Size reduction and performance improvement of a microstrip Wilkinson power divider using a hybrid design technique

In the design of a microstrip power divider, there are some important factors, including harmonic suppression, insertion loss, and size reduction, which affect the quality of the final product. Thus improving each of these factors contributes to a more efficient design. In this respect, a hybrid technique to reduce the size and improve the performance of a Wilkinson power divider (WPD) is introduced in this paper. The proposed method includes a typical series LC circuit, a miniaturizing inductor, and two transmission lines, which make an LC branch. Accordingly, two quarter-wavelength branches of the conventional WPD are replaced by two proposed LC branches. Not only does this modification lead to a 100% size reduction, an infinite number of harmonics suppression, and high-frequency selectivity theoretically, but it also results in a noticeable performance improvement practically compared to using quarter-wavelength branches in the conventional microstrip power dividers. The main important contributions of this technique are extreme size reduction and harmonic suppression for the implementation of a filtering power divider (FPD). Furthermore, by tuning the LC circuit, the arbitrary numbers of unwanted harmonics are blocked while the operating frequency, the stopband bandwidth, and the operating bandwidth are chosen optionally. The experimental result verifies the theoretical and simulated results of the proposed technique and demonstrates its potential for improving the performance and reducing the size of other similar microstrip components.

As modern communication systems have grown rapidly, the demands for microwave components with low energy loss, compact size, and filtering response have increased significantly. In this regard, wireless components should be integrated for the multiple function ability in embedded systems. For example, integrating a filter with a power divider will result in a compact size and low energy loss in the microwave components. Power dividers and couplers are two important microstrip passive components that can benefit from such modifications. Accordingly, they can have more appropriate harmonic suppression and higher performance than the conventional ones, leading to higher efficiency in aspects of the performance and energy 1,2 .
Power dividers play an important role in modern wireless communication systems 3 . Wilkinson power divider (WPD) is one of the most popular types of dividers. In fact, the WPD was first proposed by Ernest J. Wilkinson in 1960 4 . Since then it has widely used in modern communication systems, such as Doherty power amplifiers 5 , balanced power amplifiers 6,7 , push-pull power amplifiers 8 , antenna feed networks 9 , phase shifters 10 , and RF/ microwave frontend systems 11 .
One of the disadvantages of the typical WPD is that the spurious harmonics can easily pass through the power divider paths and decrease its performance. Another disadvantage of the WPD is its large size, which is about approximately 0.0156 λ 2 . Recently, several approaches have been proposed and performed to solve these problems. For example, coupled lines 12 , open-ended stubs 13 , T-shaped and Π-shaped resonators 14 , and embedded filters 15 .
Open-ended stubs are usually used in the main quarter wavelength branches of the divider as studied in 13,16 to reduce the size and suppress a few harmonics. Open-ended stubs can also be used at the input port to improve the www.nature.com/scientificreports/ the most challenging drawbacks with such structures is to have a large size due to utilizing the large quarterwavelength branches, which are not favorable in modern wireless systems. Another important disadvantage, which can be mentioned for this type of design, is to suffer from the existence of spurious harmonics because the typical quarter-wavelength branches cannot provide a suppression band for the divider. Nevertheless, the WPD layout structure plays an important role in determining the overall size of WPDs. Generally, two common forms of the WPD have been utilized in the design of WPDs, namely squared-shape and circular-shaped, which are depicted in Fig. 2a and b, respectively. As you can see in Fig. 2a, the overall size of the square-shaped WPD, is 0.125 λ × 0.125 λ, which is equal to 0.0156 λ 2 while the overall size for circular one is 0.0198 λ 2 , indicating this point that the circular type of the WPD is typically larger than the square-shaped one. It should be noted that in both square-shaped and circular-shaped WPDs, the size of the resistor is neglected in calculation of the total size theoretically. Regardless of this difference, the size of WPD and many other microstrip components significantly depend on their quarter-wavelength branches, such as branch-line couplers, rat-race couplers, and several types of discrete power amplifiers. The proposed structure will be discussed in the next section.

