# Characterization of Tiled Architecture for C-Band 1-Bit Beam-Steering Transmitarray
## 3 Unit Cell Design and Characterization
Thus, the effect of the discontinuity, i.e., the width of the gap between the adjacent unit cells, on the tile radiation performance is inherent to the design of the tiled transmitarray and we aimed to minimize its impact within the operating band. The effect can be elucidated with the aid of the compact circuit model of the tiled unit cell shown in Figure 2a. It is noteworthy that the circuit model is loosely related to the actual geometry of the unit cell and it is derived essentially by emulating the bandpass response of the unit cell in the two phase-states. Nevertheless, the compact model provides useful insights on the interactions of different parts of the unit cell structure. The circuit model topology constitutes a canonical parallel-parallel connection of the cascaded two-ports, Figure 2a. Being reduced to equivalent elements, the circuit comprises two parallel RLC-circuits (\(R_{p}\), \(L_{p}\), and \(C_{p}\)) associated with the receiving and emitting square-ring patches loaded by the respective U-shaped resonators and coupled via the two ideal admittance inverters, \(J_{0}\) and \(J_{g}\), with characteristic admittances \(Y_{0}\) and  
Figure 2: Equivalent-circuit modelling of the unit cells of the single-panel (\(g=0\) mm) and tiled (\(g=1\) or \(2\) mm) transmitarrays: (**a**) network topology (left) and compact electrical circuit model (right); (**b**) comparison of the circuit model with full-wave electromagnetic simulations (CST Microwave Studio) for the phase state I; (**c**) same as (**b**) but for the phase state II; (**d**) effect of the edge gap width, \(g\), on the differential phase shift. \(Y_{g}\), respectively. The circuit model differs for the two phase states, due to the opposite direction of the current flowing on the receiving patch and this difference is implemented by changing the sign of the inverter admittance \(Y_{0}\), with its positive value corresponding to the phase state I and negative to the phase state II. The \(J_{0}\)-inverter represents the primary coupling of the patches by the via connection, see Figure 1a. The effects of the edge gap are modelled by the additional inverter with a characteristic admittance \(Y_{g}\), which can accurately model the out-of-band transmission zeros, see Figure 2c. Putting \(R_{p}\) to zero, it can be shown that the transmission zeros appear at frequencies where the following condition fulfils:  
\[Y_{0}=-Y_{g}/\left(1-Y_{g}^{2}Z_{p}^{2}\right), \tag{6}\]  
where \(Z_{p}\) is the complex impedance of the parallel LC circuit. The resonance nulls in (6) can appear only when \(Y_{0}\) and \(Y_{g}\) are in phase, due to the negative sign of the denominator in the vicinity of the resonant frequency of the LC circuit. This condition determines the out-of-band 180\({}^{\circ}\) steps of the differential phase shifts, demonstrated in Figure 2d when the differential circuit mode with the opposite direction of the currents on the receiving and emitting patches is superseded by the common mode that is driven by the floating ground plane. The model parameters are shown in Table 1. The parameters were extracted by best-fitting to the full-wave electromagnetic simulations, as follows. Firstly, the initial 'patch' circuit parameters \(R_{p}\), \(L_{p}\), and \(C_{p}\) were fitted using the full-wave simulation of the reflection (S11) for the rectangular patch over an infinite ground plane and simplified circuit model without the inverters. In the second step, characteristic admittance of the \(Y_{0}\)-inverter is extracted by fitting to the full-wave simulations of transmission (S21) of the single-panel transmitarray unit cell (i.e., \(g\) = 0 mm). Finally, characteristic admittance of the \(J_{g}\)-inverter is obtained by fitting the model to the full-wave simulations of S21 of the two square-ring patches coupled only through the slotted ground plane, i.e., in the absence of the \(J_{0}\)-inverter. It appeared that the absolute value of the characteristic admittance \(Y_{g}\) decreases for the wider gap.