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Article

Design and Fabrication of a Compact Branch-Line Coupler Using Resonators with Wide Harmonics Suppression Band

by
Sobhan Roshani
1,
Salah I. Yahya
2,3,
Saeed Roshani
1,* and
Meysam Rostami
1
1
Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah 6718997551, Iran
2
Department of Communication and Computer Engineering, Cihan University-Erbil, Erbil 44001, Iraq
3
Department of Software Engineering, Faculty of Engineering, Koya University, Koya KOY45, Iraq
*
Author to whom correspondence should be addressed.
Electronics 2022, 11(5), 793; https://doi.org/10.3390/electronics11050793
Submission received: 29 January 2022 / Revised: 25 February 2022 / Accepted: 2 March 2022 / Published: 3 March 2022
(This article belongs to the Section Microwave and Wireless Communications)
Browse Figures
Versions Notes

Abstract

:
The branch-line coupler (BLC) is an important device in radio frequency (RF) and microwave (MW) circuits. The main drawbacks of the conventional BLC are as follows: first, the four long quarter-wavelength (λ/4) transmission line sections occupy a large size, especially at the low frequencies, and second, the presence of unwanted harmonics. This research paper presents a compact 750 MHz BLC with harmonics suppression using resonators. The typical BLC consists of four λ/4 branches, two series arms of 35 Ω and two shunt arms of 50 Ω impedances. In the proposed BLC, these long branches are replaced with two types of compact resonators. The proposed resonators have the same responses at the operating frequency of 750 MHz and suppress higher frequencies. The designed BLC is simulated, fabricated and measured. The results show that the proposed BLC has good performance at 750 MHz with a bandwidth of 200 MHz, which provides more than 26% fractional bandwidth (FBW). It has a very compact size, about 84% size reduction, as compared with the typical BLC. Moreover, the fabricated BLC suppresses the 2nd up to 7th unwanted harmonics with a high suppression level.

1. Introduction

Couplers are widely used in radio frequency (RF) and microwave (MW) circuits for combining/dividing input power [1]. The typical branch-line coupler (BLC) consists of four λ/4 branches. It consists of two series arms with 35 Ω and two shunt arms with 50 Ω impedances, which make this component undesirably large, especially at low frequencies, and susceptible to unwanted harmonics. The typical BLC passes all unwanted harmonics along with the main signal.
So far, various techniques have been reported to miniaturize the branch-line coupler structure and/or suppress the harmonics.
In many designs [2,3,4,5], low-pass filters (LPFs) are used as the coupler branches to miniaturize the structure and suppress the harmonics. This technique gives good results but increases the design complexity and the insertion loss.
Other techniques [6,7,8,9] have used external lumped components, such as capacitors and inductors, to overcome the structure’s large size and the presence of harmonics in typical BLCs. Applying lumped reactive components significantly reduces the circuit size and rejects unwanted harmonics but limits the frequency range.
Several works [10,11,12,13,14,15,16] have used a defected ground structure (DGS), photonic bandgap (PBG) cells and electromagnetic bandgap (EBG) cells for cancelling the harmonics and reducing the large size of BLCs. These cells need an extra implementation process, which increases the design complexity. Moreover, recently, the crystal photonic structures were used for higher-frequency circuits, which can be used for coupler structures [17,18,19,20,21,22,23,24,25].
Applying open-ended stubs is another effective method, which was previously widely used to modify typical couplers [26,27,28,29,30,31]. Using open stubs in couplers leads to achieving a simple structure. However, in this method, each open stub produces only a single transmission zero, which cannot provide a wide rejection band.
The coupled line structure [32,33,34,35] is another method that provides a bandpass response and impressively rejects other frequencies. Because of the coupled structure, the insertion loss is very high in this method.
In the design process of the coupler, to achieve the best performance, the dimensions of the applied stubs should be tuned. In [36,37,38,39], compact couplers are investigated for which the size reductions are not significant. To find the optimal dimensions of applied stubs and also to solve a variety of engineering problems, several models, artificial intelligence methods [40,41,42,43,44,45,46,47,48,49], and neural networks are used [50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66]. Additionally, artificial intelligence methods have been utilized to design microwave devices, such as power dividers and couplers [67,68].
In this work, two types of resonators are applied instead of the two types of long branches in the typical BLC. The applied method efficiently reduces the size of the circuit and eliminates undesirable harmonics.

