## 2 Methods
### Design and Fabrication of the Combiner  
#### 2.3.1 The 4 to 1 Combiner Design  
Based on the above analysis, the four-way to one-way combiner was composed of three two-way to one-way combiners, and the two-way to one-way combiner was designed with two branches and an isolation resistor, as shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameter** & \(\mathbf{Z_{0}}\) **(\(\Omega\))** & \(\mathbf{\beta_{1}}\) **(\({}^{\circ}\))** & \(\mathbf{\beta_{1}}\) **(\({}^{\circ}\))** & **C (pF)** &
\begin{tabular}{c} **S11/S22** \\ **(dB)** \\ \end{tabular} & **S21 (dB)** \\ \hline Data & 43 & 19 & 20 & 64 & \(<\)\(-\)28 & \(<\)0.08 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation results for a single ideal microstrip branch of the combiner. Figure 3: Hybrid capacitive-loaded microstrip combiner. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Parameter** & \(\mathbf{Z_{0}}\) **(\(\Omega\))** & \(\mathbf{\beta_{1}}\) **(\({}^{\circ}\))** & \(\mathbf{\beta_{1}}\) **(\({}^{\circ}\))** & **C (pF)** &
\begin{tabular}{c} **S11/S22** \\ **(dB)** \\ \end{tabular} & **S21 (dB)** \\ \hline Data & 43 & 66 & 69.5 & 2.5 & 6.0 & 67 & \(<\)\(-\)28 & \(<\)0.08 \\ \hline \end{tabular}
\end{table} 
Table 3: Simulation results for a single FR4 microstrip branch of the combiner. In this design, ports P\({}_{2}\) and P\({}_{3}\) are inputs, and P\({}_{1}\) is the combined output. The source and load impedances (Z\({}_{s}\), Z\({}_{l}\)) are 50 \(\Omega\), with a 100 \(\Omega\) power resistor. The remaining microstrip lines have characteristic impedance Z\({}_{0}\) and lengths \(\beta\)1\({}_{1}\), \(\beta\)1\({}_{2}\), and \(\beta\)1\({}_{3}\). Each Z\({}_{0}\) line is paired with capacitor C. The combiner's output power must exceed 69.1 dBm, while the power resistor requires \(\geq\)400 W on average and \(\sim\)8000 W peak dissipation (duty cycle \(\leq\) 5%) for MRI application. Based on ADS simulations, Z\({}_{0}\) was determined as 45 \(\Omega\) with a corresponding line width of \(\sim\)6 mm. A two-way to one-way combiner 3D model (Figure 4) was established in HFSS for optimization, and the model uses the FR4 substrate with an ideal copper conductor at the bottom. The top layer includes golden copper microstrip lines of lengths 11 and 12, a 35 um-thick conductor layer, and incorporates a 100 \(\Omega\) ideal resistor (R) and a capacitor (C) in its structure. The simulation process retains conditions (1), (2), (4), and (5), while condition (3) was adjusted to a 4-10 mm line width range. Ports P\({}_{1}\)-P\({}_{3}\) were assigned, with the combiner parameters and S-parameter results summarized in Tables 4 and 5, respectively. Table 5 confirms compliance with all the performance requirements. Post simulation, three two-to-one combiners were cascaded into a four-way configuration with a total loss of \(\sim\)0.4 dB. The PCB design like as Figure 5, red zone is the 35 um thickness copper of top layer, and bottom layer is 35 um thickness of copper as ground. The PCB demonstrated \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Combiner** \\ **Parameter** \\ \end{tabular} & \begin{tabular}{c} **\(I_{2}\)** \\ **Width/Length** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **\(I_{1}\)** \\ **Width/Length** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **C (pF)** \\ **(pF)** \\ \end{tabular} & \begin{tabular}{c} **Material** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Thickness** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **R (\(\Omega\))** \\ **R (\(\Omega\))** \\ \end{tabular} \\ \hline Data & 6.2/66 & 6.2/69.5 & 67 & FR4 & 2.5 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Design parameters of the two-to-one combiner. Figure 4: Two-to-one combiner HFSS simulation model.