# GUI for Analysis of Parameters, Accurate Design and Optimization of Microstrip Filters
## 6 Results and Discussion
### Filter Analysis with MicroStripOptim
For each filter, the values  
Figure 8: Data displayed by the program for a requested filter design. Figure 7: Plots generated using the “Scattering” button in the GUI to visualize the response of a filter design. (**a**) Scattering parameters \(\mid S_{11}\mid\) in red and \(\mid S_{21}\mid\) in black. (**b**) Derivative of attenuation, \(L_{A}^{\prime}\). \(W_{Lmax}\) and \(W_{Cmin}\) are computed using the previous analysis, while \(W_{Lmin}\) and \(W_{Cmax}\) are taken by default as 4 mm and 50 mm, respectively, and are obtained from the edit-boxes in the lower-left side of the GUI. The values for \(W_{Lmin}\) and \(W_{Cmax}\) were selected considering 4 mm as a feasible thin line for \(W_{L}\) and considering 50 mm as the widest desirable \(W_{C}\). However, the values for \(W_{Lmin}\) and \(W_{Cmax}\) can be modified by the user. Figure 10a shows the values of \(TL_{min}\) and \(TL_{max}\) for the feasible filters, i.e., the Butterworth MAXIMALLY FLAT and the three Chebyshev considered. This plot shows that the Butterworth MAXIMALLY FLAT filter yields a lower \(TL\), while the Chebyshev--\(L_{Ar}\) = 0.1 dB filter yields greater values of \(TL\). Another important analysis considering the maximal and minimal values for \(W_{C}\) and \(W_{L}\) is the variation in \(\max(L_{A})\). In this case, the maximum value of \(\max(L_{A})\) is obtained with \(W_{Lmin}\) and \(W_{Cmax}\), and the minimum value of \(\max(L_{A})\) is obtained with \(W_{Lmax}\) and \(W_{Cmax}\). Figure 10b shows a plot of the maximum attenuation for different filter types versus the order, \(n\). From this figure, it can noticed that the maximum attenuation increases with the order of the filter. By comparing the filters, it can be seen that the Butterworth--MAXIMALLY FLAT filter gives the highest attenuation in the third-order response but gives the least attenuation for higher orders. The filter that reaches the highest attenuation for \(n>3\) is Chebyshev--\(L_{Ar}=0.01\) dB. Figure 10: (**a**) Total length versus \(n\) for different types of filters. (**b**) \(\max(L_{A})\) versus \(n\) for different types of filters. These figures indicate the range of values that can be obtained with each type of filter and order, for total length and Maximum Attenuation. Figure 9: Boundary values of width for \(W_{C}\) and \(W_{L}\) versus filter order, \(n\), for different types of filters. When designing a filter of a specific type and order \(n\), only \(W_{C}>W_{Cmin}\) and \(W_{L}<W_{Lmax}\) values within these limits should be considered to ensure the filter is realizable. The fourth button of the GUI, \"limits vs \(Z_{0}\)\", performs an analysis of the limits for \(W_{\rm C}\) and \(W_{L}\), for one filter with the characteristics expressed in the GUI edit-boxes, varying two parameters: the source impedance, \(Z_{0}\), from 25 \(\Omega\) to 50 \(\Omega\), and the dielectric constant, \(\varepsilon_{r}\) from 4 to 12. The plots in Figure 11 show that the limit values for \(W_{\rm C}\) and \(W_{L}\) decrease when \(Z_{0}\) and/or \(\varepsilon_{r}\) increases. It can be seen, from the figure, that at \(Z_{0}=50\)\(\Omega\), a high value of \(\varepsilon_{r}\) could lead to a filter unfeasible since this reduces considerably the limit for \(W_{Lmax}\). The total length of a filter, \(TL\), is greatly affected by the cutoff frequency, \(f_{c}\). The fifth button, \"\(TL\) vs. \(f_{c}\)\", carries out this analysis. The function of this button is to take the data from the edit-boxes to select the characteristics of the filter, but, this time, the total length will be obtained for \(f_{c}\) in a rank from 0.5 to 5 GHz. From Figure 12 it can be seen that \(TL\) decreases exponentially as \(f_{c}\) increases. The discontinuous leaps are due to the fact that the length of the source impedance line, \(l_{Z0}\), from Equation (19), changes according to the criterion discussed in Section 4.1, which affects the total length. The sixth button in the GUI is \"Simulate\".