2. The Conventional Coupler

The typical BLC consists of four λ/4 branches, two series arms of 35 Ω and two shunt arms of 50 Ω impedances. The schematic diagram of the conventional BLC is depicted in Figure 1a. The microstrip realization of the conventional BLC with RT/Duroid-5880 substrate of 5 mil thickness, εr = 2.2 and loss tan = 0.0009 at 750 MHz is shown in Figure 1b. The conventional BLC has a large size of 73 mm × 73 mm (0.25 λ × 0.25 λ) and passes higher frequencies along with the signal without any suppression. The EM frequency response of the typical BLC is depicted in Figure 1c.

3. Proposed Resonators

The BLC consists of two horizontal series lines of 35 Ω and two vertical shunt lines of 50 Ω impedances. In the proposed structure, two vertical resonators are used instead of the two long vertical branches, and two horizontal resonators are used instead of the two long horizontal branches.

3.1. Design Procedure of the Proposed Circuit

The design procedure of the proposed coupler is graphically explained in Figure 2. The conventional BLC at 750 MHz is designed at Step 1, which has a large size and suffers from the presence of unwanted harmonics in its frequency response. The conventional BLC consists of two long series branches and two long shunt branches. In Step 2, at first, the LC model resonator is presented, and related equations are extracted. Then, the TZ location can be obtained by equating the input impedance to zero. In addition, the TZ location can be adjusted by tuning the lumped element values in the LC circuit. In Step 3, two compact resonators are realized based on the proposed LC model, which are used instead of the long branches of the conventional coupler. The obtained resonators are used to form preliminary prototype of the coupler in Step 4, and the final coupler structure is achieved in Step 5 by adding four extra resonators.

3.2. Vertical Branches

The structure of the vertical λ/4 branch with 50 Ω (w = 1.15 mm) is depicted in Figure 3a. The frequency response of this vertical line is depicted in Figure 3b. As the results show, the vertical λ/4 branch easily passes the signal at 750 MHz without any attenuation (S12 near zero), and the S11 parameter is more than 10 dB. Note that S12 = S21, as the BLC is a reciprocal passive component. Unfortunately, this line passes other higher frequency signals without any attenuation (S12 near zero), exactly like the main signal.

3.3. Horizontal Branches

The structure of the horizontal λ/4 branch with 35 Ω (w = 2 mm) is depicted in Figure 4a. The frequency response of this horizontal line is shown in Figure 4b. As the results show, the horizontal λ/4 branch easily passes the signal at 750 MHz without any attenuation (S12 near zero), and the S11 parameter is more than 20 dB. Unfortunately, this line passes other signals at higher frequencies without any attenuation (S12 near zero), exactly like the main signal.
These vertical and horizontal lines have the same length of λ/4, but their widths are different. In the proposed design, triangular shaped resonators are used to improve the performance of the coupler.

3.4. Proposed Vertical Resonator

The layout structure of the proposed vertical resonator is depicted in Figure 5. This resonator consists of a triangle-shaped resonator at the middle and two flag-shaped suppressing cells on both sides.
The dimensions of the applied stubs in the proposed vertical resonator are listed as follows: Lb1 = 4.1, Wb1 = 0.6, Lb2 = 19.6, Lb3 = 5.6, Wb2 = 0.1 (all in millimeters). The frequency responses of the proposed vertical resonator are depicted in Figure 6. The designed structure easily passes 750 MHz, like the vertical line, and also creates a strong transmission zero at 1.7 GHz frequency.
The LC-equivalent (LCE) model of the proposed vertical resonator is extracted as illustrated in Figure 7.
The extracted LCE model has an asymmetrical structure, where the obtained values for the applied lumped reactive elements are listed in Table 1.
In Figure 8, the EM simulation of the proposed vertical resonator and its LCE model simulation response are compared. In this figure, the LCE model is simulated with a circuit simulator and the vertical resonator is simulated with electromagnetic (EM) simulation in Advanced Design System (ADS) software. There is good agreement between these responses, which shows the validity of the LCE model.
The values of ZA, and ZB (which are indicated in Figure 7) can be calculated according to the following equations:
Z A = L 3   S + 1 C 3   S + L 4   S C 2   S   1 C 2   S + 1 C 3   S + L 4   S
Z B = L 5   S + 1 C 6   S + L 6   S C 5   S   1 C 5   S + 1 C 6   S + L 6   S
where, “S” refers to the Laplace transform. The input impedances, indicated in Figure 7 by Z1 and Zin, can be extracted based on Equations (1) and (2), which are written in Equations (3)–(5).
Z 1 = Z A   R + L 1   S C 1   S   Z A + R + L 1   S C 1   S   R + 1 C 1   S + L 1   S   R + 1 C 1   S + L 1   S
Z i n = L 1   S + Z A   L 2   S + σ 1 C 1   S   1 C 1   S + Z A   L 2   S + σ 1 Z A + L 2   S + σ 1   Z A + L 2   S + σ 1
σ 1 = Z B   L 2   S + Z 1 Z B + L 2   S + Z 1
where “R” refers to 50 Ω impedance at port 2, and “σ1” is a parameter defined in Equation (5) to simplify the Zin equation. The real part of the input impedance Zin is shown in Figure 9. The TZ location can be obtained by equating the input impedance to zero. Additionally, the TZ location can be adjusted by tuning the lumped element values in the LC circuit.

