# Continuously Beam-Steered Phased Array Antenna Using GaN Varactors for Millimeter-Wave Applications
## 3 Design of Analog GaN-Based Phase Shifter  
This section discusses the design analysis of a mm-band phase shifter using GaN HEMT devices and based on the reflective structure employing a quadrature 3-dB 90\({}^{\circ}\) hybrid coupler, as illustrated in Figure 4a. The varactor, GaN_Lg110 nm, at the \"thru\" and \"coupled\" ports reflects the signal with a tunable phase shift corresponding to its reactance, which is controlled by the gate bias voltage. Based on this phase shifter structure, one varactor diode placed at the two coupler output ports could be enough to achieve a theoretical phase shift of 180\({}^{\circ}\), as explained in [21; 22]. However, varactor diodes are not perfect. This means that there are losses due to their equivalent series resistance; also, these diodes have a limited tuning capacitance range, thus making it hard to achieve a 180\({}^{\circ}\) complete phase shift. This clearly limits the achievable beam steering range, which can be theoretically increased as much as wanted by multiplying the number of the used GaN varactors by a multiple of 2. However, more varactor diodes added will directly introduce more losses. This means that a tradeoff between beam steering range and losses should be defined, along with the targeted application where the phase shifter will be used. The proposed phase shifter was designed using a low-permittivity substrate, Rogers RT5880 [23], with an \(\rm\varepsilon_{r}\) of 2.2 and a thickness of 127 \(\rm\upmu\)m, and simulated using Advanced Design System (ADS) Momentum [24] proposed by Keysight. Here, the already developed GaN HEMT varactor small-signal model in [15] was used for the GaN_Lg110 nm device as the tuning load. Two identical GaN_Lg110 nm varactors were placed at the transmitted and coupled ports of the hybrid coupler. These two signals reflect from the two tunable loads, the GaN varactors; they add up in the phase at the hybrid's isolated port if both of the loads are identical and will keep matched the phase shifter's input signal. Figure 4: (a) A schematic illustration of the fabricated phase shifter, (b) a photograph of the fabricated phase shifter, (c) a zoomed-in image of one of the GaN_Lg110 devices along with the wire bonding. Figure 4b depicts a photograph of the fabricated phase shifter. Wafer vias are used to connect the GaN varactors to the backside ground circuit metal. The wire bonding technique is used for all GaN varactors' PADs and was carried out at IETR's facilities. The overall size of this phase shifter design is 13 \(\times\) 13 mm\({}^{2}\) and it was simulated and optimized to provide a maximum continuous phase shift at 41 GHz. First, to design this phase shifter topology, a 3-dB 90\({}^{\circ}\) hybrid coupler has been designed and simulated. The Momentum-simulated layout results for the complete hybrid coupler are plotted in Figure 5. The insertion loss at port 3 and port 4 are, respectively, \(-\)0.40 dB and \(-\)0.25 dB at 41 GHz and has a maximum variation of \(-\)0.4 dB over a 2 GHz bandwidth from 40.50 GHz to 42.50 GHz. The amplitude imbalance at the center frequency is almost 0.15 dB. The phase difference between the outputs of ports 3 and 4 is about 87\({}^{\circ}\) at 41 GHz, while the return loss is greater than \(-\)20 dB and the isolation between the ports is greater than \(-\)25 dB. Now, the two output terminals will be loaded with the developed GaN_Lg110 nm varactor small-signal model to achieve the phase shift purpose. Then, two identical GaN varactors, GaN_Lg110 nm, were properly placed at the transmitted and coupled ports as tuning loads to provide the continuous tunability. Therefore, to discuss clearly the EM simulation as well as the measurement results, only two output phase shift difference values will be addressed and analyzed. Here, the two extreme values are chosen to conduct this analysis. Those values are achieved at a \(\mathrm{V_{g}}\) of \(-\)2 V for the minimum value of the phase shift and at 2 V for the maximum value of the phase shift.