## 2 The Principle and Components of CPFTA
### Planar Feed Antenna  
In order to integrate the feed antenna and reflectarray, a planar four element microstrip antenna with U-shaped gap is designed, as shown in Figure 8. The substrate is identical to the reflectarray. The detailed parameters of the feed antenna are as follows: _p3_ = 14 mm, _w3_ = 10.4 mm, _l3_ = 8 mm, _w4_ = 1.9 mm, _l4_ = 6.1 mm, and _w5_ = 3.8 mm.  
Figure 6: The schematic geometry of reflectarray unit cell.  
Figure 7: (**a**) The PCR of reflectarray with incident angle less than 30\({}^{\circ}\). (**b**) The reflection amplitudes and phases in \(u\)-\(v\) coordinate.  
Figure 9a depicts the re ection coef cients (S11) and realized gains of the proposed planar feed antenna. There are two resonant frequencies at 8.7 GHz and 10 GHz. The measured 10-dB S11 bandwidth is from 8.5 GHz to 10.7 GHz. The realized gain is stable in the operation bandwidth. The radiation patterns at the two resonant frequencies are plotted in Figure 9b,c, which are almost coincident within 10-dB beam width. The proximity of the rst branch of the feeding line and the patch sides affects antenna radiation performance. As a result, the radiation patterns of 8.7 GHz and 10 GHz deviate from the broadside 5 on phi = 0 plane. The second branch of the feeding line cause the cross polarized component at phi = 90, as shown in Figure 9b,c. The planar feed antenna has the advantage of broadband, low pro le and easy integration.  
Figure 8: (a) The schematic geometry of planar feed antenna. (b) The fabricated planar feed antenna.  
The reflectarray contains 34 \(\times\) 34 cells with total size of 238 mm \(\times\) 238 mm \(\times\) 2.5 mm (8 \(\lambda\)\(\times\) 8 \(\lambda\)\(\times\) 0.1 \(\lambda\)). 4 \(\times\) 4 cells are replaced by planar feed antenna in the middle of reflectarray, as shown in Figure 10.  
The anisotropic patches on the top layer of the transmitarray are uniformly arranged, as shown is Figure 11a. As mentioned in Section 2, rotating the bottom E-shaped metallic patches of transmitarray can realize 1-bit transmission phase adjustment. \(f_{0}\) is the center working frequency of the feed antenna, and \(c_{0}\) is light speed. (_m_, _n_) is used to represent the position of the transmitarray cell. The compensation phase of the unit (_m_, _n_) can be expressed as:  
\[\phi(m,n)=\frac{2\pi f_{0}}{c_{0}}\cdot(F_{mn}-F) \tag{4}\]  
Figure 11: (**a**) The arrangement of 24 \(\times\) 24 anisotropic patches on the top layer of transmitarray with size of 240 mm \(\times\) 240 mm. (**b**) The arrangement of 24 \(\times\) 24 E-shaped patches on the bottom layer of transmitarray with size of 240 mm \(\times\) 240 mm.  
Figure 10: The schematic of GCPFTA.  
\(F_{mn}\) is the distance from focus to cell (\(m\), \(n\)), and \(F\) is the equivalent focal length. The compensation phase of the cell (\(m\), \(n\)) can be discretized by the formula:  
\[C(m,n)=\left\{\begin{array}{ll}0^{\circ},&-90^{\circ}<mod[\phi(m,n),360^{ \circ}]\leq 90^{\circ}\\ 180^{\circ},&90^{\circ}<mod[\phi(m,n),360^{\circ}]\leq 270^{\circ}\end{array}\right. \tag{5}\]  
Consequently, the obtained arrangement of E-shaped patches on the bottom metallic layer is illustrated in Figure 11b.  
The GCPFTA based on low-cost printed circuit board technique is fabricated and assembled, as shown in Figure 12. The height between transmitarray and reflectarray is controlled by dielectric cylinders. The measurement of GCPFTA is carried out in an an anechoic chamber and the data was processed by averaging multiple measurements.