4/5.2 | 1.4/2.7 | 30/12 | 20/20 | 2 f_{1} | 6–11 | -/- | 0.0324 |

[38] | 1.57/2.4 | 1.26/2.4 | 17.5/22.6 | 20/20 | 3 f_{1} | 2.7–5.5 | -/- | 0.0108 |

[39] | 2.4/5.8 | 1.35/1.97 | 17/15 | 20/20 | 3 f_{1} | 6–9 | -/- | 0.0975 |

[40] | 1.6/2.56 | 0.74/0.93 | 20/20 | 20/20 | 2 f_{1} | 2.7–4.5 | -/- | 0.005 |

[41] | 2.5/3.5 | 1.2/1.2 | 12/12 | 20/20 | 3 f_{1} | 4–9 | -/- | - |

_{1}: First passband, f

_{2}: Second passband, IL

_{1}: Insertion loss at f

_{1}, IL

_{2}: Insertion loss at f

_{2}, RL

_{1}: Return loss at f

_{1}, RL

_{2}: Return loss at f

_{2}, SL

_{1}: Suppression level in lower stopband, SL

_{2}: Suppression level in upper stopband, USB: Upper Stopband bandwidth, TR

_{1}: Tuning range of f

_{1}, TR

_{2}: Tuning range of f

_{2}.

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## Share and Cite

**MDPI and ACS Style**

Lalbakhsh, A.; Ghaderi, A.; Mohyuddin, W.; Simorangkir, R.B.V.B.; Bayat-Makou, N.; Ahmad, M.S.; Lee, G.H.; Kim, K.W.
A Compact C-Band Bandpass Filter with an Adjustable Dual-Band Suitable for Satellite Communication Systems. *Electronics* **2020**, *9*, 1088.
https://doi.org/10.3390/electronics9071088

**AMA Style**

Lalbakhsh A, Ghaderi A, Mohyuddin W, Simorangkir RBVB, Bayat-Makou N, Ahmad MS, Lee GH, Kim KW.
A Compact C-Band Bandpass Filter with an Adjustable Dual-Band Suitable for Satellite Communication Systems. *Electronics*. 2020; 9(7):1088.
https://doi.org/10.3390/electronics9071088

**Chicago/Turabian Style**

Lalbakhsh, Ali, Amirhossein Ghaderi, Wahab Mohyuddin, Roy B. V. B. Simorangkir, Nima Bayat-Makou, Muhammad Sajjad Ahmad, Gwan Hui Lee, and Kang Wook Kim.
2020. "A Compact C-Band Bandpass Filter with an Adjustable Dual-Band Suitable for Satellite Communication Systems" *Electronics* 9, no. 7: 1088.
https://doi.org/10.3390/electronics9071088