# Small-Size Square Ring 1-Bit Reconfigurable Transmitarray Unit Cell for C-Band Applications
## 2 Unit-Cell Design  
The unit cell design is represented in Figure 1a. The transmitarray unit cell consists of receiving and transmitting square ring antennas allocated at opposite sides of the stacked seven-layer structure. To provide coupling between two patch antennas a coupling element containing U-shaped resonators connected by a metalized via hole is used. The two ground planes in the middle of the stack eliminate parasitic coupling between the patch antennas. Introducing two ground planes instead of a single one is conditioned by PCB process demands. The metallic patterns are formed on four dielectric layers of 0.508 mm thick Rogers RO4003 material (\(\epsilon_{\rm r}\) = 3.55, tan \(\delta\) = 0.0027). Three layers of 0.204 mm bonding film Rogers RO4450B (\(\epsilon_{\rm r}\) = 3.3, tan \(\delta\) = 0.004) are used to attach the layers of RO4003. The lateral size of the unit cell is 24 mm \(\times\) 24 mm (\(\approx\) 0.46 \(\lambda_{0}\)) and the thickness is \(<\) 0.045 \(\lambda_{0}\) (where \(\lambda_{0}\)-free-space wavelength at 5.9 GHz). Introducing the U-shaped resonators allows providing more flexible coupling control to obtain equal-ripple scattering parameters response of the unit-cell. Hence, the design brings an additional possibility to control the bandwidth (BW) by changing the coupling between two antennas while keeping the via hole size and substrate parameters to be constant. It should be noted that the overall maximum thickness of the structure is limited by PCB process facilities. To study the influence of BW on unit-cell insertion loss, the two cases with different couplings between the antennas were considered while maintaining the substrate thickness between antenna and ground plane equal to 1.2 mm, which corresponds to \(\lambda\)g/20, where \(\lambda_{\rm g}\)-transmission line wavelength at 5.9 GHz, and along with keeping the reflection coefficient module less than \(-\)10 dB. The unit-cell scattering parameters for different overlapping of the coupling element and patch antennas have been simulated using full-wave EM software (Ansys HFSS) with perfect electrical and magnetic boundary conditions. As a result of the EM simulation presented in Figure 1b, decreasing the overlapping area between the coupling element and the antennas leads to the BW broadening up to \(-\)1.4 times from 220 MHz (3.5%) to 300 MHz (5%). The insertion loss is estimated as 0.8 dB and 1.04 dB, respectively. The higher insertion loss for extended BW is due to a higher reflection coefficient, which increases from \(-\)22 dB to \(-\)10 dB. The unit-cell response corresponds to Chebyshev two-pole bandpass filter characteristics. Thus, the insertion loss could be predicted by using the following equation [16]:  
\[IL=4.34\frac{f_{0}}{BW}\frac{1}{Q}\sum_{i=1}^{N}g_{i}, \tag{1}\]  
where \(N\) is the filter order, \(Q\) is the unloaded Q-factor of the resonators, \(BW\) is the 3-dB passband, \(f_{0}\) is the central frequency, and \(g_{i}\) is the normalized filter element value for a given filter prototype. According to Equation (1), the calculated insertion loss corresponds to 0.84 dB and 1.15 dB for the cases of increased and decreased couplings (see Figure 1b), respectively, which is in a good agreement with the EM modelling results. Typically, the insertion loss is decreased with the \(BW\) broadening [17]. Even though the BW was extended, the insertion loss became higher since the transmission and reflection coefficients ripples increased. The increased ripples from 0.027 dB to 0.45 dB were taken into account by g-parameters in Equation (1). The antennas unloaded Q-factor equal to 150 was used. Figure 1: Non-reconfigurable unit cell structure (**a**), and EM simulation results of the unit cells scattering parameters modules for different coupling between patch antennas (**b**). The unloaded Q-factor has been estimated at half-power bandwidth of the reflection coefficient module for a single patch antenna [18].