A Compact Filtering Coupler with Unwanted Harmonic Rejection Using LC Composite Lines for Communication Systems Applications

Abstract

In this paper, new LC lumped components and composite lines are used to create a filtering branch line coupler (FBLC) with a small size and wide suppression band. New composite lines are proposed using applied LC lumped components, which are used as the coupler main branches. The proposed FBLC suppresses second to sixth harmonics with high attention level and provides a wide stopband from 1.6 GHz to 5 GHz with more than 20 dB of attention. The presented coupler is analyzed, designed, simulated, and implemented. The measured results show that the proposed FBLC correctly operates at 800 MHz with less than 0.25 dB of insertion loss. In addition, more than 29 dB of return loss and isolation is measured at operating frequency, which shows the correct performance of the proposed design. The size of the proposed FBLC is equal to 23.7 mm × 25.5 mm (0.086λ × 0.093λ), which shows an 87% size reduction. The proposed FBLC with the designed frequency can be used in the communication systems for narrow-band Internet of things (NB-IoT) and traffic control radar applications.

1. Introduction

The branch line couplers (BLCs) are widely used components in microwave and RF circuits, which have different types such as branch line, hybrid, and rat race. The coupler devices are commonly being used in balanced power amplifiers [1], Doherty power amplifiers [2,3], array antennas [4,5], and phase shifters [6]. Conventional BLCs are composed of four λ/4 transmission lines (TLs), which occupy a large area. Moreover, another disadvantage of the conventional couplers is that there is no suppression band in these devices, which cannot suppress the undesirable signals at unwanted frequencies. Several approaches have been presented to improve the performance and solve the conventional coupler disadvantages, which are explained in what follows.

A dual-band coupler is designed with coupled lines in [7], operating at 1.8 GHz and 0.9 GHz; however, the designed coupler has a large size. In [8], a differential coupler using a coupled line structure is designed with long parallel coupled lines. High insertion loss and rather large size are disadvantages in the designed coupler in [8].

Resonators, which can improve the performance of the electronic components [9], are widely used to provide a wide suppression band for the microwave devices, such as couplers [10], filters [11,12], and diplexers [13]. FBLC is designed using resonators in [14] and meandered lines to decrease the area and increase the performance of the device. According to the results in [14], the meandered lines have reduced the length of the coupler’s main branches; moreover, the applied resonators and open stubs have created transmission zeros to provide a suppression band for the coupler. A rat-race coupler (RRC) is designed in [15], in which capacitive open stubs and T-shaped resonators are incorporated to present an RRC with reduced size and high performance. The E-shaped impedance transformer is used in [16] to design a dual-band coupler with high frequency ratio. Open stubs are also used in [16] to create desired transmission zeros. In [17], capacitive open stubs are applied in the BLC structure to achieve compact size, but the obtained insertion loss is high. Open stubs and resonators can be used together in the BLC structure to obtain high performances of the device [18].

The electromagnetic bandgap (EBG) has also been used in the design of the microwave devices, such as couplers to reduce the size or to improve the functionality of the devices. However, the EBG method increases the design and fabrication complexity. Substrate-integrated gap waveguide (SIGW) and EBG methods are used for designing of a wideband coupler in [19]; however, the obtained coupler has a large size. Couplers are also designed using a photonic crystal for higher frequencies [20,21,22,23,24,25].

Recently, artificial neural network (ANN) techniques and optimization algorithms [26,27] have helped electronics designers to improve the performances of their devices [28,29,30,31,32], which also have been used in the designing of the couplers [33,34,35]. In [33], a feedforward network was used to predict the BLC transfer function. By using the transfer function, the locations of the transmission zeros can be obtained, which help to design the coupler with desired specifications. In [36], a neural network and the back propagation method with Bayesian regularization are used to improve the filters’ performance. In addition, a feedforward ANN is used in [37] to design a power divider with reduced size. A combination of ANNs and optimization algorithms is also used together to present a design method for amplifier design in [38].

Recently, lumped elements have been used in coupler designs for achieving a miniaturized size or filtering response [39]. Capacitors are used in [40] to create a compact coupler with suppression of harmonics; however, the obtained operating band is very narrow, which may be because of frequency shifting in the fabrication. In addition, varactor diodes can be used in the coupler structure, which can provide tunable and reconfigurable performance of the coupler [41]. Capacitors and inductors are used in the coupler structure designed in [42], but the obtained insertion losses in the output ports are high.

