## 3 Performance Analysis  
This work presents a high-power combiner for 3.0T MRI systems, and a comparison of its performance with respect to conventional designs is presented in Table 10. The proposed combiner achieves superior compactness, efficiency, and integration, enabling system-level high-power output. Integrated into RFPA systems, it enhances power-combining efficiency while reducing system volume.  
Table 10 highlights the proposed high-power combiner's advantages in compactness, performance, and system integration. The combiner enables final-stage power combining to meet high-power requirements and, when integrated into RFPA systems, enhances the combining efficiency while reducing equipment size. To quantify these benefits, a figure of merit (FoM) was established as a weighted product of critical metrics:  
\[FoM=\frac{1}{\textit{Insertion Loss}}\textit{ Combining Efficiency Integration Factor}\frac{1}{\textit{Normalized Volume}} \tag{15}\]  
where  
insertion loss (IL): lower is better \(\rightarrow\) inversely proportional term (1/IL);  
combining efficiency (\(\eta\)): direct percentage value (e.g., 91% \(\rightarrow\) 0.91);  
integration factor (IF): IF = 1.2 for fully integrated designs (e.g., our work, [18]);  
IF = 1.0 for non-integrated designs (e.g., [19; 20]);  
Normalized volume (V):  
The volume was calculated as L \(\times\) W \(\times\) H and then normalized to the largest volume in the table (e.g., [19; 20]: 200 \(\times\) 200 \(\times\) 40 = 1.6 \(\times\) 10\({}^{6}\) mm\({}^{3}\)):  
\[V_{norm}=\frac{Volume\ of\ Design}{Max\ Volume} \tag{16}\]  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Combiner Type** & **Insertion Loss (dB)** & **Port VSWR (dB)** & **Dimensions (L \(\times\) W \(\times\) H)** & **Integration with RFPA** & **Integration with RFPA** & **Integration Power (Capability (kW)**)** & **Integration Efficiency** & **RFPA Output Size (mm)** \\ \hline Microstrip Combiner (4 to 1) [18] & \(\geq\)0.6 dB & \(<\)\(-\)25 dB & 350 \(\times\) 200 \(\times\) 10 & Fully Integrated & \(>\)25 dB & High (\(\cdot\)8 kW) & 87\% & 350 \(\times\) 250 \(\times\) 25 \\ Lumped-Element (4 to 1) [19; 20] & \(\geq\)0.6 dB & \(<\)\(-\)25 dB & 200 \(\times\) 200 \(\times\) 40 & Not Integrated & \(>\)25 dB & High (\(\cdot\)8 kW) & 87\% & 350 \(\times\) 250 \(\times\) 45 \\ This Work (4 to 1) [19; 20] & \(\leq\)0.4 dB & \(<\)\(-\)25 dB & 320 \(\times\) 200 \(\times\) 10 & Fully Integrated & \(>\)25 dB & High (\(\cdot\)8 kW) & \(>\)91\% & 320 \(\times\) 200 \(\times\) 25 \\ Result & Superior & Comparable & Superior & Superior & Comparable & Comparable & Superior & Superior & Superior \\ \hline \hline \end{tabular}
\end{table}
Table 10: Performance comparison of this work.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Power Amplifier Model** &
\begin{tabular}{} \end{tabular} & **Dimensions (L \(\times\) W \(\times\) D: mm)** & **Receive Coil** & **Phantom Model** & **SNR** & **Excitation Efficiency** \\ \hline Original RFPA & 480 \(\times\) 480 \(\times\) 700 & 16-channel Head Coil & 001 & 390 & 92\% \\ RFPA with combiner & 450 \(\times\) 480 \(\times\) 600 & 16-channel Head Coil & 001 & 396 & 98\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of excitation efficiency and SNR.  
This FoM emphasizes low insertion loss, high efficiency, full integration, and compactness. Table 11 shows that the proposed design achieved an FoM of 6.83, surpassing the next best design ([19], FoM = 4.0) by 1.5\(\times\) and non-integrated counterparts ([20; 21; 22], FoM = 1.45) by 4\(\times\). These results highlight its superiority in balancing performance, integration, and miniaturization for high-power MRI systems.