# Compact Design of Annular-Microstrip-Fed mmW Antenna Arrays
## 2 Theory and Analysis of Annular Microstrip Feeding Design
### Outer-Annular Microstrip-Fed Antenna Array
In the simulation, the dielectric substrate is set as infinite plane. Besides, the four identical shaped patch array branches are all designed for implementing the input impedance of 200 \(\Omega\) in order  
Figure 1: Outer-annular microstrip-fed antenna array, (**a**) top view, (**b**) side view. to match the requirement of input impedance value 50 \(\Omega\) at the coaxial probe feed port from the observed antenna terminal. The final width of each microstrip line depends on formulas (1) and (2) and the final length of each microstrip line depends on the simulation results. Each patch is designed as working in the central frequency of 60 GHz according to formulas (3)-(5), with the length of 1.05 mm and the width of 0.78 mm. After analyzing and calculating, we set the inner diameter of the outer annular microstrip line as \(R\) = 16.50 mm and the width of the outer annular microstrip line as \(d_{1}\) = 0.110 mm. Other detailed parameters of this structure have been demonstrated in Table 1. The meanings of these parameters are shown in Figure 1a. The gain and the reflection coefficient of the outer-annular microstrip-fed antenna array have been shown in Figure 2.  
The maximum gain of the outer-annular microstrip-fed antenna array is 8.4 dBi at 60.0 GHz and the minimum reflection coefficient of it is \(-\)20.2 dB at 60.1 GHz with the impedance bandwidth of 0.3 GHz. Moduli and the detailed vector plots of the instantaneous surface current distribution of the outer-annular microstrip-fed antenna array are shown in Figure 3.  
After analyzing the surface current distribution in Figure 3, we find that the edge feeding mode will generally cause the currents on the side feeding units too little. This is the reason why the radiation range of antenna is relatively narrow and non-uniform. What is more, looking at the detailed vector plot of the surface current on patches, it is shown that patches on the parallel main feeding units are the same in phase while patches on the side feeding units are in opposition of phase. The opposition of phase of the opposite branches will influence the gain and the aperture efficiency of the antenna array to some extent. We also show the \(x\)-\(z\) plane, \(y\)-\(z\) plane, and \(x\)-\(y\) plane of the radiation pattern of the outer-annular microstrip-fed antenna array in Figure 4. The pure line represents the co-polarization, whereas the dashed line represents the cross-polarization pattern. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** \\ \hline \(W_{x}\) & 1.050 & \(L_{1}\) & 0.830 \\ \(L_{x}\) & 0.780 & \(d_{1}\) & 0.110 \\ \(d_{0}\) & 0.130 & \(R\) & 16.500 \\ \(L\) & 2.830 & \(d\) & 0.800 \\ \(q\) & 0.006 & \(H\) & 0.12 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of outer-annular microstrip-fed antenna array. Figure 2: Simulation results of outer-annular microstrip-fed antenna array, (**a**) gain of this antenna array, (**b**) reflection coefficient of this antenna array.