*A planar four-way wideband power divider with compact size, good isolation and output port impedance matching uses quarter-wavelength coupled lines, instead of the quarter-wavelength transmission lines used in a conventional Wilkinson power divider, to implement stopband rejection and the four-way power dividing function. Even and odd mode equivalent circuits are presented and design equations are derived. A compact planar four-way power divider is designed, optimized, fabricated and measured. Measured results show good agreement with simulation.*

Power dividers play an important role in power-combining amplifiers and antenna arrays. Current development is focused on wide bandwidth,^{1-4} multi-band response,^{5-7} miniaturization,^{8,9} high isolation^{10,11} and harmonic suppression,^{12,13} as well as small size, low cost and ease of integration.^{14-19} Xu^{16} reported on a four-way power divider interconnecting power dividers with several output ports, but it was large. Xu et al.^{18} used composite right/left-handed transmission lines to construct parallel three-way and four-way power dividers;^{18} however, since no isolation elements were used, isolation and match at the output ports were poor. They mentioned that reasonable isolation, good output match and compact size are difficult to realize in multi-way planar power dividers.

Filters are needed in RF systems to reject unwanted signals. Power dividers and filters are often connected together to achieve low insertion loss, miniaturization and low cost. At present, power dividers with filtering are normally constructed in two types: Type I power dividers with harmonic suppression^{20,21} and Type II power dividers with bandpass filter responses.^{22-29} Power dividers with single and dual bandpass responses have been developed;^{30,31} however, planar multi-way power dividers with bandpass response or stopband rejection, good output isolation and good output impedance matching are very few.

In this article, we describe a compact, planar, four-way power divider with stopband rejection, good isolation and impedance matching at its output ports. The power divider is constructed using coupled lines. Its frequency response is similar to a coupled line filter. Coupled lines are utilized instead of the quarter-wavelength line in a conventional Wilkinson power divider to reduce the size. Measured results show that this planar four-way power divider with stopband rejection has several advantages: excellent input impedance matching, low insertion loss, a good balance of amplitude and phase at the output ports, good filter response and good isolation within the passband.

**DESIGN**

The coupled line four-way power divider (see ** Figure 1**) can be described as equivalent to a combination of a coupled line filter and a Wilkinson power divider. Stopband rejection is realized with the same λ/4 microstrip lines of the Wilkinson power divider. The length (L

_{1}) of the coupled line is about λg/4, where λg is the guided wavelength of the microstrip line at the center frequency. Output ports 2 and 3 are located at the two ends of the upper folded microstrip line, while output ports 4 and 5 are located at the two ends of the lower folded microstrip line.

The operating bandwidth is determined by the coupling gap, S_{1}, between the transmission lines, which can be obtained by simulation. Isolation resistors (R_{1} in Figure 1) are located between ports 2 and 3 and ports 4 and 5. Another isolation resistor, R_{2}, is located between the two central coupled lines. Since the power divider is symmetric, the even/odd mode method can be used for analysis.

**EQUIVALENT CIRCUIT ANALYSIS**

Under odd mode excitation, the symmetrical plane PP’ shown in Figure 1 is an electrical wall (see ** Figure 2**). Part 1 in Figure 2 is a coupled line, which can be viewed as a four-port network. One of the four ports is a short circuit and another connects to the resistance R

_{2}. According to microwave network theory, part 1 can also be viewed as a two-port network. The two ports are designated 1 and 2, respectively. The impedance matrix elements of the two-port network are obtained as follows:

Z_{11}, Z_{12}, Z_{13}, Z_{14}, Z_{21} and Z_{22} are the impedance matrix elements of the four-port network. The transmission matrix [A_{1}] of part 1 is obtained by the relationship between the impedance matrix and the transmission matrix. In addition, the transmission matrix [A_{2}] of part 2 is obtained as follows:

where θ is the electrical length of part 3. The transmission matrix [A_{3}] of part 3 is obtained by combining Equations 1 and 2.

Meanwhile, the admittance matrix [Y_{3}] of part 3 is also obtained by using the relationship between the transmission matrix and the admittance matrix. The admittance matrix [Y_{4}] is as follows:

The admittance matrix [Y_{w1}] or transmission matrix [A_{w1}] of the entire network can be obtained by

When port 1 and port 2 are simultaneously matched, the following condition must be satisfied:

where A_{w1}, B_{w1}, C_{w1} and D_{w1} are the elements of the transmission matrix [A_{w1}].

Under even mode excitation, the symmetrical plane PP’ is a magnetic wall, as shown in ** Figure 3**. The analysis method is similar to the odd mode. According to transmission line theory, the input impedance Z

_{in1}is determined by

Based on microwave network theory, the impedance matrix [Z_{2}] of part 5 is

The transmission matrix [A_{w2}] of the entire network is determined in a manner similar to that for the odd mode analysis. When ports 3 and 4 are simultaneously matched, the condition that must be satisfied is

where A_{w2}, B_{w2}, C_{w2} and D_{w2} are the elements of [A_{w2}]. The isolation resistances R_{1} and R_{2} can be calculated by combining Equations 1 to 9 after the other parameters are confirmed.