Proposed WPD structure
As is mentioned, the typical WPD suffers from large size and spurious harmonics existence. Therefore, by modifying the transmission lines used in the WPD that are more responsible in increasing the size, not only will the size of components made by this technology be far more compact, but it can also lead to increasing the efficiency. Overall, to reach these objectives, some important parameters like selectivity and suppressing the unwanted harmonics should be considered. In this regard, a novel hybrid solution to improve the size and performance of a WPD has been presented here. In addition, the proposed method can be used in a wide range of microstrip components using transmission lines.
Proposed LC branch lines. The proposed method includes replacing long quarter wave length transmission lines, which are used in WPDs or any other microwave components, such as filters, diplexers, matching networks, couplers, and power amplifiers, with the proposed compact LC branches. Figure 3 demonstrates the proposed hybrid approach using microstrip lines and LC branches in a microwave component. As is observed in Fig. 3, microstrip branch lines of the conventional WPD are replaced by the proposed LC branch lines. The LC branch lines include a resonance capacitor (C 0 ), a resonance inductor (L 0 ), a miniaturizing inductor (L m ), and two transmission lines (Z 1 , θ 1 ). The resonance capacitor and inductor, which form a series LC circuit, should be tuned at the desired operating frequency (f 0 ). The series LC circuit is shorted at f 0 while it is opened at other frequencies, resulting in the bandpass response of the divider. Therefore, the LC branch structure can be used to reduce the desired harmonics.   www.nature.com/scientificreports/ Furthermore, the size of each microstrip branch line significantly decreases from a large size to a very small size that will be discussed in the next sections. In fact, the miniaturizing inductor results in reducing the LC branch length. The inductances of L 0 and L m are in series and can be considered as the inductance of L in practice. After applying the proposed LC branches, a new structure will be obtained for the WPD. The proposed structure of the WPD with the presented LC branches is shown in Fig. 4.

Analyses of the proposed WPD
The structure of the proposed WPD is analyzed using the ABCD matrix. The ABCD matrix of the proposed LC branch has to be equaled to the ABCD matrix of a conventional quarter wavelength (QWL) branch. Therefore, the obtained equation is written in Eq. (1) where, in M 1 , M LCB , and M QWL are ABCD matrices of the transmission line (Z 1 , θ 1 ), LC branch (LCB), and quarter wavelength line ( √ 2 Z 0 , λ/4), respectively. In addition, the values of M 1 , M LCB , and M QWL matrices are defined in Eq. (2).
As mentioned before, the series L 0 C 0 is tuned at the main frequency (f 0 ), which is shorted at the main frequency. Hence, if it is assumed to perform the analyses in the main frequency, the LC branch matrix can be simplified as written in Eq. (3).
By solving Eq. (7), which is a second-order equation, the normalized value of Z 1 can be calculated as written in Eq. (8). Figure 5 demonstrates the proposed approach, including the prototype of a microstrip WPD and the suggested method to solve the equations in order to obtain circuit parameters. As it can be seen in this figure, in the first stage, the prototype of the understudied component is indicated. In the second stage, the values of the key parameters for the component, such as the amount of size reduction (SR%), operating frequency (f), and operating bandwidth are arbitrarily determined. Next, θ 1 is computed based on the selected SR% in the previous stage. In the third stage, Z 1 is calculated using Eq. (8). The calculated circuit values in the third stage are listed in Table 1 at the operating frequency of 2.4 GHz and 0.8 GHz. In the fourth stage, the value of L m is obtained by using Eq. (4). As is observed, the value of Z 1 is independent of the operating frequency, while the value of L m depends on the operating frequency. By adding L 0 and L m , the total value of L is achievable in the fifth stage. The values of L 0 and C 0 are achieved based on values of Q (quality factor) being available in Tables 2 and 3 at the operating frequency of 2.4 GHz and 0.8 GHz. Besides, the value of Q is obtained through bandwidth, which will be more discussed at the next Sections. Finally, the new proposed divider with desirable parameters based on (θ 1 , Z 1 , C 0 , and L) can be achieved.
