## 5 Simulation Results  
The proposed ultra-wideband I/Q signal generation network is designed in GlobalFoundries 45 nm CMOS SOI process. Full-wave electromagnetic simulator Ansys and Cadence Virtuoso were used to simulate the circuit. The layout of I/Q signal generation network is shown in Figure 12, with a core chip area of 845 \(\upmu\)m \(\times\) 495 \(\upmu\)m (including input passive balun), demonstrating a compact layout footprint. Figure 11: Simulated S-parameters of a passive balun. Figure 10: 3D EM model of a passive balun. Figure 13 shows the typical S-parameter results of the proposed I/Q signal generation network. The input return loss is lower than \(-10\) dB from 22 GHz to 45 GHz, which validates wideband operation capability of the proposed network. The minimum passive insertion loss of the I/Q generation network is only 5.74 dB at 25 GHz and increases to 7.4 dB at 45 GHz (including 3 dB contribution from 1:2 power splitting and loss from passive balun). Therefore, the passive loss of the core cascaded transformer-based quadrature hybrid is only 1.9 dB at 25 GHz and increases to 2.9 dB at 45 GHz. S-parameter results validate the design methodology of our proposed I/Q generation network for wideband and low-loss characteristics. For an I/Q signal, the phase imbalance is defined as:  
\[\text{Phase Imbalance}=\mid\text{90}^{\circ}-\mid\text{Phase}(\text{ I\_Output}\,,\,\text{Input}\,)-\text{Phase}(\text{ Q\_Output}\,,\,\text{Input}\,)\mid\mid\]  
The magnitude imbalance is defined as:  
\[\text{Magnitude Imbalance}=\mid\text{dB}(\text{ I\_Output}\,,\,\text{Input}\,)- \text{dB}(\text{ Q\_Output}\,,\,\text{Input}\,)\mid\]  
The phase/magnitude imbalance of the proposed I/Q generation network is depicted in Figure 14. The phase imbalance is lower than \(2^{\circ}\) from 16.5 GHz to 54.7 GHz and lower than \(5^{\circ}\) from 12 GHz to 59 GHz. The magnitude imbalance is lower than 0.5 dB at  
Figure 12: Layout of the proposed ultra-wideband quadrature signal generation network. Figure 13: S-parameters of the proposed ultra-wideband I/Q signal generation network. 16-60 GHz and lower than 1 dB from 13 GHz to 60 GHz. The phase/magnitude imbalance performance of our proposed I/Q generation network demonstrates its ability to output ultra-precise, fully-differential quadrature signals over an extremely wide bandwidth. The quality of I/Q signal (including phase and magnitude imbalance) is often evaluated using IRR [12], which can be calculated as:  
\[\text{IRR}=\frac{\left(1+\varepsilon\right)^{2}+2(1+\varepsilon)\cos(\Delta \theta)+1}{\left(1+\varepsilon\right)^{2}-2(1+\varepsilon)\cos(\Delta\theta)+1}\]  
where \(\varepsilon\) is the magnitude imbalance, and \(\Delta\theta\) is the phase imbalance. When \(\varepsilon\) and \(\Delta\theta\) are both small, IRR can be simplified as [22]:  
\[\text{IRR}\approx\frac{4}{\varepsilon^{2}+\Delta\theta^{2}} \tag{20}\]  
The IRR of the proposed I/Q signal generation network is calculated and plotted in Figure 15, together with the IRR of transformer-based quadrature hybrid. Both circuits are loaded with 100 \(\Omega\) resistor at differential I/Q output ports. The transformer-based quadrature hybrid can only achieve >30 dB IRR from 28 GHz to 30 GHz and >20 dB IRR from 22 GHz to 50 GHz, which indicates that the quadrature hybrid cannot generate a precise I/Q signal over a wide bandwidth, whereas our proposed I/Q generation network achieves >30 dB IRR from 16.5 GHz to 56 GHz and >40 dB IRR from 21.5 GHz to 53.5 GHz. Compared with one-stage quadrature hybrid, the proposed I/Q generation network can support an ultra-high IRR over a wide bandwidth without calibration. Table 1 summarizes the performance of our proposed ultra-wideband quadrature signal generation network and presents a comparison with state-of-the-art quadrature generation schemes. Figure 16 presents a comparison in terms of figure.