Filtering Power Divider Design Using Resonant LC Branches for 5G Low-Band Applications

: This paper proposes an ultra-compact ﬁltering power divider with a wide harmonic suppression band. In this design, the proposed power divider (PD) in the ideal case has 100% size reduction and an inﬁnite number of harmonics suppression. However, in the real case, the proposed divider has a 92% size reduction and suppresses the 2nd to 45th harmonics. The small-proposed divider is designed at 0.9 GHz. The typical Wilkinson divider has two long quarter-wavelength branches. In the proposed design, new resonant series LC branches are used instead of the divider’s typical branches, leading to performance improvements in the proposed PD. To the best of the authors’ knowledge, the proposed ﬁltering PD has the best size reduction, and harmonics suppression reported thus far. The proposed divider has a ﬁltering response with good insertion loss at the passband, which is desirable for modern communication systems.


Introduction
Power dividers (PDs) are essential devices commonly used in communication circuits. PDs are used for power division or combination in amplifiers, antennas, phase shifters, mixers, modulators, and frequency multipliers [1]. Dividers have been widely used in modern 5G communications circuits and systems-the specifications of sub-6 GHz, 5G applications are explained in [2,3]. In addition, the dividers can be integrated into the MIMO antenna applications [4,5].
Two common types of PDs in microwave applications are Wilkinson and Gysel. A typical Wilkinson power divider (WPD) has two long quarter-wave (λ/4) length branches with a 100 Ω lumped resistor between output ports. A Gysel power divider has six λ/4 length branches, and two 50 Ω lumped resistors. Both of these dividers are large (especially Gysel) and have undesirable harmonics. Several works have partially made improvements on these drawbacks in recent decades. Open-ended stubs were exploited to address the large size and undesirable harmonics in [1]. However, this method is simple: many openended stubs are needed to remove many harmonics, and each applied stub creates one narrow transmission zero, which helps the suppression band.
In some designs, the electronic band gap (EBG) cells [6,7] and defected ground structure (DGS) [8,9] are used to overcome these drawbacks of the standard dividers. An additional stage is needed for these two structures in the fabrication process, which results in the complexity of circuit design. Resonator cells [10][11][12][13][14] are widely used in the divider branches to create filtering responses, remove harmonics and reduce the length of the long branches. The applied resonators increase the insertion losses of the dividers, and all these mentioned power dividers suffer from high insertion losses.
In some research [15,16], coupled lines were used in the divider structure to suppress unwanted harmonics. With the applied coupled lines method, only signals at operating frequency were passed, and the signals at other frequencies were eliminated, which creates filtering responses. Unfortunately, the coupled lines method cannot improve the size of the circuit. For example, the size of both dividers in [15,16] is more significant than the typical divider. Recently higher frequencies for power dividers have been achieved using optical fiber substrates [17,18]. In addition, methods of optimization and artificial intelligence (AI) have been recently used to design power dividers and other microwave components [19,20].
All the discussed works in the literature have partially improved the large size and harmonic presence drawbacks of the typical power divider. However, the proposed work has solved these two drawbacks with the best results compared to the previous works, such that to the author's best knowledge, the best size reduction and harmonic suppression are achieved simultaneously. This paper incorporates the LC lumped elements into proposed developed LC branches, which can be used instead of the power divider main branches. The proposed new branches have resulted in a compact design of the power divider with the desired percentage of miniaturization. In addition, a filtering response with a wide suppression band has been obtained for the proposed divider using the developed LC branches.

Structure of the Typical WPD
As depicted in Figure 1, the typical Wilkinson divider has two long λ/4 branches and a lumped 100 ohms resistor. The microstrip realization of the normal WPD is shown in Figure 2. This structure has a large size of λ/8 × λ/8. This large size is the first drawback of this typical divider.   An Agilent ADS simulator carried out the divider design, and the circuit simulator and electromagnetic (EM) simulator were carried out based on the Duroid5880 substrate with εr = 2.2 and 0.508 mm thickness.
The typical WPD frequency response is depicted in Figure 3. The typical divider performs well at the operating frequency. Nonetheless, this structure passes unwanted signals at higher frequencies, like the desired signals at operating frequencies, without suppression.

