Journal of information and
communication convergence engineering
(J. Inf. Commun. Converg. Eng.)

The conventional Wilkinson power divider (WPD) operates as a lossy three-port network capable of absorbing and balancing all ports while maintaining isolation between the output ports. It is a widely used passive radio-frequency (RF) component that divides a single input signal into two equal output signals, achieving power division between the output ports. The WPD consists of four quarter-wavelength transmission-line sections and two parallel resistors. The quarter-wavelength sections ensure equal power division between the output ports, whereas the resistors provide isolation. The conventional WPD typically performs impedance matching of Z₁, which is achieved using an electrical length of λ/4, and incorporates an isolation resistor R₁ between port2 and port3 [1,2].

Based on the requirements of a WPD for three-way output ports (WPD3OP), the algorithm for the impedance formula is chosen after choosing the impedance Z₁. The impedance of the unequal or asymmetric WPD is determined based on a power ratio of 2:1, considering the characteristic impedance Z₀ at the final output terminations of all ports [3,4]. Recently, the integration of defected ground structure (DGS), which is selected based on the desired performance objectives, has gained attention as a technique to improve the performance of the RF and microwave components [5,6]. DGS is used in RF and microwave circuit designs to manipulate the propagation characteristics of electromagnetic waves. It involves introducing specific patterns or structures into the ground plane of a circuit to achieve desired effects such as frequency filtering, improved signal integrity, reduced crosstalk, and enhanced isolation. The DGS can be regarded as an equivalent-circuit representation of a physical structure, providing a simplified model for analysis and design [7-9].

This study presents the design of a WPD3OP, incorporating a DGS, as indicated in Fig. 1. The objective is to improve the performance in terms of the power-division ratio, return losses, and isolation between output ports. The design process involves determining the operating frequency, designing the WPD, selecting a specific DGS design, and optimizing its dimensions and placement using electromagnetic simulations [10,11].

Figure 1. Proposed design of the Wilkinson power divider for three-way output ports, integrated with a DGS. The substrate ε_r = 0.762 mm and thickness = 0.035 mm.

The proposed design offers potential benefits in terms of function, wherein precise power division and high isolation between output ports are required. By exploiting the advantages of both the WPD3OP and the DGS, this design aims to provide an improved solution for RF and microwave systems. The electromagnetic (EM) simulation software ANSYS HFSS is used to optimize the DGS dimensions and placement, ensuring the desired performance improvements. The subsequent sections of this paper discuss the design methodology, including the design equations, simulation techniques, fabrication considerations, and testing procedures. The designed WPD3OP integrated with a DGS is fabricated using standard printed circuit board (PCB) techniques. Subsequently, the performance of the power divider is tested. The testing process involves measuring the power-division ratio, isolation between output ports, and other relevant parameters. The results are presented and discussed to evaluate the performance of the designed WPD3OP, with a DGS.

The WPD3OP employs an electrical length of λ/4 and ensures that the characteristic impedance of output ports 2, 3, and 4 matches Z₀, as depicted in Fig. 2. The ideal design of the Wilkinson power divider for three-way output ports integrated with a DGS was a perfect model for fabrication and measurement to achieve preferable results. Moreover, a DGS structure is incorporated into the WPD3OP to achieve better power transmission and insertion losses and wider isolation bandwidth.

Figure 2. Schematic of the designed Wilkinson power divider for three-way output ports.

A. Analysis of Input Impedance Part I

The designed WPD3OP can be divided into two parts for analysis. Part I encompasses the even and odd modes of output ports 2 and 3, as illustrated in Fig. 3(a) and (b), respectively. Part II consists of the even and odd modes of output ports 3 and 4, as depicted in Fig. 3(c) and (d), respectively. Part I, uses a transmission line of electrical length λ/4 with input impedance Z_in2 and Z_in3. Additionally, the asymmetric power-divider ratio is $K^2=\frac{P_2}{P_3}=2$, as indicated in Eq. (1).

Figure 3. Schematic bisections of the Wilkinson power divider for three-way output ports: a) even-mode analysis of Part I, b) odd-mode analysis of Part I, c) evenmode analysis of Part II, d) odd-mode analysis of Part II.

Using the equation $Z_{in2}=Z_0\sqrt{2}\left(1+\frac{1}{K^2}\right)$, we obtain

Then, we define as the input impedance of port 3.

