Design of a Patch Power Divider with Simple Structure and Ultra-Broadband Harmonics Suppression

This paper introduces a simple H-shaped patch Wilkinson power divider (WPD), which provides ultra wide harmonics suppression band. The presented WPD designed at 1.8 GHz, and exhibits good performance at the operating bandwidth. In the proposed divider structure, two simple patch low-pass filters (LPFs) are employed at each branch, and three open ended stubs are added at each port. The proposed divider, implemented using the aforementioned structures has a good performance at both higher frequencies, and the operating frequency. In particular, the designed divider provides an ultra wide suppression band from 3 GHz to 20 GHz, which encompasses the 2nd up to the 11th harmonic. The proposed WPD has an operating band from 1.62 GHz to 2.1 GHz, with the operating bandwidth exceeding 480 MHz. Consequently, the fractional bandwidth (FBW) of 25.8 percent is obtained. The results indicate |S11|, |S12|, |S22|, and |S23|, are equal to –17 dB, –3.5 dB, –20 dB, and –17 dB, respectively, at the operating frequency. The simulation results are corroborated through the measurements of the fabricated divider prototype. The superior harmonic suppression capability is also demonstrated through comparisons with state-of-the-art divider circuits from the literature.


I. INTRODUCTION
The dividers belong to popular components in microwave circuits and systems. A conventional Wilkinson divider exhibits good performance at its operating frequency, yet it transmits unwelcome harmonics along with the main signal without any suppression, which is undesirable in many applications [1]. Consequently, design of modified dividers with harmonics elimination has become an important design consideration in modern communication systems. Some of available methods introduced to suppress unwanted harmonics are outlined below. In [2][3][4][5][6], harmonic elimination has been achieved by means of electromagnetic bandgap (EBG) cells. This approach has been demonstrated effective but needs additional steps in both the design and the fabrication processes, thereby making it difficult to implement. In a number of works, e.g., [7][8][9][10][11][12], defected ground structures have been used to realize harmonics canceling. The defected ground methods prove suitable for the purpose yet-similarly as EBG-additional design and fabrication steps are required, which is a downside.
In many designs, lumped reactive components, such as inductors and capacitors [13][14][15][16][17][18][19], are applied to provide wide harmonics elimination range. On the other hand, while the usage of lumped components is effective for harmonics suppression, it limits the operating frequency and increases the losses at higher frequencies.
Open-ended and short-ended stubs also are widely used to suppress unwanted harmonics in dividers [20][21][22][23][24][25][26]. These techniques allow for simple structures and planar designs. However, a single stub only suppresses a single harmonic, therefore, to implement a broad harmonic suppression band, several stubs have to be used, which increases the circuit complexity. Yet another approach to harmonics cancelling are power dividers based on coupled line architectures [27][28][29][30][31][32]. Coupled lines provide bandpass responses and eliminate unwanted harmonics, but suffer from high insertion losses in the passband. Perhaps the most common method to reduce harmonics in the divider structures is utilization of resonators. Several dividers have been reported in the literature with different types of resonators to suppress unwanted harmonics [33][34][35][36][37][38][39][40][41][42][43]. Resonators are effective in suppressing of unwanted harmonics, but also contribute to insertion losses, which increase the overall insertion loss of the divider. In terms of algorithmic approaches, artificial intelligence methods, which has been widely used to solve engineering problems [44][45][46][47][48][49][50][51], can be employed to modeling and design of power dividers [52,53].
Recently, patch structures have become popular in the design of microwave devices, examples including patch resonators, patch filters, and patch antennas [54][55][56][57][58][59][60]. Patch resonators exhibit a number of attractive features, the most important of which are geometrical simplicity and straightforward design process as compared to other structures [37]. So far, patch resonators have been only sparsely used in the design of power dividers. In this work, we demonstrate that patch resonators and patch filters can be useful in design of compact and filtering power dividers. In particular, we propose a divider operating at 1.8 GHz, and implemented using two-patch LPFs featuring simple structure, and three open stubs at each port. The LPFs provide wide stopband with low insertion loss. The wide stopband enables suppression of the unwanted harmonics of the divider. Additional harmonics suppression is achieved by the aforementioned open stubs at each port. The major technical contribution of this work include the development of a filtering H-shaped patch power divider featuring simple structure and harmonic suppression ability. The design exhibiting similar properties has not been demonstrated in the literature before. Furthermore, it is shown that the H-shaped patch resonator along with the open-ended stubs at each port can be used in the Wilkinson power divider, which results in performance improvement of the device. Comprehensive comparison of the proposed design with the state of the art power dividers demonstrates superior performance of the proposed device. The proposed divider is validated numerically and experimentally, and favorably benchmarked against the state-of-the-art circuits reported in the literature.