Proposed WPD Structure
As mentioned in the previous section, the typical divider not only has a large size but also suffers from undesirable harmonics. To overcome these drawbacks proposed LC An Agilent ADS simulator carried out the divider design, and the circuit simulator and electromagnetic (EM) simulator were carried out based on the Duroid5880 substrate with ε r = 2.2 and 0.508 mm thickness.
The typical WPD frequency response is depicted in Figure 3. The typical divider performs well at the operating frequency. Nonetheless, this structure passes unwanted signals at higher frequencies, like the desired signals at operating frequencies, without suppression. An Agilent ADS simulator carried out the divider design, and the circuit simulator and electromagnetic (EM) simulator were carried out based on the Duroid5880 substrate with εr = 2.2 and 0.508 mm thickness.
The typical WPD frequency response is depicted in Figure 3. The typical divider performs well at the operating frequency. Nonetheless, this structure passes unwanted signals at higher frequencies, like the desired signals at operating frequencies, without suppression.

Proposed WPD Structure
As mentioned in the previous section, the typical divider not only has a large size but also suffers from undesirable harmonics. To overcome these drawbacks proposed LC

Proposed WPD Structure
As mentioned in the previous section, the typical divider not only has a large size but also suffers from undesirable harmonics. To overcome these drawbacks proposed LC branch is designed to provide a suppression band and miniaturize the circuit size. The proposed LC branch's structure is shown in Figure 4. The developed LC branch has a very short length and provides a filtering response at the desired frequency. branch is designed to provide a suppression band and miniaturize the circuit size. The proposed LC branch's structure is shown in Figure 4. The developed LC branch has a very short length and provides a filtering response at the desired frequency.

Proposed LC Branch Analysis
The typical and proposed branches should have the same response at the operating frequency. Thus, the ABCD matrix of these branches should be equal. The main λ/4 branch line has one microstrip line, and the ABCD matrix for this part is demonstrated with MMB.

Proposed LC Branch Analysis
The typical and proposed branches should have the same response at the operating frequency. Thus, the ABCD matrix of these branches should be equal. The main λ/4 branch line has one microstrip line, and the ABCD matrix for this part is demonstrated with M MB . The proposed branch line has two microstrip lines with an electrical length of θ 1 and a series of lumped components. The ABCD matrix for the first part is noted with M 1 , and the ABCD matrix for the series lumped elements is noted with M LMP .
As mentioned, the ABCD matrices of the proposed LC branch and normal branch should be equal; therefore, the equation is written in (1): The values of M 1 , M LMP , and M MB are written in Equations (2)- (4): The applied inductor in the proposed branch consists of two series inductors of L 0 and L m . The L m with two adjacent transmission lines creates a composite line, which provides a miniaturization of the power divider. The L 0 C 0 is tuned at the central frequency (f 0 ), as illustrated in Figure 5. Therefore, the M LMP matrix can be written in the analysis at the central frequency as (5).

Proposed WPD with LC Branch Analysis
The proposed structure of the WPD with the presented LC branches is shown in Figure 6. The design goal is a 900 MHz divider with a 90% size reduction.

Proposed WPD with LC Branch Analysis
The proposed structure of the WPD with the presented LC branches is shown in Figure 6. The design goal is a 900 MHz divider with a 90% size reduction. Figure 6. Structure of the proposed WPD with the series LC branches. Figure 6. Structure of the proposed WPD with the series LC branches.
The occupied size of the typical WPD is λ/8 × λ/8. In the proposed WPD, to have a 90% size reduction, the occupied size should be 0.1 × (λ/8 × λ/8). Therefore, the proposed branch length (θ 1 + length of lumped components + θ 1 ) should be 30 • , which is equal to 0.08 λ. Thus, the θ 1 should be approximately 15 • (0.04 λ). The lengths of the lumped components (L and C) are neglected. Until now, the value of the θ 1 has been calculated, and to calculate the unknown parameter of Z 1 , from (10) and considering Z 0 = 50 Ω, the Z 1 can be determined as follows: The value of impedance is equal to Z 1 = 18.9 Ω. The dimensions of the proposed branches with the applied substrate of Duroid5880 substrate with ε r = 2.2 and 0.508 mm thickness are depicted in Figure 7. The occupied size of the typical WPD is λ/8 × λ/8. In the proposed WPD, to have a 90% size reduction, the occupied size should be 0.1 × (λ/8 × λ/8). Therefore, the proposed branch length (θ1 + length of lumped components + θ1) should be 30°, which is equal to 0.08 λ. Thus, the θ1 should be approximately 15° (0.04 λ). The lengths of the lumped components (L and C) are neglected. Until now, the value of the θ1 has been calculated, and to calculate the unknown parameter of Z1, from (10) and considering Z0 = 50 Ω, the Z1 can be determined as follows: The value of impedance is equal to Z1 = 18.9 Ω. The dimensions of the proposed branches with the applied substrate of Duroid5880 substrate with εr = 2.2 and 0.508 mm thickness are depicted in Figure 7. As seen in Figure 5, the applied inductor consists of two series inductors of L0 and Lm. The value of Lm can be easily obtained from Equation (6), considering the 900 MHz operating frequency as follows: with Z1 = 18.9 Ω and w = 2π × (900 MHz), the value of Lm is 11.58 nH. L0 and C0 can be obtained from (13), which have several answers. If we select 0.5 PF for the applied capacitor according to (13), the L0 value is 62 nH: As seen in Figure 5, the applied inductor consists of two series inductors of L 0 and L m . The value of L m can be easily obtained from Equation (6), considering the 900 MHz operating frequency as follows: Sustainability 2022, 14, 12291 6 of 14 with Z 1 = 18.9 Ω and w = 2π × (900 MHz), the value of L m is 11.58 nH. L 0 and C 0 can be obtained from (13), which have several answers. If we select 0.5 PF for the applied capacitor according to (13), the L 0 value is 62 nH: The value of the applied inductor can be calculated from (14), which is equal to 73.5 nH:

