## 2 Analysis and Design of the Active Phase Shifter Circuit
### Vector Modulator Design  
The vector modulator designed in this paper consists of two sets of variable-gain amplifiers (VGAs), each responsible for modulating the four orthogonal signals generated by the preceding quadrature signal generator. The output signals are then combined to produce two differential signals. The phase of the output differential signals depends on the relative amplitudes of the orthogonal signals. The VGA circuits used in this design are Gilbert cells with switch control, as shown in Figure 7a. In the Gilbert cell configuration, transistors M1 and M4 and transistors M2 and M3 form two differential amplifiers. The  
Figure 5: A schematic of the two-stage polyphase filter obtained by cascading RC-CR networks.  
Figure 6: The layout of the proposed highly symmetrical miniaturized two-stage RC-CR polyphase filter.  
control signals \(S_{\text{I}}\) and \(S_{\text{IB}}\) are oppositely phased switches. When switch \(S_{\text{I}}\) is on and switch \(S_{\text{IB}}\) is off, the differential amplifier formed by M1 and M4 operates normally, while the amplifier formed by M2 and M3 is turned off. Conversely, when \(S_{\text{IB}}\) is on and \(S_{\text{I}}\) is off, the differential amplifier formed by M2 and M3 operates, while the amplifier formed by M1 and M4 is turned off. At any given time, only one differential amplifier is active, and the phase difference between the two output signals is \(180^{\circ}\).  
The vector modulator designed in this paper consists of two sets of Gilbert cells with switch control, as shown in Figure 7b. The set of transistors II-I4 forms one VGA, and I5-I8 forms another. As previously analyzed, the switches \(S_{\text{I}}\), \(S_{\text{IN}}\), \(S_{\text{Q}}\), and \(S_{\text{QN}}\) control the activation and deactivation of the four differential amplifiers in the two VGAs, ensuring that only one differential amplifier from each VGA is active at any given time. Additionally, the phase difference between the output signals of a single VGA in its two switching states is \(180^{\circ}\). For example, consider the VGA formed by II-I4. The differential signals \(I^{*}\) and \(I^{-}\) are the input signals from the quadrature signal generator, which serve as inputs to the VGA. By controlling the tail current \(I_{\text{I}}\), the gain of the differential amplifier is adjusted, which in turn changes the amplitude of the output signal. Similarly, the input signals \(Q^{+}\) and \(Q^{-}\) for the second VGA, formed by I5-I8, control the output signal amplitude by adjusting the tail current \(I_{\text{Q}}\). The output signals from the two VGAs are then combined at the output, where a balun is used to sum the I and Q paths. The inductors in the four branches perform impedance matching. The switches \(S_{\text{I}}\), \(S_{\text{IN}}\), \(S_{\text{Q}}\), and \(S_{\text{QN}}\) control the combination of the four quadrature signals, producing four distinct output states, corresponding to the four quadrants of the constellation diagram [22]. The switching signal is controlled by the on-chip Serial Peripheral Interface (SPI), and the relationship between the corresponding quadrant and the switching signal is shown in Table 1.  
The output phase shift of the phase shifter is determined by the ratio of the tail currents \(I_{\text{I}}\) and \(I_{\text{Q}}\) in in the Gilbert cells. To minimize amplitude fluctuations in the phase shift, it is essential to maintain a constant gain in the vector modulator. Thus, the sum of the tail currents for the two sets of Gilbert cells must remain constant. To improve phase shifting accuracy, a six-bit gate voltage control circuit is used to provide the gate voltage for the tail current transistors. The six-bit gate voltage is also produced by the on-chip SPI. It controls the quadrature signal synthesis of adjacent quadrants to obtain different phase offsets,  
Figure 7: Schematic of the core circuit of the vector modulator. (**a**) Gilbert cell; (**b**) vector modulator.