II. DESIGN PROCEDURE OF THE PROPOSED WPD
A conventional Wilkinson power divider (WPD) contains two main branches with the lengths of a quadrature wavelength, and a lumped 100-ohm resistor between the two output ports. This structure is affected by the presence of unwanted harmonics in the frequency response. To overcome this drawback, an alternative structure of a divider is proposed, which will be discussed in the next sections. The conceptual illustration of the design procedure of the proposed WPD has been shown in Fig. 1. Step 1 depicts the key idea of the divider, which incorporates the filtering property of the low pass filters (LPFs) while retaining the overall structure of the conventional WPD. To design the circuit, a new LPF is proposed, as illustrated in Step 2 (a basic LPF) and Step 3 (two high impedance open-ended stubs added to the basic filter). In Step 4, the designed filters are inserted into the main branches of the conventional WPD. Subsequently, based on the major idea of the proposed circuit, three open ended stubs are added at each port to arrive at the final architecture, as shown in Step 5.
Step 6 demonstrates the photograph of the fabricated divider prototype.

III. PROPOSED PATCH LPF
As elaborated on in Section II, one of the main components of the proposed divider is a patch LPF. It is designed to suppress at least the second and the third harmonics. To develop the filters, the basic LPF is first obtained, followed by the final filter architecture.

A. Basic LPF Circuit Model
The circuit model of the presented basic lowpass filter includes three shunted branches of series LC resonators as suppressors, along with two inductors as the main signal path, which is shown in Fig. 2(a). The S-parameters of the circuit model are shown in Fig. 2(b). The series LC resonators consisting of l3C1 and l2C2 create two transmission zeros denoted as TZ1, and TZ2, respectively, which are indicated in By adjusting the locations of the transmission zeros, the desired passband and the suppression band for the basic filter can be obtained. Subsequently, the equivalent transmission line dimensions can be calculated using the relations. 10    Table 1. that provide the ABCD matrices of a series LC resonator and the open-ended stub (eqns. (3) and (4)), shown in Fig. 3. Equivalent dimensions of the open-ended stub can be found by comparing (3) and (4), which leads to representing the electrical length of the equivalent open-ended stub. Equation (5) Table I. After calculating the transmission line dimensions of the basic LPF, it can be realized using microstrip transmission lines, which is described in the next subsection.

B. Basic LPF Design
The basic filter is implemented using the high impedance line of a 0.1-mm width inserted between the ports, loaded by two low impedance capacitive open-ended stubs on both sides of the filter, along with a smaller single open-ended stub in the middle of the filter. Figure 6 demonstrates the layout and simulated S-parameters of the proposed basic LPF, implemented on the Rogers RT5880 substrate. The circuit dimensions are provided in Fig. 6(a). It should be observed that the basic LPF frequency response is not sharp enough. The filter exhibits a 3 GHz suppression band from 3900 MHz to 6900 MHz with 20 dB attenuation.

C. Proposed Patch LPF
As mentioned, the basic LPF does not have a sufficiently sharp response, and features a limited stopband, which fails to suppress the second harmonic in the final power divider at Tune the resonator circuit parameters using Equations (1) and (2) Calculate dimensions of equivalent transmission line by solving ABCD matrices using Equation (5)     3.6 GHz. To improve the filter performance, the structure is enhanced by adding two high impedance open-ended stubs as shown in Fig. 7(a). The simulated frequency response of the proposed patch LPF is demonstrated in Fig. 7(b). A sharp transmission response can be observed as well as the enhanced stopband of 3200 MHz to 6500 MHz with 20 dB attenuation. The cutoff frequency of the patch LPF is 2.2 GHz. This is suitable for designing the 1.8 GHz power divider, as the location of the cutoff frequency of the LPF should be higher than the desired operating frequency of the power divider. At the same time, the cutoff frequency of the LPF should be lower than the frequency of the second harmonic to enable suppression of the latter. Both conditions are met by the proposed LPF structure.

IV. PROPOSED PATCH POWER DIVIDER
As explained in Section III, by utilizing the LPFs presented therein, the entire structure of the designed WPD can be developed. At first, the LPFs LC models are added to the divider circuit model. The final LC model and its frequency response for the proposed patch power divider is depicted in Fig. 8. Also, the values of lumped elements of the proposed patch divider LC model are listed in Table II. In the following subsections, the transmission line realization of the proposed divider circuit model is studied.

A. Basic Patch Power Divider
By replacing the conventional WPD branches with the new LPFs, the structure of the basic patch power divider is formed, which is illustrated in Fig. 9. The overall size of WPD is 29.9 mm × 18.3 mm (0.25 λ × 0.15 λ).   the layout and the simulated S-parameters of the designed basic patch power divider. The basic divider structure works at the operating band of 1.8 GHz to 2 GHz. As depicted in Fig. 9, the isolation and return loss do not reach acceptable levels in the operating band, whereas the suppression band is not sufficiently broad. Both need further improvements, which is described in the next subsection.