In this paper, lumped components, four capacitors, and four inductors are used with transmission lines to create composite lines to design a branch line coupler, which has resulted in improvement of coupler performances, such as miniaturized size and wide suppression band. The achieved suppression band of the device has helped to attenuate the unwanted frequencies, such as undesired harmonics.

2. Design Process

In this section, the design process of the typical and proposed couplers is explained as follows.

2.1. Typical 800 MHz Coupler

The structure of the typical 0.8 GHz FBLC is shown in Figure 1, which consists of four λ/4 branches. With the applied RT-Duroid 5880 substrate (ε_r = 2.2 and 20 mil thickness), the size of the typical coupler is 71.1 mm × 69.8 mm. Large occupied size is the first drawback of this coupler.

The typical 800 MHz FBLC frequency response is depicted in Figure 2. The amplitudes of S₁₂ and S₁₃ are −3.1 dB and −3.2 dB, which shows less than 0.2 dB insertion loss at operating frequency. The amplitude of S₁₁ is about −32 dB, and the amplitude of S₁₄ is about −36 dB, which shows good performance of the typical coupler at operating frequency. A typical FBLC has good performance at operating frequency, but the performance of this coupler at higher frequency is not acceptable, and undesirable signals are passed, without any suppression at higher frequencies, which is another drawback of the typical FBLC.

2.2. Proposed Coupler

As mentioned in the previous section, the typical FBLC has two main drawbacks. Firstly, it has a large size, and secondly it passes undesirable signals at higher frequencies such as the main signal without any suppression. In order to overcome these drawbacks, a proposed structure is presented in Figure 3, in which four lumped inductors and four capacitors are used.

3. Proposed FBLC Analysis

In the conventional coupler, four long branches are used, which occupies large area, so the length reduction of these branches is an important parameter to miniaturize the device [43]. In the proposed FBLC, two types of composite lines are used instead of two long conventional branches. In Figure 4a, the conventional horizontal branch is depicted, which has 90 degrees of length and has 35.5 ohms of impedance. In the proposed coupler, a new horizontal composite branch is proposed as depicted in Figure 4b, which is applied instead of the long conventional branch. These two lines must have the same performance at an operating frequency of 800 MHz. As mentioned, the proposed branches not only reduce the size of the device but also improve the performance of the frequency response. The scattering parameters of the conventional horizontal λ/4 line and the proposed compact horizontal TL are compared in Figure 4c. As seen, both lines have the same insertion loss of 0.05 dB at the 0.8 GHz operating frequency. The proposed horizontal transmission line provides a wide suppression band, while the conventional TL does not provide any harmonics suppression.

The ABCD parameters for the conventional and the proposed horizontal branches should be equated as written in Equation (1):

$$\begin{array}{l}\left[M\_ABCD\_C\right]\times \left[M\_ABCD\_TL\right]\times \left[M\_ABCD\_L\right]\times \\ \left[M\_ABCD\_TL\right]\times \left[M\_ABCD\_C\right]\\ =\left[M\_ABCD\_BR\right]\end{array}$$

(1)

wherein (1) M_ABCD_C is the ABCD matrix of the capacitor. Moreover, M_ABCD_TL, M_ABCD_L, and M_ABCD_BR are ABCD matrices of the transmission line, inductor, and conventional 90-degree branch line, respectively. The ABCD matrices are defined in Equations (2)–(5) as follows [44]:

$$\left[M\_ABCD\_C\right]=\left(\begin{array}{cc}1& 0\\ \frac{C\omega \mathrm{i}}{2}& 1\end{array}\right)$$

(2)

$$\left[M\_ABCD\_TL\right]=\left(\begin{array}{cc}\cos \left({\theta }_1\right)& Z_1\sin \left({\theta }_1\right)\mathrm{i}\\ \frac{\sin \left({\theta }_1\right)\mathrm{i}}{Z_1}& \cos \left({\theta }_1\right)\end{array}\right)$$

(3)

$$\left[M\_ABCD\_L\right]=\left(\begin{array}{cc}1& L\omega \mathrm{i}\\ 0& 1\end{array}\right)$$

