# Microwave Photonic Devices Based on Liquid Crystal on Silicon Technology
## 5 Microwave Photonic Couplers with Low Amplitude and Phase Imbalance
shows the amplitude and phase response at the I- and Q-phase output of the 90\({}^{\circ}\) hybrid coupler. It can be seen that the 90\({}^{\circ}\) hybrid coupler can operate over a wide 3 dB operating frequency range from 10.5 to 26.5 GHz. The experimental results demonstrate an amplitude imbalance of \(<\)\(\pm\)0.3 dB and a phase imbalance of \(<\)\(\pm\)0.15\({}^{\circ}\) over the 16 GHz bandwidth. The SNR measured at both the I and Q-phase output are above 121 dB for a 1 Hz noise bandwidth. The idea of using an LCOS based optical processor to implement a 90\({}^{\circ}\) hybrid coupler can be extended to realize a 4-way RF hybrid splitter, which is also known as a quadrifilar. A 4-way hybrid splitter is used to split an RF signal into four with a phase difference of 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\) and 270\({}^{\circ}\). It has applications in the circularly polarized square slot antenna array [57] and the four-arm spiral antenna in a beamforming network [58]. A broadband 4-way hybrid splitter formed by connecting the two outputs of a broadband 90\({}^{\circ}\) hybrid coupler with two broadband 180\({}^{\circ}\) power splitters can have a phase error as large as \(\pm\)20\({}^{\circ}\). This problem can be solved by a photonics-based 4-way RF hybrid splitter implemented using LCOS technology, which has a structure as shown in Figure 2[59]. Only a single-wavelength laser source is used and the optical phase modulator is driven by an RF signal as the 90\({}^{\circ}\) hybrid coupler implemented using LCOS technology. Here four LCOS based optical processor  
Figure 11: The amplitude and phase response profile of the LCOS based optical processor designed for the 90\({}^{\circ}\) hybrid coupler (**a**) I-phase channel and (**b**) Q-phase channel. Figure 12: (**a**) The amplitude and (**b**) phase response of the I-phase channel, and (**c**) amplitude and (**d**) phase response of the Q-phase channel of the 90\({}^{\circ}\) hybrid coupler. output ports are connected to four photodetectors. The LCOS based optical processor amplitude and phase response profile for the 0\({}^{\circ}\) and 90\({}^{\circ}\) channel of the 4-way RF hybrid splitter are the same as that shown in Figure 11. The amplitude and phase response profiles for the 180\({}^{\circ}\) and 270\({}^{\circ}\) channels are designed based on the same manner as the 0\({}^{\circ}\) and 90\({}^{\circ}\) channels. Figure 13 demonstrates the function of the 4-way RF hybrid splitter using LCOS technology. It can be seen from the figure that the 4-way RF hybrid splitter can be operated over a wide 3 dB operating frequency range from 10.5 GHz to 26.5 GHz. The phase errors for all the four channels were measured and was found to be \(<\)\(\pm\)0.35\({}^{\circ}\) over the 10.5-26.5 GHz frequency range. This demonstrates that the 4-way RF hybrid splitter has an excellent phase error performance compared to its electronic counterparts. The 4-way RF hybrid splitter 0\({}^{\circ}\) channel was calibrated as a reference to measure the amplitude imbalance for the other three channels. It was found that there is a \(<\)1 dB amplitude imbalance in all channels over the 10.5-26.5 frequency range. The amplitude imbalance is \(<\)0.5 dB for the RF signal frequencies above 14.5 GHz. The 90\({}^{\circ}\) hybrid coupler and the 4-way RF hybrid splitter with a low amplitude imbalance and phase deviation described above have a fixed and standard characteristic. A microwave hybrid coupler with a tunable coupling ratio and phase difference can be realized by utilizing the programmable amplitude and phase control functions in an LCOS based optical processor. Figure 14 shows the structure of a broadband tunable hybrid coupler. It has two input ports (Port 1 and 3) and two output ports (Port 2 and 4) [60]. This enables two RF signals to be combined into one output port and one RF signal to be split into two output ports.