3.5. Proposed Horizontal Resonator

The horizontal resonator is used instead of the 35 Ω series arm, and this is very similar to the vertical resonator because the horizontal arm and series arm have the same structure, same length and only a little difference in the line thickness. The layout structure of the horizontal resonator is depicted in Figure 10.
The dimensions of the applied stubs in the proposed horizontal resonator are listed as follows: Lc1 = 0.7, Lb2 = 19.6, Lb3 = 5.6, Wc1 = 0.1, Wb1 = 0.6, Wb2 = 0.1 (all in millimeters). The EM simulation response of the proposed horizontal resonator is illustrated in Figure 11. The proposed structure easily passes 750 MHz, like the simple horizontal line, and also creates a strong transmission zero at 1.6 GHz frequency.

3.6. The LC Models of the Preliminary and the Final Prototypes of the Coupler

The LCE model for the preliminary and the final prototypes of the coupler are depicted in Figure 12a. In the LCE circuit, CZ and LZ only exist in the final prototypes of the coupler, i.e., by adding four series LC branches containing CZ and LZ in the preliminary prototype, the final prototype of the coupler is constructed. The horizontal LC values in the LCE circuit of the final prototype of the coupler are the same as the values in Table 1. However, according to the impedance difference in the vertical branches of the coupler, the vertical LC values in the LCE circuit of the final prototype of the coupler are tuned, which are listed in Table 2. The comparison between the LCE model frequency responses of the preliminary and the final prototypes of the coupler are shown in Figure 12b, which shows acceptable results with a wide rejection band.

4. Proposed Coupler Design

In the proposed coupler design process, the horizontal and vertical resonators are used instead of four long branches.

4.1. The Preliminary Prototype of the Designed Coupler

The preliminary prototype of the designed coupler is designed by placing vertical and horizontal resonators instead of the vertical and horizontal lines. The structure and frequency responses of the preliminary prototype of the designed coupler are shown in Figure 13. This coupler rejects the third to sixth harmonics and provides wide rejection bands from 1.75 GHz to 3.85 GHz, with more than a 20 dB attenuation level.

4.2. The Final Prototype of the Designed Coupler

The preliminary prototype of the designed coupler only eliminates the third to sixth harmonics, but it does not have the ability to suppress the second harmonic. To remove the second harmonic, four small triangular shaped open-ended stubs are added in the final prototype of the deigned coupler. The added triangular open-ended stubs can create extra transmission zeros, which helps to improve the harmonic suppression in the device [69,70]. The structure and S-parameters curves of the final prototype of the designed coupler are shown in Figure 14. This coupler rejects the second to seventh harmonics and provides a wide rejection band from 1.5 GHz to 5.4 GHz.

5. Fabrication and Measurements

The final prototype of the designed BLC is fabricated on a substrate of Rogers RT-5880 substrate with 15 mil thickness, εr = 2.2 and loss tan = 0.0009. The photo of the fabricated BLC is presented in Figure 15.
The conventional coupler has a size of 0.25 × 0.25 λg2, whereas the size of the final prototype of the designed coupler is only 0.08 × 0.12 λg2 (24.4 × 35.3 mm2), where λg is obtained at 750 MHz working frequency. The final prototype of the designed BLC demonstrates an 84% size reduction, in comparison with the typical BLC. The layout of the proposed and conventional couplers, which is designed on the same substitute and operates at the same frequency, is depicted in Figure 16, which shows an extreme size reduction in the final prototype of the designed coupler.
The simulated and measured S-parameters of the final prototype of the designed BLC are depicted in Figure 17. As seen from the obtained S-parameters in Figure 17a,b, the final prototype of the designed BLC has good performance at 750 MHz with a bandwidth of 200 MHz, which provides more than 26% FBW. Moreover, it provides wide rejection band from 1.5 GHz to 5.4 GHz, which suppresses the 2nd to 7th harmonics.
In Figure 18, the measurement and EM simulation results for the output ports phase difference are depicted. As the results show, at 750 MHz, the phase difference is −270.5°, which shows good performance of the final prototype of the designed coupler.
In Table 3, some related couplers, which were published in recent years, are compared with the final prototype of the designed coupler.