B. Proposed Patch Power Divider
By adding three open stubs at each port of the basic patch power divider, intended to improve the operating bandwidth and the suppression band, the final architecture is constructed. Figure 10 shows the layout of the proposed patch power divider. Adding three open stubs does not change the overall size of the divider, which is still 0.24 λ × 0.15 λ. The current distributions of the proposed divider at different frequencies are depicted in Fig. 11. As it can be seen, the high-magnitude current is conducted by the divider at the main frequency, while it is reduced at harmonics frequencies.

V. Even-and Odd-Mode Analyses of the Proposed Patch Power Divider
In this Section, even-and odd-mode circuits of the proposed divider are extracted, as shown in Fig. 12, and the divider is analyzed based on these circuits.

A. Odd-Mode Analysis
The odd-mode equivalent circuit of the proposed divider, extracted for odd-mode analysis has been shown in Fig. 12(a).
To extract the odd-mode circuit of the divider, a short circuit line is placed along the plane of symmetry. The proposed LPF is equated by a single transmission line with ZLPF and θLPF dimensions. Also, ZOS2 and θOS2 corresponds to the openended stub, connected to Port2. Equation (6) shows that the overall impedances seen from Port2 should match Z0 = 50 Ω or the normalized value of Z0 = 1.
By substitution the corresponding values of ZA, ZB, and ZC, (6) can be written as Equating the real parts of both sides of (7) yields normalized R = 2 (Resistor = 100 Ω), whereas equating the imaginary parts results in (8).

B. Even-Mode Analysis
The even-mode equivalent circuit of the proposed divider is depicted in Fig. 12(b). Also, in this figure, the proposed LPF is represented by a single transmission line with ZLPF and θLPF dimensions. Subsequently, the even-mode circuit is analyzed by providing the ABCD matrix, which yields to (9).
As it can be concluded from the even-mode circuit, the total impedance, seen from Port1, should be equal to 2Z0, or the normalized value of 2 (100 Ω). By solving (9) and equating input impedance, extracted from ABCD matrix, to the normalized value of 2, the following relationships can be obtained In practice, to facilitate the design procedure of the proposed divider, the length of the open-ended stubs can be considered equal, so by using (8) and (11), the relation between impedances of the open-ended stubs will be obtained as 21 2 The lengths of the open-stubs should be adjusted in order to allocate the transmission zeros at the frequencies ensuring the best possible suppression band. Therefore, the lengths of the open-stubs are considered equal as θ = 20º, and, subsequently the values of ZOS1 = 30 Ω and ZOS2 = 60 Ω are selected based on (12) and size limitation of the power divider structure. Finally, based on (10) and (11), the overall values of equivalent transmission line for the LPF along with its lateral branches will be achieved as ZLPF = 78.3 Ω, θLPF = 64.6º.

VI. FABRICATION AND MEASUREMENT RESULTS
The proposed patch divider has been fabricated on the Rogers RT5880 substrate. Figure 13 demonstrates the simulated and measured S-parameters of the designed patch power divider circuit. According to the results, the divider correctly works at the main frequency of 1.8 GHz. The operating bandwidth is 480 MHz, from 1620 MHz to 2100 MHz, which corresponds to a relative bandwidth of 25.8 percent. Furthermore, the measured results indicate that |S11|, |S12|, |S13|, |S22|, and |S23|, are -17 dB, -3.5 dB, -3.33 dB, -20 dB, and -17 dB, respectively, all at the operating frequency. Also, a suppression band of more than 5 GHz is obtained from 2850 MHz to 8160 MHz, showing 2 nd to 4 th harmonic suppression, considering 20 dB attenuation level. In order to provide a better clarification of the harmonic suppression ability of the divider, the overall frequency response of the proposed patch power divider is illustrated in Figure 14, showing 2 nd to 11 th harmonic suppression, considering 10 dB attenuation level. The photographs of the fabricated prototype of the proposed divider circuit and the measurement setup are depicted in Fig.  15. The measurement of the circuit S-parameters has been carried out using the Agilent E8362B Network Analyzer. Table II shows a performance comparison between the designed patch WPD and the state-of-the-art circuits from the literature. Although the proposed structure is geometrically simple, its performance is superior over the benchmark,   including power dividers that are much more topologically involved. This is also pertinent to the harmonic suppression capability, which is unmatched by the structured included in the comparison set.

VII. Conclusion
In this paper, a simple patch power divider with ultrawideband harmonics suppression band has been proposed. For the first time, a simple H-shaped patch filter has been incorporated into the divider structure along with additional open-ended stubs, which results in extremely wide range of frequency rejection, up to the eleventh harmonic. A detailed design procedure has been provided to facilitate the parameter adjustment. Full-wave EM simulations and physical measurements of the fabricated divider prototype corroborate the efficacy of the proposed circuit solution. Moreover, the performance of the presented divider has been favorably compared to the related state-of-the-art dividers, showing the advantages of the proposed work, which include considerably better harmonic suppression capability while maintaining topological simplicity of the circuit.