## 2 Design of Dual-Band Matching Networks
### Implementation of Dual-Band Input Matching Network
By applying the proposed dual-band matching network design methodology, the required transformer parameters of the input matching network can be determined. Moreover, the incorporation of the reconfigurable transformer in this work substantially expands the inductance range of the practical transformer, thereby enabling more effective dual-band input matching. We then take the next step to implement the input matching network with optimum values. The layout of the reconfigurable transformer is shown in Figure 12, with a turn ratio of 2:2 for the main transformer and the tuning coil located on the outermost layer. All inductor coils employ the same metal layer to enhance the quality factor of the transformer. To avoid a significant impact on the \(Q\) values of \(L_{p}\) and \(L_{s}\), the maximum value of \(C_{t}\) should not exceed 3 pF. The value of \(C_{t}\) in this design is 2.8 pF. Figure 11: (a) Equivalent inductance and quality factor versus \(C_{t}\). (b) Equivalent quality factor versus \(R_{t}\). Figure 7:0 Simplified schematic of the tunable inductor. When the switching capacitor \(C_{t}\) changes, the values of the reconfigurable transformer are changed and are shown in the table below. It can be seen that the proposed reconfigurable transformer in this paper achieves a change of approximately 100 pH in inductance with an acceptable decrease in \(Q\). This feature is advantageous for achieving dual-band input matching. The final schematic of the dual-band input matching network is shown in Figure 7:1 The transistor sizes of the switch \(C_{inp}\) and \(C_{t}\) are 450 \(\upmu\)m/280 n and 540 \(\upmu\)m/280 n, respectively. The off capacitances of the switches are 307 fF and 513 fF. The parameter of the reconfigurable transformer is shown in Figure 7:2  
In comparison to a fixed transformer, the reconfigurable transformer proposed in this article demonstrates excellent impedance matching, as shown in Figure 7:3 It is evident that under the same matching capacitor conditions, the lowest point of \(S_{11}\) for the fixed transformer deviates significantly from the expected frequency bands. To match within the desired frequency bands, the capacitance value needs to be increased to 3.7 pF under fixed transformers, which is unacceptable for the circuit. On the one hand, this decreases the \(Q\) value of the switch capacitor, leading to a reduction in gain. On the other hand, it increases off-state parasitic capacitance, resulting in poor \(S_{11}\) performance in the 5 G frequency band. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **SW-Off** & & **SW-On** \\ \hline \(L_{p}\) & 1.03 nH & \(L_{p}\) & 1.15 nH \\ \hline \(Q_{p}\) & 8.39 & \(Q_{p}\) & 7.55 \\ \hline \(L_{s}\) & 877.15 pH & \(L_{s}\) & 936.65 pH \\ \hline \(Q_{s}\) & 9.56 & \(Q_{s}\) & 9.21 \\ \hline \(k\) & 0.76 & \(k\) & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of reconfigurable transformer. Figure 12: The layout of the reconfigurable transformer. It can be seen that with the implementation of the proposed reconfigurable transformer, favorable matching results are achieved in dual bands.