The design process of the proposed technique is described in Fig. 5. In addition, some design examples for circuit parameters values are calculated and shown in Table. 1. Moreover, the relation between calculated circuit parameters from the analysis is shown in Fig. 6 for more clarification. The calculated values of divider maximum size reduction versus total electrical length of the branch and versus the value of Z 1 (Ω) are demonstrated in Fig. 6a and b. The word "maximum" is used for maximum size reduction because the L and C component elements occupy a small size practically, which is not considered in the theory design. As mentioned above, the main branch line length of the conventional WPD is λ/4, while the proposed LC branch length is considered 2θ 1 . Therefore, the maximum size reduction is calculated according to the ratio of the size of the square shape WPD with the proposed LC branches to the size of the conventional square shape WPD with typical λ/4 branches. Figure 6b illustrates the lower size of the divider which is corresponding with the lower value of Z 1 , leading to a wider transmission line. Moreover, the calculated values of Z 1 (Ω) versus the total electrical length of the branch are depicted in Fig. 6c. As can be seen in Fig. 6c, the lower size of the divider is corresponding with the wider transmission line. Besides that, Fig. 6d shows the calculated inductance L m values versus maximum size reduction at different frequencies. According to this figure, the higher values of L m are needed for higher size reduction and lower operating frequencies. Therefore, the values of Z 1 are independent of the operating frequency, while the value of L m depends the on operating frequency. Additionally, from both analyses and Fig. 6, it can be concluded that any value of maximum size reduction can be theoretically achieved using the proposed LC branches.
In the final design, in addition to L m , resonant inductor (L 0 ) and capacitor (C 0 ) will be applied to form the LC branch. The series LC circuit should be tuned at the desired operating frequency.   www.nature.com/scientificreports/ Figure 5. The process of design and solving the equations of a WPD based on the proposed technique. First, the conventional WPD with 0% size reduction, no harmonic suppression and no bandwidth tuning ability is considered. The desired values of SR%, operating frequency, and bandwidth are then assumed arbitrarily. Next, with the use of the proposed analyses, the equations are solved and the desired circuit parameters (θ1, Z 1 , C 0 , and L) are achieved. By applying these circuit parameters, and the proposed structure to the typical WPD, the new compact divider with desirable SR%, extreme harmonic suppression, and desirable operating bandwidth is obtained. www.nature.com/scientificreports/ (Z 1 ) and length (θ 1 ) dimensions of LC branches transmission lines are 40.8 Ω and 30˚ for 55.5% size reduction, while they are 33 Ω and 25° for 69.1% size reduction, respectively. The values of L m are calculated equal to 3.1 nH and 3.7 nH for 55.5% and 69.1% size reduction values, respectively. In the next step, the series L 0 C 0 circuit should be tuned at the operating frequency. However, the quality factor (Q) of the series L 0 C 0 circuit can be tuned by changing the L 0 and C 0 values. The results of the circuit simulations for the first and second design examples at 2.4 GHz are illustrated in Fig. 7. Accordingly, the effects of the series L 0 C 0 circuit with different quality factors on the simulated frequency responses of the presented design examples are shown in this figure. As can be seen in Fig. 7, by increasing the quality factor, the bandwidth decreases, whereas the stopband increases. In other words, by increasing the quality factor more harmonic suppression can be achieved. Therefore, the arbitrary bandwidth can be achieved by tuning the quality factor in LC branches. In the case indicated with "only L m " in Fig. 7, the  www.nature.com/scientificreports/ L m is only considered in the LC branch, while the resonant inductor (L 0 ) and capacitor (C 0 ) are not applied. This situation can also be assumed as a series resonant circuit with a small quality factor. In the next step, the values of L 0 and C 0 should be determined according to the desired harmonic suppression and operating bandwidth of the WPD. Different values of L 0 and C 0 combinations are considered at 2.4 GHz operating frequency in Table 2 The frequency responses of the prototype dividers at 2.4 GHz for the first and second design examples are depicted in Fig. 9. The circuit simulation and electromagnetic (EM) simulation are compared in this Figure. As is observed, the obtained EM simulation results verify the circuit simulation results. According to the EM simulation results, for both first and second design examples, an appropriate suppression band is obtained, which can suppress 2nd up to 8th spurious harmonics. In addition, for both first and second design examples, insertion loss is below 0.1 dB in the operating frequency, and isolation between output ports is better than 35 dB in the operating frequency. The information about the EM simulation results for the first and second design examples is listed in Table 4 in "Measurement results" section.  Hence, by increasing the quality factor, the bandwidth decreases while the stopband increases. In other words, by increasing the quality factor more harmonics can be suppressed.
