## 2 Novel Phase Shifter Design  
The proposed novel phase shifter based on a standard composite right/left-handed transmission line (CRLH-TL) unit cell [28] is shown in Figure 1. The top layer consists of two symmetrical printed stubs with length \(L_{s}\) and width \(W_{s}\). There are six inter-digital fingers each having length \(L_{f}\) and width \(W_{f}\) with spacing \(s\) among the fingers. The phase constant \(\beta\) of the CRLH-TL unit cell can be expressed as [28]:  
\[\beta=\omega\sqrt{L_{R}C_{R}}-\frac{1}{\omega\sqrt{L_{L}C_{L}}} \tag{1}\]  
where \(L_{R}\) is the right-handed (RH) series inductance, \(C_{R}\) is the RH shunt capacitance, \(L_{L}\) is the left-handed (LH) shunt inductance and \(C_{L}\) is the LH series capacitance. \(L_{R}\) represents the parasitic inductance of the CRLH-TL introduced by current flowing through the transmission line and \(C_{R}\) is the parasitic capacitance between the printed conductors on top of the substrate and the ground plane. \(C_{L}\) is due to the inter-digital capacitors and \(L_{L}\) is introduced due to the short-circuit stubs. The RF signal traveling through the CRLH transmission line unit cell will have a phase shift given by: \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Research Work**} & **Type of Phase** & \multirow{2}{*}{**Advantages**} & \multirow{2}{*}{**Disadvantages**} \\  & **Shifter/RF Switch** & & & & \\ \hline \multirow{4}{*}{[30,31]} & \multirow{4}{*}{PIN diodes tunable CRLH phase shifter} & \multirow{4}{*}{Desired phase shift is achieved} & \multirow{4}{*}{*} & Surface mount components such as resistors, capacitors and inductors are required to operate the PIN diodes \\  & & & & Additional electronic circuitry is \\ \cline{1-1}  & & & required to isolate the RF signal from dc \\ \hline \multirow{4}{*}{[This work]} & Magnetic field & \(\bullet\) & Provides desired & \\  & controlled CRLH & & phase shift & \(\bullet\) & Magnetic field control circuitry is \\ \cline{1-1}  & phase shifter & \(\bullet\) & A 60\% reduced size as compared to [29] & under research \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Research Work**} & **Operational** & \multirow{2}{*}{**Insertion Loss**} & \multirow{2}{*}{**Physical Size**} & \multirow{2}{*}{**Comments**} \\  & **Bandwidth** & & & \\ \hline \multirow{2}{*}{[9]} & \multirow{2}{*}{(4-4.5) GHz} & 8 dB (sim) & \multirow{2}{*}{40 mm \(\times\) 29.25 mm} & \\  & & 9 dB (meas) & & \\ \hline \multirow{2}{*}{[12,14]} & \multirow{2}{*}{(11–14) GHz} & 8 dB (sim) & \multirow{2}{*}{6 mm \(\times\) 4 mm} & A \(\pm\) 25\({}^{\circ}\)-scanning range for a 4 \(\times\) 4 \\  & & 12 dB (meas) & & planar array is demonstrated. \\ \hline \multirow{2}{*}{[13]} & \multirow{2}{*}{(8–10) GHz} & 8 dB (sim) & \multirow{2}{*}{8 mm \(\times\) 6 mm} & \\  & & 9 dB (meas) & & \\ \hline \multirow{2}{*}{[16]} & \multirow{2}{*}{(8–10) GHz} & \multirow{2}{*}{6.6 dB} & \multirow{2}{*}{6 mm \(\times\) 5 mm} & A \(\pm\) 50\({}^{\circ}\)-scanning range for 4 branches \\  & & & series-fed planar array is demonstrated. \\ \hline \multirow{2}{*}{[20]} & \multirow{2}{*}{920 MHz} & 1.67 dB & \multirow{2}{*}{26.4 mm \(\times\) 3.55 mm} & \\  & & 2.45 GHz & & \\ \hline \multirow{2}{*}{[22]} & \multirow{2}{*}{(9–15) GHz} & 2 dB (sim) & \multirow{2}{*}{5 mm \(\times\) 2.1 mm} & \\  & & 2.6 dB (meas) & & \\ \hline \multirow{2}{*}{[29]} & \multirow{2}{*}{(5-6) GHz} & 1.2 dB (sim) & \multirow{2}{*}{22 mm \(\times\) 9 mm} & A \(+\) 30\({}^{\circ}\)-scanning range for \\  & & & a 1 \(\times\) 4 cylindrical array is demonstrated. \\ \hline \multirow{2}{*}{[This work]} & \multirow{2}{*}{(5-6) GHz} & 0.5 dB (sim) & \multirow{2}{*}{8.8 mm \(\times\) 8 mm} & A \(+\) 30\({}^{\circ}\)-scanning range for a 1 \(\times\) 4 linear \\  & & 1.7 dB (meas) & & array is demonstrated. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative comparison of the proposed work with selected existing techniques.