6. Conclusions

A compact branch-line coupler (BLC) with improved harmonic suppression ability is designed, analyzed, and fabricated in this manuscript. In the designed coupler, the main drawbacks of the conventional coupler, which are the large size and harmonics presence in the frequency response, are corrected. The triangular shaped and trapezoidal shaped resonators are incorporated into the proposed resonators to form a compact coupler and provide extra transmission zeros. The design coupler has achieved 2nd to 7th harmonics suppression with a wide rejection band and high attenuation. In addition, the obtained overall size of the fabricated coupler is only 0.08 × 0.12 λg2, which demonstrates an 84% size reduction.

Author Contributions

Conceptualization, S.R. (Sobhan Roshani), S.I.Y. and S.R. (Saeed Roshani); methodology, S.R. (Sobhan Roshani), M.R. and S.R. (Saeed Roshani); software, M.R. and S.R. (Saeed Roshani); validation, S.I.Y.; formal analysis, S.I.Y. and S.R. (Saeed Roshani); investigation, S.R. (Saeed Roshani); resources, S.R. (Sobhan Roshani) and M.R.; writing—original draft preparation, S.I.Y. and S.R. (Saeed Roshani); writing—review and editing, S.R. (Sobhan Roshani) and S.I.Y.; visualization, S.R. (Saeed Roshani) and S.I.Y.; supervision, S.R. (Saeed Roshani); project administration, All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

All the material conducted in the study is mentioned in article.

Conflicts of Interest

The authors declare no conflict of interest.

