# A 37-40 GHz 6-Bits Switched-Filter Phase Shifter Using 150 nm GaN HEMT
## 2 Design of 6-Bits Switched-Type Phase Shifter  
The switched-type phase shifter (STPS) operates by controlling multiple single-bit phase shifters (SBPS) using a digital control signal to achieve the desired overall phase adjustment. This involves arranging each SBPS in a series configuration. The STPS is built around a foundational 180\({}^{\circ}\) SBPS circuit and requires multiple bits to achieve precise beam steering. However, limitations related to insertion loss and the physical size of each SBPS impact its configuration. Additionally, variations in performance and phase errors result from the phase control and the positioning of individual SBPS units. Consequently, a comprehensive design approach is necessary to consider all possible phase control states. As depicted in Figure 1, the block diagram showcases a 6-bit phase shifter design. By arranging six SBPS units in series, spanning from 180\({}^{\circ}\) to 5.625\({}^{\circ}\), a beam steering range of 360\({}^{\circ}\) is attainable with a resolution of 5.625\({}^{\circ}\). The phase shifter's sequence is structured as 11.25\({}^{\circ}\)/22.5\({}^{\circ}\)/180\({}^{\circ}\)/90\({}^{\circ}\)/5.625\({}^{\circ}\)/45\({}^{\circ}\). This order takes into account phase shifter performance and input/output return loss, and since the characteristics of 90\({}^{\circ}\) and 180\({}^{\circ}\) SBPS are sensitive, they are located in the center. A delay element used within the delay path can adopt an LC filter structure comprising T and Pi types. The choice was made to employ the LCL structure, forming a low-pass T-type filter, given its suitability for the relevant frequency band and implementation considerations. GaN HEMT processes offer the advantage of using inductors with high Q values and more than twice the inductance over the same length compared to CMOS processes. Consequently, opting for an LCL-based T-type filter is advantageous. To capture the influence of parasitic elements, electromagnetic (EM) simulations were conducted for the complete layout. Figure 2 presents a schematic of an SBPS featuring a low-pass T-type filter, along with the corresponding equivalent circuit contingent upon the selected path. Transistor M1 is chosen to have a suitably low on-resistance in the bypass state, while the values of L1 and C1 are established to ensure the desired phase in the delay state, as determined by Equation (1). Transistors M2 and L2 are configured to either open or short node 'a' based on the selected state. \[\text{L1}=\frac{Z_{0}\text{tan}|\frac{\varphi}{2}|}{\omega_{0}},\;\text{C1}= \frac{\text{sin}|\varphi|}{\omega_{0}Z_{0}} \tag{1}\]  
All SBPS units, except for the 180\({}^{\circ}\) configuration, were designed using a single filter. However, a single filter-based phase shifter is limited to achieve phase delay more than 90\({}^{\circ}\)[26]. Therefore, two 90\({}^{\circ}\) phase shifters were arranged in series to achieve the 180\({}^{\circ}\) SBPS configuration. Figure 3 displays a photomicrograph of a phase shifter designed for the n260 (37-40 GHz) frequency band, manufactured utilizing the 150 nm GaAs HEMT process. The size of the phase shifter is 2.82 \(\times\) 1.19 mm\({}^{2}\), encompassing RF and DC pads. For phase shift control, the control voltage was applied through wire bonding to a printed circuit board (PCB). Furthermore, on-wafer measurements were conducted using a Ground-Signal-Ground (GSG) probe tip for RF signal. The control voltage is set to 0 V when the transistor is active and ranges from \(-\)2.5 V to \(-\)5 V when it is inactive. The characteristics of the off-state transistor vary depending on the control voltage. The minimum root mean square (RMS) phase error was attained when the control signal operated at \(-\)3 V. Since there was not a significant impact on the matching characteristics and insertion loss based on the off-state control voltage, we selected \(-\)3 V to minimize the RMS phase error. Figure 1: Block diagram of 6-bit phase shifter.