(4)

where $\omega$ = 2πf. After simplifying Equations (1)–(4), the final equation can be calculated as written in Equation (5):

$$\begin{array}{l}\left(\begin{array}{cc}\cos {\left({\theta }_1\right)}^2+\frac{C\omega {\sigma }_1\mathrm{i}}{2}+\frac{\sin \left({\theta }_1\right)\left(Z_1\sin \left({\theta }_1\right)\mathrm{i}+L\omega \cos \left({\theta }_1\right)\mathrm{i}\right)\mathrm{i}}{Z_1}& {\sigma }_1\hfill \\ \cos \left({\theta }_1\right){\sigma }_4+\frac{\sin \left({\theta }_1\right){\sigma }_3\mathrm{i}}{Z_1}+\frac{C\omega {\sigma }_2\mathrm{i}}{2}& {\sigma }_2\hfill \end{array}\right)\hfill \\ =\left(\begin{array}{cc}0& j{Z}_{BR}\\ j{Y}_{BR}& 0\end{array}\right)\end{array}$$

(5)

where the values of σ₁–σ₄ are defined in Equations (6)–(9) as the following:

$${\sigma }_1=\cos \left({\theta }_1\right)\left(Z_1\sin \left({\theta }_1\right)\mathrm{i}+L\omega \cos \left({\theta }_1\right)\mathrm{i}\right)+Z_1\cos \left({\theta }_1\right)\sin \left({\theta }_1\right)\mathrm{i}$$

(6)

$${\sigma }_2=\cos \left({\theta }_1\right){\sigma }_3+Z_1\sin \left({\theta }_1\right){\sigma }_4\mathrm{i}$$

(7)

$${\sigma }_3=\cos \left({\theta }_1\right)-\frac{C{Z}_1\omega \sin \left({\theta }_1\right)}{2}+Lw{\sigma }_4\mathrm{i}$$

(8)

$${\sigma }_4=\frac{\sin \left({\theta }_1\right)\mathrm{i}}{Z_1}+\frac{C\omega \cos \left({\theta }_1\right)\mathrm{i}}{2}$$

(9)

Equation (5) has an infinite number of solutions. Therefore, some assumptions should be considered for calculating this equation. The values of capacitors (C) and inductors (L) are considered as written in

Table 1. The obtained value of applied stubs and lumped elements components.

L	C	Z1	θ1	Z2	θ2
6 nH	5.2 pF	10 Ω	15°	161 Ω	5°

. Moreover, the values of Z₁ and θ₁ are calculated based on Equation (5) and the desired size reduction. The value of applied stubs and lumped elements components is listed in the Table 1.

In Figure 5a, the conventional vertical branch is depicted, which has 90 degrees of length and has 50 ohms of impedance. In the proposed coupler, a new vertical composite branch is proposed as depicted in Figure 5b, which is applied instead of the long conventional branch. These two lines must have the same performance at an operating frequency of 800 MHz. The scattering parameters of the conventional vertical λ/4 line and the proposed compact vertical TL are compared in Figure 5c. As seen, both lines have the same values of insertion loss of 0.05 dB at the 0.8 GHz operating frequency. Moreover, the proposed vertical transmission line provides a wide suppression band, while conventional TL cannot provide any harmonics suppression.

Similar to the horizontal analyses, the ABCD parameters for the conventional and the proposed vertical branches should be equated using Equations (1)–(9). The values of Z₂ and θ₂ are calculated as listed in Table 1.

