## 3 Minimum Nonlinearity PL Design Guidelines
### PL Design Trade-Offs
There can also be appreciated that most configurations are matched at a frequency above that of the basic antenna, suggesting that when starting a new design, the base antenna should resonate at a lower frequency than that of the intended central frequency. An important remark  
Figure 11: Parasitic-Layer-based Reconfigurable-antenna. from this figure, is that a reconfigurable bandwidth greater than 10% can be achieved for separations lower than \(\lambda/8\). On the other hand, Figure 12b, illustrates the power margin variation with \(h\). Although high power margins \(\sim\)9 dB can be achieved for some configurations with very narrow separations, average margins in excess of 6 dB are achieved for separations beyond \(\lambda/12\). However, there must be noted that the average \(\Delta_{P}\) increment is not linear, and beyond \(\lambda/8\) growth is slower. Variation of directivity with \(h\) is shown in Figure 12c. Directivity is preferred over gain to isolate the effect of the PL on the shape of the radiated field, without including the effects of port matching. This figure shows that directivity can be improved up to a pair of dBs with respect to that of the basic antenna. Most importantly, for a wide range of height variations \((\lambda/20-\lambda/6)\), on average, the effect of the PL does not lead to a degradation of directivity when compared to that of the base antenna. Finally, the angular variation of the pattern maximum with the PL height over the basic antenna, allows to determine the feasibility of finding patterns with maximum radiation pointing towards specific directions \((\theta_{0},\phi_{0})\). A 2D-histogram of the \((\theta_{0},\phi_{0})\) distribution was created for each value of \(h\) to get an exact description of the angular distribution of  
Figure 12: Parasitic-Layer-based Reconfigurable-antenna tradeoffs. pattern maximum. From this depiction a trend was observed, and is that the maximum deviation tends to cluster at \((\theta_{0},\phi_{0})=(45^{\circ},\{60^{\circ},120^{\circ},240^{\circ},300^{\circ}\})\), and \((30^{\circ},\{0^{\circ},180^{\circ},360^{\circ}\})\). Taking this into consideration, a simpler diagram of the maximum \(\theta\) deviation, for all the possible \(\phi\) values, is created as illustrated in Figure 12d, where configurations with \(D<6\) dB have been filtered out. From this figure, it is apparent that the maximum deviation changes little with height, and that up to \(\lambda/5\) deviations around \(50^{\circ}\) are achievable. However, the angular distribution shows that there are more configurations with larger steering for PL separations in the range \(\lambda/20-\lambda/10\). Finally, aiming to capture the overall reconfigurability potential of the PL-based-RA, and as a general purpose design guideline, the average metrics encountered are expressed by means of a tradeoffs surface as illustrated in Figure 13, showing how much bandwidth reconfigurability, power margin and steering can be expected for a particular setup. The set of plots of Figures 12 and 13 have presented a general description of the effects of the PL on the fundamental parameters of a basic antenna, and important guidelines for the design as the optimum height region for placing the PL to achieve a desired compromise of objectives.