# Leaky Wave Generation Through a Phased-Patch Array
## 4 Discussion  
In this paper, we have considered the possibility of sampling a continuous distribution of current to achieve a discrete representation of the same field. We chose a leaky-wave antenna to be the first element of the comparison, due to the continuous current that flows on its metallization, and we compared its field with the one produced by a patch-antenna array. The coefficients that excited this array were chosen to be equal in amplitude and phase with the field samples taken from the LWA radiating at a 45-degree angle and at a frequency of 12 GHz, properly chosen to represent the total field. We used four different estimators, one performed in far field and three in near field, to evaluate the agreement of  
Figure 21: Comparison between the amplitude \(|E_{x}|\) of the electric field normalised by its maximum for the LWA in [7] and the phased array designed here along the \(z=k\) planes, where \(z=0\) represents the plane at the antenna aperture: **(a)** LWA field at \(z=1\) mm; **(b)** phased-array antenna field at \(z=1\) mm; **(c)** LWA field \(z=11\) mm; **(d)** phased-array antenna field at \(z=11\) mm; **(e)** LWA field \(z=21\) mm; **(f)** phased-array antenna field at \(z=21\) mm; **(g)** LWA field \(z=50\) mm; **(h)** phased-array antenna field at \(z=50\) mm.  
the two structures, also considering the RMS error as the \"quality factor\" to evaluate the goodness of the process. Depending on the degree of the acceptable agreement, this study has shown that it is possible, within certain limits, to consider an equivalence between the field radiated by a continuous current source and a discrete one.  
After this preliminary analysis, we moved to a more practical scenario, where we tried to verify the suitability of the approach taken, by designing an array that mimicked the behaviour of an LWA design recently proposed for hyperthermia treatment.  
In this paper, we made use of phase shifters, but other alternatives could be explored in future research. An interesting one would be the application of true time delays, which introduce a delay constant in the frequency. In this way, the squint phenomenon in the frequency does not occur.  
Also, it should be noted that since phase shifters have a minimum phase step that can be introduced, there is a quantization error in the phase that can be applied. This is also true for variable attenuators, which cannot introduce any desired attenuation, but this is limited to a fixed step. These technical aspects were not developed in this paper, but a more comprehensive study taking into account these non-idealities will be conducted.  
This study also demonstrated that with the approach taken it is possible to mimic the behaviour of a leaky-wave antenna, using only a patch array for a specific frequency. Additionally, the stop band was reproduced. However, while frequency-scanning behaviour can also be achieved with the patch array, it differs significantly from that of a leaky-wave antenna, both in terms of direction (which shifts toward broadside as frequency increases) and frequency range (which is much larger). Future research will need to explore alternative approaches to replicating this additional feature, if it is needed by the considered application.