The Proposed Power Divider Design
The design process of the proposed divider is depicted in Figure 8. At first, a typical WPD at 900 MHz, with a large size, is designed. The first design of WPD is proposed according to the analysis, which has an 82% size reduction. The length of the proposed transmission line is obtained analytically. Finally, the optimized WPD is presented and fabricated with a 92% size reduction.

Typical WPD Design
In this section, the typical WPD at 900 MHz is realized with microstrip lines to have better compression at first. The realized typical WPD is shown in Figure 9a. The typical WPD has a size of 33.9 mm × 34.7 mm. The scattering parameters of typical WPD are depicted in Figure 9b, showing the divider's correct performance at 900 MHz.

Typical WPD Design
In this section, the typical WPD at 900 MHz is realized with microstrip lines to have better compression at first. The realized typical WPD is shown in Figure 9a. The typical

Typical WPD Design
In this section, the typical WPD at 900 MHz is realized with microstrip lines to h better compression at first. The realized typical WPD is shown in Figure 9a. The typ WPD has a size of 33.9 mm × 34.7 mm. The scattering parameters of typical WPD depicted in Figure 9b, showing the divider's correct performance at 900 MHz.

First Design of the Proposed WPD without Optimization
In the second step, two proposed developed LC branch lines, designed in Section 5 with calculated dimensions, are used instead of the long branches of the typical divider. The proposed WPD is depicted in Figure 10. The overall size of the proposed WPD is 13.9 mm × 15.3 mm, which offers an 82% reduction in size compared to typical WPD. In the simulation process, some values are tuned to have better results. The obtained values from analysis, simulation and measurement are listed in Table 1.

First Design of the Proposed WPD without Optimization
In the second step, two proposed developed LC branch lines, designed in Section 5 with calculated dimensions, are used instead of the long branches of the typical divider. The proposed WPD is depicted in Figure 10. The overall size of the proposed WPD is 13.9 mm × 15.3 mm, which offers an 82% reduction in size compared to typical WPD. In the simulation process, some values are tuned to have better results. The obtained values from analysis, simulation and measurement are listed in Table 1. The first design of the proposed WPD response at the main frequency is shown in Figure 11a. These parameters at a wide frequency range are depicted in Figure 11b. This divider performs correctly at 900 MHz and suppresses the 2nd to 45th unwanted harmonics with a high level of attenuation. The first design of the proposed WPD response at the main frequency is shown in Figure 11a. These parameters at a wide frequency range are depicted in Figure 11b. This divider performs correctly at 900 MHz and suppresses the 2nd to 45th unwanted harmonics with a high level of attenuation.  Figure 10. The first design of the proposed WPD at 900 MHz 82% size reduction.

S-Parameters
The first design of the proposed WPD response at the main frequency is shown in Figure 11a. These parameters at a wide frequency range are depicted in Figure 11b. This divider performs correctly at 900 MHz and suppresses the 2nd to 45th unwanted harmonics with a high level of attenuation.

Second Design of the Proposed WPD with Improvement
In the final step, the proposed WPD is presented, and the layout of the proposed divider is depicted in Figure 12. The proposed WPD final size is only 9.9 mm ×10.4 mm, which shows a 92% size miniaturization.

