## 4 Transformer-Based Ultra-Wideband I/Q Signal Generation  
As demonstrated in the previous section, our proposed quadrature hybrid has the capability to generate a fully differential I/Q signal over a wide bandwidth. However, due to limited perfect phase balance bandwidth, it fails to satisfy a wideband frontend targeted at the \(5\)G frequency band. For example, the magnitude mismatch is still below \(1\) dB from \(37\) GHz to \(43\) GHz, whereas the phase mismatch is larger than \(3^{\circ}\), which means that the  
Figure 5: 3D EM model of the proposed transformer-based quadrature hybrid. Figure 6: (**a**) Simulated S-parameters of the proposed transformer-based quadrature hybrid. (**b**) Magnitude (blue line) and phase (red line) mismatch of the proposed transformer-based quadrature hybrid. front end cannot achieve an IRR \(>\) 30 dB (phase mismatch \(<\)3\({}^{\circ}\) with magnitude mismatch \(<\)0.25 dB) with only one quadrature hybrid. However, the I/Q imbalance could be considerably suppressed by cascading quadrature hybrid unit stages after a quadrature hybrid [18]. The block diagram is depicted in Figure 7. The quadrature hybrid unit stage is composed of two identical quadrature hybrids in a symmetric manner and an eight-to-four signal combination route, so the unit stage has two differential input ports and four differential output ports. The operation principles of transformer-based quadrature hybrid unit stage are demonstrated as follows. The transformer-based quadrature hybrid first converts a fully-differential signal into two fully-differential quadrature signals at the output ports. Two pairs of differential signals are then fed to the first transformer-based quadrature hybrid unit stage. As a result, two differential signals with 90\({}^{\circ}\) phase difference are generated at the output of the first unit stage after signal combination and connected to the second unit stage. The common-mode and differential-mode characteristics of the transformer-based quadrature hybrid unit stage will suppress I/Q imbalance that originates from the previous circuits [18]. Finally, two differential signals with high-quality quadrature performance occur at the output of the nth transformer-based quadrature hybrid unit stage. Figure 8 shows the signal combination mechanism in the transformer-based quadrature hybrid unit stage. Two quadrature differential signals are fed to the unit stage after the quadrature hybrid. A pair of differential signals is connected to quadrature hybrid A (represented by black lines in the upper part of the quadrature hybrid unit stage in Figure 7) in the unit stage, whereas another signal is fed to quadrature hybrid B (represented by gray lines in bottom part of the quadrature hybrid unit stage in Figure 7). Therefore, at the output of the unit stage, there are total eight output signals but with only four different phases, which is also shown in Figure 8. In this way, eight output signals can be combined and converted into two quadrature differential signals. For example, the output 0\({}^{\circ}\) signal is composed of an input 0\({}^{\circ}\) signal passing through the THRU port in quadrature hybrid A and an input \(-\)90\({}^{\circ}\) signal passing through the CPL port in quadrature hybrid B. The signal combination operation of the transformer-based quadrature hybrid unit stage can average out existing phase/magnitude imbalance from previous stages. The 3D EM model of proposed ultra-wideband two-stage cascaded transformer-based quadrature hybrid (composed of a transformer-based quadrature hybrid and one transformer-based quadrature hybrid unit stage) is depicted in Figure 9, together with circuit blocks and port notations. Ground walls from M1 to LD are placed around each block to improve the magnetic coupling isolation. The input port is driven by a 100 \(\Omega\) differential port, and two output ports are each terminated with a 100 \(\Omega\) differential port. Figure 7: Block diagram of cascaded transformer-based quadrature hybrid.