# Wide Scanning Angle Millimetre Wave 1 \(\times\) 4 Planar Antenna Array on InP at 300 GHz
## 2 Design of the Unit-Cell
#### Array Design  
By using the unit cell, a linear, uniformly spaced \(1\times 4\) array was also designed. The total area of the array is 2 \(\times\) 0.6 mm\({}^{2}\). The top view of the designed array is shown in Figure 4. Such an array can provide a gain of 10.85 dBi with a steering angle scanning range of 100\({}^{\circ}\). The proximity of the radiating elements alters the boundary conditions of the unit-cell. This effect can be observed by plotting the active reflection coefficient for each unit-cell for different steering angles. For a steering angle of 0\({}^{\circ}\), or when no phase shift is applied between elements, it can be observed that all the four radiating elements present an identical reflection coefficient across the whole bandwidth (Figure 5). As the phase shift between the driving signals of each element increases, the impedance matching bandwidth deteriorates. For extreme angles, i.e., \(\pm\)50\({}^{\circ}\), the array provides a bandwidth of merely 4-5 GHz, and the central elements are not matched at frequencies below 300 GHz. In Figure 6a,b, the beam steering pattern and sidelobe levels (SLL) are plotted as a function of frequency and steering angle. The SLLs shown in Figure 6b are asymmetric for varying steering angles. A signal with a wide bandwidth will be subjected to non-uniform gain and grating lobes at different frequencies, which can result in channel degradation and signal transmission loss. The peak realised gain (where realised gain is the gain of an antenna reduced by the losses due to mismatch of the antenna input impedance to a specified impedance [20]) shown in Figure 6c,d is not symmetric for positive and negative steering angles, indicating that the gain performance will not be uniform across the entire scanning range. The gain of the array will be significantly impacted for higher frequencies. Figure 4: Top view of the designed \(1\times 4\) antenna array. Figure 3: (**a**) Gain of unit cell, (**b**) return loss of unit cell. Thus, a signal centred around 300 GHz will experience a non-uniform response, and consequently a drop in performance. The problem of mutual coupling is complex due to the dependence of the array's parameters on the phase of the driving signal. A circuit model of mutual impedance is  
Figure 5: (**a**) Active return loss of Element #1 for varying steering angles, (**b**) active return loss of Element #2 for varying steering angles, (**c**) active return loss of Element #3 for varying steering angles, (**d**) active return loss of Element #4 for varying steering angles of radiating elements. Figure 6: (**a**) Steering pattern for 1 \(\times\) 4 array, (**b**) SLL of the array, (**c**) Peak realised gain vs. frequency for varying steering angles, (**d**) Peak realised gain vs. steering angle for different frequencies. presented in Figure 7. The impedance \(Z_{ij}\) (where \(i\
eq j\)) has two components, i.e., static and dynamic. The static part of \(Z_{ij}\) is caused by a shared ground plane and the propagation of substrate waves. The array structure loosely resembles a slab waveguide with metal plates on the top and bottom. The width and height of such a structure can support mode propagation, which causes a mutual coupling between elements. The dynamic part of \(Z_{ij}\) is caused by near-field interaction between radiating elements. The radiation patches form a capacitor, with the initial condition being determined by the driving signal. For example, if Element #1 is excited, the other elements will accumulate a specific amount of charge due to capacitive coupling. When Element #2 is excited, it already has some charge accumulation which acts as a capacitive load with non-zero initial condition. For time-varying signals, the problem of determining the initial condition of a coupler capacitor is more complex. The effect of mutual coupling can be reduced by increasing the impedance \(Z_{ij}\).