**SIMULATION AND MEASUREMENT**

To verify and demonstrate the design method and circuit performance, a four-way planar power divider was built on an RF-35 substrate with relative permittivity of 3.5, thickness of 0.508 mm and loss tangent of 0.0018. The circuit model was constructed in HFSS. After simulation and optimization, the dimensions of the fabricated planar four-way power divider were chosen to be L_{1} = 43.2 mm, L_{2} = 45.65 mm, L_{3} = 2 mm, W_{1} = 0.1 mm, W_{2} = 0.1 mm, W_{3} = 0.1 mm, S_{1} = 0.1 mm, R_{1} = 100 Ω and R_{2} = 100 Ω. A photograph of the fabricated planar four-way power divider is shown in ** Figure 4**. The circuit size is just 0.014 × 0.26 λg.

Measured versus simulated results are shown in ** Figures 5** and

**. The measured input return loss is greater than 15 dB, while the simulated input return loss is greater than 20 dB over the operating frequency range, as shown in**

*6***. The center frequency is about 1.05 GHz, and the 10 dB input return loss bandwidth is about 28 percent. Insertion loss is about 0.4 dB within the passband, and the 1 dB insertion loss bandwidth is about 45 percent. A maximum amplitude imbalance of ±0.15 dB is observed over the operating passband. Lower stopband rejection is greater than 15 dB from 0 to 0.45 GHz, while upper stopband rejection is greater than 15 dB from 1.75 to above 2.75 GHz.**

*Figure 5a*Measured return loss for the four output ports is greater than than 13.5 dB at the center frequency, as shown in ** Figure 5b**. Since ports 2 and 3 are symmetric with ports 4 and 5, the curves of S

_{22}and S

_{33}are similar to the curves of S

_{55}and S

_{44}, respectively. Because port 2 is not symmetric with port 3, the curve of S

_{22}is not similar to the curve of S

_{33}. Likewise, the curve of S

_{44}does not match the curve of S

_{55}.

The measured insertion phase of port 2 is similar with that of ports 3, 4 and 5 (see ** Figure 6a**) with a maximum phase imbalance of ±2 degrees from 0.5 to 1.4 GHz. Amplitude and phase imbalance is likely due to fabrication and assembly tolerances.

**shows the isolation between output ports, which is greater than 15 dB over the passband.**

*Figure 6b***CONCLUSION**

A compact planar four-way wideband power divider with stopband rejection uses coupled line technology not only provides a four-way power dividing function but also a bandpass response. Even and odd mode equivalent circuits are presented and design equations are derived. Measurement is in good agreement with simulation, verifying the theoretical analysis. This structure has excellent input and output impedance matching, low insertion loss, good balance of amplitude and phase at the four output ports, a filter response and good isolation within the passband.n

**ACKNOWLEDGMENT**

The work for this grant was supported by National Natural Science of China (Grant No: 61271026) and by the Program for New Century Excellent Talents in University (Grant No: NCET-11-0066).

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**Kaijun Song*** received his master’s degree in radio physics and his Ph.D. degree in electromagnetic field and microwave technology from the University of Electronic Science and Technology of China (UESTC), Chengdu in 2005 and 2007, respectively. Since 2007, he has been with the EHF Key Laboratory of Science, School of Electronic Engineering, UESTC, where he is currently a full professor. His current research fields include microwave and mmWave/THz power-combining technology; UWB circuits and technologies; microwave/mmWave devices, circuits and systems; and microwave remote sensing technologies.*

**Yu Zhu*** received his bachelor’s degree in electrical information engineering from Southeast University Chengxian College in 2014, and is currently pursuing his master’s in electrical engineering at UESTC. His research interests are in the areas RF/microwave and mmWave devices.*

**Shunyong Hu*** received his bachelor’s degree in applied physics from Shandong University of Science and Technology, Qingdao, Shandong in 2010 and is currently working toward his Ph.D. degree in electromagnetic fields and microwave technology at UESTC. His research interests include microwave and mmWave power-combining technology and microwave passive component design.*

**Fan Zhang*** received his bachelor’s degree from the Hefei University of Technology, Hefei in 2012. He is currently working toward his Ph.D. in the School of Electronic Engineering, UESTC. His research interests are microwave/mmWave passive structures, including filters and power dividers/combiners. He is also involved in the investigation of quasi-optical, beam-shaping techniques, diffractive optics and reflector design.*

**Maoyu Fan*** received her bachelor’s degree in physics from UESTC in 2014 and is currently working toward her master’s degree at UESTC as well. Her current research interests include electromagnetic, metamaterials and microwave/mmWave devices, circuits and systems.*

**Yong Fan*** received his bachelor’s degree from Nanjing University of Science and Technology, Nanjing, Jiangsu in 1985 and his master’s degree from UESTC in 1992. He is a senior member of the Chinese Institute of Electronics. His research interests include mmWave communication, electromagnetic theory, mmWave technology and mmWave systems.*