### I. Introduction

### II. System Description

*θ*

*induces voltages in the receiving elements with a progressive phase shift of*

_{i}*kd*sin

*θ*

*, where*

_{i}*k*is the propagation constant and

*d*is the element spacing. Due to the way receive/transmit pairs are arranged and connected, the signal will be retransmitted in the direction of

*θ*

*. In our design, since transmit and receive frequencies are different, the transmission line lengths in the feed network and transmit and receive array element spacing must be chosen properly to avoid beam pointing errors.*

_{i}*r*

_{0}is the pins’ radial position,

*b*is the radius of the pins,

*J*

*and*

_{n}*Y*

*are the Bessel functions of the first and the second kinds, respectively,*

_{n}*α*is the angle between the x-axis and the pins (the feeding probe is located on the x-axis),

*x*

*= 1(*

_{n}*n*≥ 1) for even mode and

*x*

*= 1/2 for odd mode,*

_{n}*d*

_{1},

*d*

_{2}and

*d*

_{3}are the distances to the pin at

*φ*=+

*α*from the other three pins, given by

*d*

_{1}= 2

*r*

_{0}sin

*α*,

*d*

_{2}= 2

*r*

_{0}, and

*d*

_{3}= 2

*r*

_{0}cos

*α*. The angle

*α*is chosen equal to 45° to maintain symmetry. Given a desired shorting pin radius

*b*and position

*r*

_{0}, Eq. (1) can be solved numerically for the required value of

*ka*to suppress the surface waves for the first order mode TM

_{1}. A graph for

*ka*versus pin position

*r*

_{0}/

*a*can then plotted, the curve is used to determine the pins’ location. Circular polarization for each patch was obtained using a diagonal slot. Aperture coupling using rectangular slots in the ground plane was used to feed the antenna subarray with a feed network placed on another substrate, as shown in Fig. 2. Sequential rotation for the 2 × 2 subarrays was also implemented to improve the axial ratio bandwidth, the fabricated subarray is shown in Fig. 3. The feeding network uses T-junction power dividers with the appropriate characteristic impedances and line lengths to obtain the necessary phase shifts. The substrate used for the feed network is RT/Duroid 6010 with a dielectric constant

*ɛ*

*= 10.2 and thickness of 1.27 mm, and the substrate used for the antenna is RT/Duroid 5870 with a dielectric constant*

_{r}*ɛ*

*= 2.33 and thickness of 1.575 mm. The complete array was simulated and optimized in ANSYS HFSS, simulation and measurement results for the antenna array were presented in [16].*

_{r}*R*

*= 25 Ω, zero-bias junction capacitance*

_{s}*C*

_{j}_{0}= 0.18 pF, breakdown voltage

*V*

*= 3.8 V, and maximum forward voltage*

_{B}*V*

*= 150 mV. The diode input impedance at 5.8 GHz obtained through simulations is*

_{F}*Z*

*= 13 −*

_{d}*j*33 Ω, a matching circuit using single open-circuited shunt stub was used to match

*Z*

*to 50 Ω.*

_{d}