Second Design of the Proposed WPD with Improvement
In the final step, the proposed WPD is presented, and the layout of the proposed divider is depicted in Figure 12. The proposed WPD final size is only 9.9 mm ×10.4 mm, which shows a 92% size miniaturization.
The scattering parameters of the proposed WPD near the orating frequency are shown in Figure 13a. The proposed WPD acts correctly at 900 MHz. The S 21 parameter at the operating frequency is −3.3 dB, which offers about 0.3 dB insertion loss. The S 11 , S 22 , and S 23 parameters are about −20 dB, which shows good divider performance at the operating frequency. The proposed WPD has noticeable performance at higher frequencies. A wide stopband has been obtained for the proposed divider from 1.8 GHz up to 40 GHz, which shows excellent harmonics suppression. The simulated results of the proposed WPD are depicted in Figure 13b.

Second Design of the Proposed WPD with Improvement
In the final step, the proposed WPD is presented, and the layout of the proposed divider is depicted in Figure 12. The proposed WPD final size is only 9.9 mm ×10.4 mm, which shows a 92% size miniaturization.  The scattering parameters of the proposed WPD near the orating frequency are shown in Figure 13a. The proposed WPD acts correctly at 900 MHz. The S21 parameter at the operating frequency is −3.3 dB, which offers about 0.3 dB insertion loss. The S11, S22, and S23 parameters are about −20 dB, which shows good divider performance at the operating frequency. The proposed WPD has noticeable performance at higher frequencies. A wide stopband has been obtained for the proposed divider from 1. The layout comparison between the proposed and typical WPD is depicted in Figure  14. The proposed WPD only occupies 0.08% of the normal WPD, showing a 92% size reduction. The fabricated photo of the proposed WPD is depicted in Figure 15. The layout comparison between the proposed and typical WPD is depicted in Figure 14.
The proposed WPD only occupies 0.08% of the normal WPD, showing a 92% size reduction. The fabricated photo of the proposed WPD is depicted in Figure 15. The proposed divider's fabrication accuracy is critical due to the narrow microstrip lines applied. Any fabrication error or substrate loss will disturb frequency response. Therefore, the photolithography method is used to create an accurate prototype, and after this step, the lumped capacitors and inductors are soldered on the prototype. The simulated and measured results of the fabricated divider are shown in Figure 16. The proposed divider frequency response is depicted in Figure 16a, and a wide operating frequency range is illustrated in Figure 16b.  The proposed divider's fabrication accuracy is critical due to the narrow microstrip lines applied. Any fabrication error or substrate loss will disturb frequency response. Therefore, the photolithography method is used to create an accurate prototype, and after this step, the lumped capacitors and inductors are soldered on the prototype. The simulated and measured results of the fabricated divider are shown in Figure 16. The proposed divider frequency response is depicted in Figure 16a, and a wide operating frequency range is illustrated in Figure 16b. The proposed divider's fabrication accuracy is critical due to the narrow microstrip lines applied. Any fabrication error or substrate loss will disturb frequency response. Therefore, the photolithography method is used to create an accurate prototype, and after this step, the lumped capacitors and inductors are soldered on the prototype.
The simulated and measured results of the fabricated divider are shown in Figure 16. The proposed divider frequency response is depicted in Figure 16a, and a wide operating frequency range is illustrated in Figure 16b.
The performances of the designed WPD and related works are compared in Table 2. The proposed WPD has the most compact size and best suppression band among the reported studies. The size reduction in Table 2 is calculated based on the normalized size of the dividers. Sim. The performances of the designed WPD and related works are compared in Table.2. The proposed WPD has the most compact size and best suppression band among the reported studies. The size reduction in Table 2 is calculated based on the normalized size of the dividers.

Conclusions
A 900 MHz WPD, with excellent size reduction and harmonics suppression, is designed, analyzed, and implemented in this paper. In this WPD, compact proposed series LC branches are used instead of the long microstrip lines in the typical WPD, which leads to excellent compact size, filtering response, and performance improvement. The designed WPD has a 92% size reduction compared to the typical WPD and suppresses the 2nd to 45th unwanted harmonics. The proposed WPD has the most compact size and best suppression band, which have been reported up until now. In this paper, the WPD is initially designed analytically, then simulated with ADS software, and the proposed device is fabricated at the end. All of the calculated, simulation and measured values have good agreements, confirming the proposed design's validity.