Using $Z_{in3}=Z_0\sqrt{2}\left(1+K^2\right)$, we obtain

B. Analysis of Input Impedance Part II

In this case, to analyze the input impedance of Part II in

Fig. 3(c) and (d), we must consider the excitation of both the even and odd modes. The input impedances of ports 3 and 4,

denoted Z_in4 and Z_in5, can be obtained as

Using the equation $Z_{in4}=Z_0\sqrt{2}\left(1+K^2\right)$, we obtain

Then, we define Z_in5 as the input impedance of port 5.

Using $Z_{in5}=Z_0\sqrt{2}\left(1+\frac{1}{K^2}\right)$, we obtain

We can obtain the value of the resistor isolation from the characteristics of all output ports as

C. Analysis of Defected Ground Structure (DGS)

The equivalent-circuit model of a DGS typically consists of lumped elements that approximate the behavior of the physical structure. The specific parameters and their values depend on the characteristics and objectives of the DGS design. The parameters of these equivalent-circuit elements such as a resistor, inductor, and capacitor (RLC) are interdependent, according to the physical layout and properties of the DGS structure, as illustrated in Fig. 4. The equivalent RLC value can be determined using the dimensional geometry of the DGS. The values of the elements are determined based on empirical measurements, electromagnetic (EM) simulations, or analytical approximations. The equivalentcircuit model of DGS provides a convenient framework for circuit analysis and simulation. It enables designers to predict and optimize the performance of DGS-integrated circuits, thereby aiding a design that reduces the need for extensive EM-simulations or prototyping.

Figure 4. Excitation of the equivalent circuit of the DGS section.

The DGS properties include the resistance, inductance, and capacitance. It can model the electric-field coupling as well as inductive and resistive losses. Some common equivalent-circuit elements that constitute the DGS, presented in Fig. 4 [12,13].

Here, ${\omega }_0=2\pi f_0$ is center resonance frequency and ${\omega }_C=2\pi f_0$ is the cutoff resonance frequency.

A. Design Process

To verify the structure of the WPD3OP with integrated DGS and the design parameters in the experiment, the characteristic impedances of the output ports must match Z₀. The calculated impedance values of the transmission line are Z₀ = 50 Ω and Z₁ = 70.71 Ω with R₁ = 100 Ω for the conventional WPD. The asymmetrical impedances of the transmission lines, from (2) and (8) are Z₂ = Z₅ = 61.24 Ω and Z₃ = Z₄ = 122. 47 Ω, from equations (4) and (6). During isolation, the resistor values are determined as R₂ = R₃ = 150 Ω as indicated in equation (9). All transmission lines have an electrical length of λ/4 and a frequency response 2 GHz with the employed design, as presented in Tables 1 and 2.

Table 1 . Characteristics of material employed in the design.

Substrate	Thickness	εr	Dielectric loss
Taconic	0.762 mm	2.97	0.0012

Table 2 . Calculation of the parameters of the Wilkinson power divider for three-way output ports without defected ground structure.

Impedance Z (Ω)	Electrical Length (θ)	Physical Length (mm)	Physical Width (mm)
Z0 = 50	45°	L50 = 12.13	W50 = 1.88
Z1 = 70.71	90°	L1 = 24.83	W1 = 1.03
Z2 = 61.24	90°	L2 = 24.58	W2 = 1.34
Z3 = 122.47	90°	L3 = 25.82	W3 = 0.26
Z4 = 122.47	90°	L4 = 25.82	W4 = 0.26
Z5 = 61.24	90°	L5 = 24.58	W5 = 1.34

The dimensions of the DGS are as follows: a = 2. 6 mm, b = 5 mm, gl = 1 mm, and g = 0.5 mm, as indicated in Fig. 5(a) and (b). The simulation results of the DGS design for the insertion loss S₂₁ and return loss S₁₁, are illustrated in Fig. 5(c). These dimensions correspond to the square lattice dimensions of the DGS, presenting the properties of an RLC circuit. The equivalent circuit parameters of the DGS are as follows: R_DGS = 8740.971692 Ω, L = 0.167853 nH, and C = 1.381903 pF, derived from equations (10), (11), and (12), respectively.

Figure 5. Design of the defected ground structure (DGS) section with impedances of Z₃ and Z₄: a) top view, b) bottom view, and c) the comparison results of simulated DGS dimensions and equivalent-circuit RLC.

