## 2 Materials and Methods
### N-Way Wilkinson Power Dividers Based on Slow-Wave Structures
#### 2.2.3 Alternative Input/Output Port Arrangements for Various Power-Division Processes  
In order to introduce various types of WPDs to be used for different feeding schemes of antenna arrays, new WPD configurations with different power-division ratios and input/output port arrangements were proposed by using meandered transmission lines. For this purpose, 3 different circuit topologies, including 3-way, 3-way double-layer, and 5-way double-layer WPDs were proposed. The main challenge of the proposed circuits is their power-halving property. Hence, the input power is halved at the next output ports and equal power-dividing ratios are achieved at the last two output ports.  
Figure 12 illustrates the circuit for two three-way WPDs located at the same side of the board. As can be seen from Figure 12a, there are two input ports located at the upper left and bottom right. The upper output ports belong to the upper circuit, whereas the bottom output ports are for the bottom circuit. Both these WPDs perform the same operations in different paths, so the proposed arrangement actually behaves like a power-divider bank to be used for a multi-input--multi-output (MIMO) system. They are useful for different antenna arrays serving different operations. Moreover, the input power is halved at output port 2, while the power at output ports 3 and 4 is equal. The simulated frequency responses are demonstrated in Figure 12b. The magnitude and phase differences are also shown in Figure 12c,d, respectively.  
The second WPD configuration was created for double-layer applications, as shown in Figure 13a. Here, a common ground plane was located between two layers, where both layers included two three-way power dividers for utilization in MIMO systems. The power divider in the upper layer is completely similar to the one in the bottom layer, so the proposed approach can be useful for bidirectional MIMO systems. The bottom and upper power dividers exhibit similar circuit performances. The S parameters of one of the two proposed WPDs are given in Figure 13b. Figure 13c,d represent the simulated magnitude and phase differences, respectively.  
The last configuration was a 5-way WPD, as shown in Figure 14a. As can be seen from the figure, two layers were combined so as to have a common ground plane. The input port was located at the upper layer, and there were five output ports for power splitting. Two of the outputs are in the upper layer, whereas the remaining ports are in the bottom layer. The designed 5-way WPD halves the input power at the next port in a similar manner to the previous configuration. Hence, port 2 has 1/2, port 3 has 1/4, port 4 has 1/8, and  
Figure 11: Conventional WPDs with meandered transmission lines: (**a**) 4-way; (**b**) 8-way.  
ports 5 and 6 both have 1/16 of the input power. This phenomenon can be seen from the simulated frequency responses shown in Figure 14b. The \(|S_{21}|\), \(|S_{31}|\), \(|S_{41}|\), \(|S_{51}|\), and \(|S_{61}|\) parameters were approximately 3, 6, 9, 12, and 12 dB at the center frequency, respectively. Figure 14c,d show the magnitude and phase difference of the simulated S parameters.  
Figure 12: (**a**) Two 3-way WPDs with different inputs and outputs: (**b**) simulation results, (**c**) magnitude differences of S-parameters, and (**d**) phase responses.  
Figure 13: (**a**) Two 3-way WPDs with a common ground plane: (**b**) simulation results, (**c**) magnitude differences of S-parameters, and (**d**) phase responses.