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Electronics 11 00793 g001a 550Electronics 11 00793 g001b 550
Figure 1. Conventional 750 MHz BLC: (a) schematic diagram, (b) layout, and (c) frequency response. Dimensions are in millimeters.
Figure 1. Conventional 750 MHz BLC: (a) schematic diagram, (b) layout, and (c) frequency response. Dimensions are in millimeters.
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Figure 2. Design procedure of the proposed coupler. In this figure, the design steps of the proposed circuit are explained in 5 steps.
Figure 2. Design procedure of the proposed coupler. In this figure, the design steps of the proposed circuit are explained in 5 steps.
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Figure 3. Vertical λ/4 branch of 50 Ω impedance at 750 MHz; (a) layout with dimensions in millimeters, and (b) the simulation of the S11 and S12 magnitudes in decibels.
Figure 3. Vertical λ/4 branch of 50 Ω impedance at 750 MHz; (a) layout with dimensions in millimeters, and (b) the simulation of the S11 and S12 magnitudes in decibels.
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Figure 4. Horizontal λ/4 branch of 35 Ω impedance at 750 MHz; (a) layout with dimensions in millimeters and (b) the simulation of the S11 and S12 magnitudes in decibels.
Figure 4. Horizontal λ/4 branch of 35 Ω impedance at 750 MHz; (a) layout with dimensions in millimeters and (b) the simulation of the S11 and S12 magnitudes in decibels.
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Figure 5. The layout of the proposed vertical resonator.
Figure 5. The layout of the proposed vertical resonator.
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Figure 6. The S11 and S12 magnitudes in decibels versus frequency.
Figure 6. The S11 and S12 magnitudes in decibels versus frequency.
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Figure 7. Extracted LCE model of the proposed vertical resonator.
Figure 7. Extracted LCE model of the proposed vertical resonator.
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Figure 8. EM simulation of the proposed vertical resonator and its LCE model response.
Figure 8. EM simulation of the proposed vertical resonator and its LCE model response.
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Figure 9. The real part of the input impedance Zin.
Figure 9. The real part of the input impedance Zin.
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Figure 10. Layout of the proposed horizontal resonator. (a) Layout extraction of the resonator from the LC equivalent circuit. (b) Dimensions of the proposed horizontal resonator.
Figure 10. Layout of the proposed horizontal resonator. (a) Layout extraction of the resonator from the LC equivalent circuit. (b) Dimensions of the proposed horizontal resonator.
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Figure 11. EM simulation response of the proposed horizontal resonator.
Figure 11. EM simulation response of the proposed horizontal resonator.
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Figure 12. (a) The LCE models of the preliminary and the final prototypes of the coupler. (b) The comparison between LCE model frequency responses of the preliminary and the final prototypes of the coupler. In LCE circuit, CZ and LZ only exist in the final prototypes of the coupler.
Figure 12. (a) The LCE models of the preliminary and the final prototypes of the coupler. (b) The comparison between LCE model frequency responses of the preliminary and the final prototypes of the coupler. In LCE circuit, CZ and LZ only exist in the final prototypes of the coupler.
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Figure 13. The preliminary prototype of the designed coupler; (a) layout with dimensions in millimeters, and (b) EM simulation response.
Figure 13. The preliminary prototype of the designed coupler; (a) layout with dimensions in millimeters, and (b) EM simulation response.
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Figure 14. The final prototype of the designed coupler; (a) layout with dimensions in millimeters, and (b) EM simulation response.
Figure 14. The final prototype of the designed coupler; (a) layout with dimensions in millimeters, and (b) EM simulation response.
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Figure 15. Photograph of the fabricated BLC.
Figure 15. Photograph of the fabricated BLC.
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Figure 16. Layouts comparison between the final prototype of the designed coupler (24.4 mm × 35.3 mm) and the conventional couplers (73 mm × 73 mm) at 750 MHz.
Figure 16. Layouts comparison between the final prototype of the designed coupler (24.4 mm × 35.3 mm) and the conventional couplers (73 mm × 73 mm) at 750 MHz.
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Figure 17. Measurement and EM simulation of the S-parameters with respect to frequency for the final prototype of the designed BLC. (a) The values of |S11|, and |S12| parameters. (b) The values of |S13|, and |S14| parameters.
Figure 17. Measurement and EM simulation of the S-parameters with respect to frequency for the final prototype of the designed BLC. (a) The values of |S11|, and |S12| parameters. (b) The values of |S13|, and |S14| parameters.
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Figure 18. Measurement and EM simulation of the output ports’ phase difference.
Figure 18. Measurement and EM simulation of the output ports’ phase difference.
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Table
Table 1. Obtained values for the applied lumped elements of the LC model of the resonator.
Table 1. Obtained values for the applied lumped elements of the LC model of the resonator.
ParametersL1L2L3L4L5L6
Values (nH)2.12.35.20.40.150.15
ParametersC1C2C3C4C5C6
Values (pF)110.8761.21.2
Table
Table 2. Obtained values for the applied lumped elements of the LC model of the coupler.
Table 2. Obtained values for the applied lumped elements of the LC model of the coupler.
ParametersLV1LV2LV3LV4LV5LV6
Values (nH)16.35.20.40.18 0.18
ParametersCV1CV2CV3CV4CV5CV6
Values (pF)5.410.8761.21.2
Table
Table 3. Performance comparison between the final prototype of the designed coupler and some related works.
Table 3. Performance comparison between the final prototype of the designed coupler and some related works.
Ref.Reduction Size (%)IL
(dB)		RL
(dB)		Isolation
(dB)		Freq.
(GHz)		FBW
(%)		Size
(λ × λ)		Suppressed Harmonics
Num.Details
[36]66%127200.93110.14λ × 0.15λ0-
[37]62%120281.5200.15λ × 0.16λ0-
[38]-1.4-151.873.50.33λ × 0.42λ0-
[39]73%-3030113.60.125λ × 0.135λ12nd: 18 dB
Conv.
Coupler		-0.235350.75200.25λ × 0.25λ0-


This work

84%

0.3

20

20

0.75

26

0.08λ × 0.12λ

6		2nd: 20 dB
3rd: 23 dB
4th: 28 dB
5th: 39 dB
6th: 52 dB
7th: 23 dB
IL = insertion loss, RL = return loss, Freq. = frequency, FBW = fractional bandwidth, and Conv. = conventional.
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MDPI and ACS Style

Roshani, S.; Yahya, S.I.; Roshani, S.; Rostami, M. Design and Fabrication of a Compact Branch-Line Coupler Using Resonators with Wide Harmonics Suppression Band. Electronics 2022, 11, 793. https://doi.org/10.3390/electronics11050793

AMA Style

Roshani S, Yahya SI, Roshani S, Rostami M. Design and Fabrication of a Compact Branch-Line Coupler Using Resonators with Wide Harmonics Suppression Band. Electronics. 2022; 11(5):793. https://doi.org/10.3390/electronics11050793

Chicago/Turabian Style

Roshani, Sobhan, Salah I. Yahya, Saeed Roshani, and Meysam Rostami. 2022. "Design and Fabrication of a Compact Branch-Line Coupler Using Resonators with Wide Harmonics Suppression Band" Electronics 11, no. 5: 793. https://doi.org/10.3390/electronics11050793

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