Fig. 5(c) presents a comparison between the square lattice dimensions of the DGS and simulation results of the equivalent-circuit RLC model, which are almost similar in shape. These dimensions effectively enhance the bandwidth of the WPD3OP.

In the design process, step-by-step algorithms for the proposed WPD design and integration with DGS for a threeway output port are illustrated through the flowchart in Fig. 6. This approach allows the assessment and approximation of the effects of variable changes in different parameters, thereby facilitating the tuning of the circuit to achieve the desired outcome. Although the circuit design steps may appear intricate and rigorous, they offer a straightforward and understandable method for attaining satisfactory results.

Figure 6. Flow of the proposed design.

B. Simulation and Optimization

In the EM-simulation results, the WPD3OP shows return losses of S₁₁, S₂₂, S₃₃, and S₄₄ with insertion losses of S₂₁, S₃₁, and S₄₁, and isolations of S₂₃, S₄₃, and S₂₄. The f requency-response performance at 2 GHz, along with the results for different S-parameters, is illustrated in Fig. 7(a). Based on the simulation findings, the insertion losses across the different output ports are approximately S₂₁ = −4.93 dB, S₃₁ = −4.50 dB, and S₄₁ = −5.22 dB, as indicated in Fig. 7(a). During the return loss at all ports S₁₁ and S₃₃ are below −30 dB and S₂₂ and S₄₄ below −20 dB, which is a good result. Furthermore, the improved attenuation of isolation between output port 2 to output port 4 and output port 3 to output port 2 matches that of output port 3 and output port 4, as determined by the values of S₂₃ and ,S₄₃ which are below −30 dB, and S₂₄, which is below −25 dB, as shown in Fig. 7(a). Overall, the EM simulation results of the WPD3OP respond well at a center frequency of 2 GHz. In the proposed method, a WPD3OP is inserted the defected ground structure (DGS). These physical DGS with the improved wide bandwidth of the simulation results as isolation transmit power better to each output port of insertion loss, as shown in Fig. 7(b). The EM simulation results of the WPD3OP integrated with DGS showed a low insertion loss and better bandwidth of isolation between output ports.

Figure 7. EM simulation results: a) Wilkinson power divider (WPD) for three-way output ports, b) the proposed WPD for three-way output ports integrated with defected ground structure.

First, we present the measurement results of the WPD with an integrated DGS and three-way output ports, as shown in Fig. 8(a) and (b). The material chosen for the experiments is presented in Table 1. The characteristic impedance Z₁ = 70.71 Ω, Z₂ = Z₅ = 61. 24 Ω, Z₃ = Z₄ = 122.47 Ω and the electrical length of each transmission line is seated at λ/4, with an operating frequency specified at 2 GHz. The values of the characteristic impedance, electrical wavelength, and operating frequency are crucial for determining the length and width required for the construction and specification of the physical properties for the fabrication of the WPD3OP, as illustrated in Fig. 8(a) and detailed in Table 2. In addition, a DGS with dimensions a = 2.6 mm, b = 5 mm, gl = 1 mm, and g = 0.5 mm, as presented in Fig. 5(b), can be constructed for the fabrication of the WPD3OP integrated with DGS, as illustrated in Fig. 8(a) and (b). The fabrication dimensions are 53 mm × 32 mm. The experiment results regarding frequency responses and impedance are obtained from the values of the S-parameters, as depicted in Fig. 8(c) and (d). The frequency responses are in good agreement with the theoretical values.

Figure 8. Experiment results of the Wilkinson power divider for three-way output ports (WPD3OP) without defected ground structure (DGS) and with DGS: a) Fabrication of the top, b) fabrication of the bottom, c) result of the WPD3OP, d) proposed result of WPD3OP integrated with DGS.