In the next step, the values of L 0 and C 0 should be determined based on the desired harmonic suppression and operating bandwidth of the WPD. Different values of L 0 and C 0 combinations are considered for 0.8 GHz  www.nature.com/scientificreports/ operating frequency in Table 3. Then the corresponding values of quality factors and operating bandwidths are extracted in Table 3.  Table 4 in "Measurement results".

Measurement results
To verify the simulation and analyses results, the fourth design example with theoretical 80.2% and practical 82.8% size reduction at the operating frequency of 0.8 GHz is implemented on the high-frequency substrate with the specifications of RT Duroid 5880 with a thickness of 0.508 mm (20 mil) and ε r = 2.2. Figure 13 compares experimental results with the EM simulation results. The fabricated divider is measured using Agilent E8362B Network Analyzer. The measurement is set up to 20 GHz frequency to clarify the harmonic suppression performance.
The measured results show that the proposed divider can practically operate at 0.7 GHz up to 0.95 GHz, which indicates 250 MHz operating bandwidth. The minimum insertion loss is 0.3 dB at this bandwidth. As is observed, the proposed divider can work properly at 0.8 GHz frequency with desirable specifications. Moreover, according to the measured results, the isolation between the output ports, input return loss, and output return loss is 15 dB, 14 dB and 22 dB, respectively. A proper suppression band is obtained for the proposed divider with a suppression level of more than 20 dB. The 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 10th, 17th, 18th, 19th, 20th, 21th, 22th, 23th, 24th, and 25th harmonics are suppressed with suppression levels of more than 15 dB, according to the measured results. The fabricated proposed WPD is shown in Fig. 14. Table 4 provides information about the proposed divider results compared to the previous filtering dividers. Design Flexibility (DF) in this table means that the main parameters of the divider, such as size reduction, harmonic suppression, and bandwidth can be changed to the desired values. According to the information provided in Table 4, the proposed hybrid method is capable of designing a WPD with high design flexibility, low design complexity (DC), compact size, and high levels of harmonic suppression. Therefore, this innovative modification can contribute to considerable improvements in the design of the next generation of microwave components.  www.nature.com/scientificreports/

Conclusions
An innovative hybrid technique for size reduction and performance improvement of a microstrip WPD has been conducted and demonstrated in this paper. In this method, microstrip lines in the WPD are replaced by the proposed LC branches. This replacement leads to extreme size reduction, filtering response, and improving performance. To assess the effectiveness of the proposed approach, four WPDs have been designed and simulated by amending their branch lines. This alteration in branches breeds an enormous size reduction and harmonic suppression in the dividers. In order to survey the practical performance of the designed WPDs, one of them was fabricated and its excremental results were measured. The results demonstrated the capability and efficiency of the introduced method to improve such components. Accordingly, 100% size reduction and an infinite number of harmonics suppression are reached theoretically. However, due to lumped element lengths, the theoretical size reduction can be mildly affected in practice, especially in high frequencies. In addition, folding and bending the microstrip lines may have slight effects on the theoretical values. Consequently, the proposed technique dramatically improves the efficiency and size of such components and provides new fields in the development of many other microstrip components, such as microstrip resonators, filters, diplexers, matching networks, couplers, power amplifiers, and the other types of dividers.
The following results can be concluded from the proposed method. www.nature.com/scientificreports/ 1. Arbitrary size reduction up to theoretically 100% can be achieved although the maximum size reduction percentage is limited to a number between 90 and 100% practically. The practicable size-reduction level also depends on the operating frequency and the lumped elements dimensions.