4. Simulations

In the design of the proposed FBLC, Duroid 5880 substrate is applied. The layout of the proposed FBLC is illustrated in Figure 6. The proposed FBLC only occupied 23.7 mm × 25.5 mm (0.086λ × 0.093λ), which shows 87% size reduction compared with the conventional coupler. As seen from Figure 6, Z₁ and θ₁, which correspond to the horizontal branches of the coupler, are shown in the coupler layout. Moreover, Z₂ and θ₂, which correspond to the vertical branches of the coupler, are indicated in the coupler layout. The values of the Z₁, θ₁, Z₂, and θ₂ are calculated based on the extracted analyses of the coupler, which are explained in Section 3, and the obtained values are listed in Table 1. By using the obtained values for Z₁, θ₁, Z₂, and θ₂, the microstrip realization of these transmission lines and also the layout of the proposed coupler can be extracted as shown in Figure 6. The simulation’s result of the proposed FBLC is illustrated in Figure 7. The proposed FBLC has good performance at the operating frequency and higher frequency bands. The amplitudes of S₁₂ and S₁₃ are −3.05 dB and −3.01 dB, which shows less than 0.05 dB of insertion loss at the operating frequency in simulation. The amplitude of S₁₁ is about −23 dB, and the amplitude of S₁₄ is about −41 dB, which shows desirable performance for the simulated proposed FBLC. At higher frequencies, the proposed coupler suppresses second to sixth harmonics with a high attention level and provides a wide rejection band from 1.6 GHz to 5 GHz with more than 20 dB of attention.

The effects of capacitors and the inductors’ result in the presented LC branches of the designed 0.8 GHz FBLC are shown in Figure 8. As seen, by tuning the values of capacitors and inductors in the presented LC branches, the operating frequency and the operating bandwidth can be adjusted.

The output ports’ phase difference of the presented FBLC is depicted in Figure 9. As seen, the output ports’ phase difference of the designed coupler is equal to −270.12°, at the operating frequency of 800 MHz, which is so close to the ideal value.

5. Fabrication

The proposed FBLC was measured and fabricated, which is depicted in Figure 10. As seen in the fabricated device, four capacitors and four inductors are soldered on the layout. The fabricated device has a small size of 23.7 mm × 25.5 mm (0.086λ × 0.093λ), which shows 87% size reduction compared with the conventional coupler.

The measured result of the presented FBLC is illustrated in Figure 11. The proposed FBLC has good performance at both operating frequency and higher frequency bands. The measured amplitudes of S₁₂ and S₁₃ are −3.1 dB and −3.25 dB, which shows less than 0.25 dB of insertion loss at operating frequency. The measured amplitude of S₁₁ is about −29 dB, and the amplitude of S₁₄ is about −28 dB, which shows desirable performance for the fabricated proposed FBLC. At higher frequencies, the proposed coupler suppresses second to sixth harmonics with high attention level and provides a wide stopband from 1.6 GHz to 5 GHz with more than 20 dB of attention.

In order to show the superiority of the proposed coupler’s achieved parameters, the performances of the proposed coupler are compared with some related couplers, listed in

Table 2. The comparison between proposed 800 MHz branch line coupler and other related works.

Ref.	Operating Frequency (MHz)	Size Reduction	Harmonics Suppression
[45]	2400	55%	-
[46]	2000	72%	2nd and 3rd
[33]	1800	66%	2nd
[47]	1350	64%	2nd and 3rd
[48]	1160	55%	-
[49]	900	64%	3rd and 5th
[50]	835	73%	2nd
[51]	750	84%	2nd–7th
[52]	1000	73%	2nd
[15]	1800	74%	2nd–7th
[53]	1000	63%	2nd and 3rd
[54]	2400	55%	2nd and 3rd
This work	800	87%	2nd–6th

. As shown, the proposed branches, which are used in the designed coupler, have resulted in the desired performance, compared with the other related works. Moreover, the wide rejection band and high miniaturization are achieved for the proposed coupler, while the desirable parameters of the coupler at operating frequency are obtained.

6. Conclusions

A compact FBLC with a wide suppression band is presented in this paper. In the conventional FBLC, four long, quarter wavelength branches are used, which occupy a large area. In the proposed design, lumped components and transmissions lines are used together to create new compact composite lines. The proposed composite lines are used instead of the long branches in the FBLC structure. The proposed FBLC correctly operates at 800 MHZ and rejects second to sixth harmonics with a high attention level. Moreover, the designed FBLC provides a wide stopband from 1.6 GHz to 5 GHz with more than 20 dB of attention. In the designed coupler, four inductors and four capacitors are used, which in addition to harmonics suppression also reduce the size of the device. The proposed FBLC has a size of 23.7 mm × 25.5 mm (0.086λ × 0.093λ), which shows an 87% size reduction compared with the conventional coupler. The proposed coupler is implemented on Rogers RT-Duroid substrate, and the measured result validates the correct performance of the coupler.