In this experiment, a comparison was made between the WPD3OP integrated with a DGS and one without a DGS. The results of a WPD3OP, presented in Fig 8(c), shows that the power output insertion losses for all ports, S₂₁ = −4.68 dB, S₃₁ = −4.53 dB, and S₄₁ = −5.21 dB. The return loss values are S₁₁ = −29.98 dB, dB, and S₃₃ = −32.33 dB. Moreover, the isolation values are S₂₃ = −33.41 dB, S₄₃ = −33.51 dB, and S₂₄ = −28.95 dB. In terms of the performance of the proposed WPD3OP integrated with DGS, the insertion losses at all output ports are better than that of the WPD3OP: S₂₁ = −4.95 dB, S₃₁ = −4.89 dB, and S₄₁ = −4.98 dB. The return losses are S₁₁ = −28.47 dB, dB, and S₃₃ = −29.80 dB. The isolation between the output ports, S₂₃ = −45.97 dB, S₄₃ = −39.60 dB, and S₂₄ = −28.68 dB, as illustrated in Fig. 8(d). There is a good agreement between the measurement results of the WPD3OP integrated DGS and the result from the EM simulation, demonstrating a significant improvement in the power output to each port. Moreover, the insertion losses of the output ports, S₁₁ = 1. 21 GHz, = 2.06 GHz, and S₃₃ = 0. 83 GHz; and the isolation for ports, S₂₃ = 1. 29 GHz, S₄₃ = 1. 32 GHz, and S₂₄ = 1.2 GHz; provide improved bandwidth, as presented in Table 3.

Table 3 . Comparison of designs of Wilkinson power divider for three-way output ports without defected ground structure (DGS) and with DGS.

Wilkinson power divider for three-way output ports					Wilkinson power divider for three-way output ports integrated with DGS
Return loss [dB]	S11	S22, S44	S33	Magnitude [dB]	Return loss [dB]	S11	S22, S44	S33	Magnitude [dB]
	-29.98	-23.32	-32.33			-28.47	-24.09	-29.80
Insertion loss [dB]	S21	S31	S43		Insertion loss [dB]	S21	S31	S43
	-4.68	-4.53	-5.21			-4.95	-4.89	-4.98
Isolation [dB]	S23	S43	S24		Isolation [dB]	S23	S43	S24
	-33.41	-33.51	-28.95			-45.97	-39.60	-28.68
Return loss [-20dB]	S11	S22, S44	S33	Bandwidth [GHz]	Return loss [-20dB]	S11	S22, S44	S33	Bandwidth [GHz]
	0.97	1.97	0.81			1.21	2.06	0.83
Isolation [-20dB]	S23	S43	S24		Isolation [-20dB]	S23	S43	S24
	1.10	1.13	1.18			1.29	1.32	1.2

The three-way WPD divides an input signal into two asymmetric output signals at a specified power ratio, thereby providing three output ports. Its performance includes various parameters such as insertion loss, return loss, isolation, and output power characteristics. When considering the frequency response, the WPD3OP exhibits improved return losses S₁₁, S₂₂, S₃₃, and S₄₄, and better isolation of S₂₃, S₄₃, and S₂₄ compared to the other configurations. However, it is noteworthy that the insertion losses S₂₁ = S₃₁ = S₄₁ and output power characteristics remain consistent across the different power divider models.

In this work, an integrated DGS was incorporated into the WPD3OP, and the outcome was impressive. The bandwidth was greater than that in the previous design, particularly in isolation for S₂₃, S₄₃, and S₂₄. Meanwhile, the results of the insertion loss, S₂₁ = S₃₁ = S₄₁ showed better power output at each port. These characteristics indicated that a welldesigned power-divider circuit could be highly effective in practical applications. With improved return loss, superior isolation, consistent insertion loss, and reliable output power characteristics, this three-way WPD demonstrated its suitability for various scenarios in which precise and efficient signal splitting is crucial. In addition, the circuit simulation verified using the measurement results indicated that the proposed design of the WPD3OP integrated with a DGS considered the improved magnitude and wide bandwidth of isolation between output ports S₂₃, S₄₃, and S₂₄, which crucially reduced the interference. Enhanced isolation prevented unwanted interference between the output ports, ensuring that signals at one port did not adversely affect or distort the signals at other ports. This was particularly important in RF and microwave systems, which multiple signals coexisted. This ensured that each output port receives an equal or predetermined power level from the original signal.

This work was supported by the Technology Innovation Program (20016657, 5G RF Component For Global Communication Service Provider) funded by the Ministry of Trade, Industry & Energy (MOTIE, Republic of Korea), the Ministry of Science and ICT (MSIT), Republic of Korea, under the ICT Challenge and Advanced Network of HRD (ICAN) program (IITP-2024-2020-0-01832) supervised by the Institute of Information & Communications Technology Planning & Evaluation (IITP) the and Soonchunhyang University Research Fund.