**4.1 Design-1 [SOMI using two open stub and three serial line sections]**

**Figure 3** presents the configuration of the design-1 SOMI, and **Table 2** displays the characteristic impedances of design-1 SOMI achieved with PSO, CSA and GSA. The algorithm steps have shown in section-3 by which these characteristic impedances are attained. The magnitude response, the AME, the phase response, the polezero plot, the fitness rate and the improvement graph are the parameters selected in **Figure 4(a)**–**(f)** for the frequency response analysis of the design-1 SOMI. **Table 3**


**Table 2.** *Optimized characteristic impedances of the design-1 SOMI.*


**Table 3.**

*Comparison summary of total magnitude and phase error for design-1 SOMI.*

records the overall magnitude error and the phase error. **Table 4** and **Table 5** summarize the statistical analysis and the qualitatively analyzed data of magnitude error of the design-1 SOMI. It is observed that GSA-based results have least values in all aspects with respect to PSO and CSA. The pole-zero plot of the Design-1 SOMI for stability analysis in which all the poles and zeros lie inside the unit circle is shown in **Figure 4(d)**. This plot asserts that the SOMI design-1 is stable. The convergence profile of all three algorithms in which GSA is clearly demonstrated to be faster than PSO and CSA in less execution time is shown in **Figure 4(e)**, which is also summarized in **Table 6**. The percentage improvement comparison in magnitude error for the design-1 SOMI as CSA to PSO, GSA to PSO, and GSA to CSA and the percentage improvement comparison in phase errors summarized in **Table 7** are shown in **Figure 4(f)**. The design-1 SOMI GSA-based magnitude response closely matches that of the ideal one in the 2.5–16 GHz frequency range. On the basis of these observations, compared to the PSO and CSA, GSA has the lowest magnitude error and the highest convergence speed.

**4.2 Design-2 [SOMI using one open stub, one short stub and three serial lines]**

*Percentage improvement in magnitude and phase error for design-1 SOMI.*

*Analysis of Wideband Second-Order Microwave Integrators*

*DOI: http://dx.doi.org/10.5772/intechopen.94843*

**Table 7.**

**Figure 5.**

**Table 8.**

**141**

*Configuration of the design-2 SOMI.*

*Optimized characteristic impedances of the design-2 SOMI.*

**Algorithm Magnitude PI (%) Phase PI (%)** PSO 4.1613 3.5758 CSA 13.4935 3.5855 GSA 9.7374 0.0099

The design-2 SOMI configuration is illustrated in **Figure 5**. The optimized characteristic impedances of design-2 SOMI obtained by PSO, CSA, and GSA. The algorithm steps have discussed in Section 3 by which these characteristic impedances are attained. **Table 8** offers the optimized characteristic impedances of the line elements of Design-2 SOMI. For the frequency response analysis of the design-2 SOMI, the same parameters are selected as the design-1 SOMI as shown in **Figure 6 (a)**–**(f)**. In **Table 9**, the total magnitude and phase errors are listed. **Table 10** and **Table 11** summarize the statistical analysis and the qualitatively analyzed data of different characteristics of magnitude error of the design-2 SOMI. It is observed that GSA-based results have the least values in all aspects as compared to the PSO and CSA. The pole-zero plot of the Design-2 SOMI for stability analysis in which all the poles and zeros lie inside the unit circle is shown in **Figure 6(d)**. This plot asserts that SOMI Design-2 is stable. The convergence profile of all three algorithms in which GSA is clearly demonstrated to be faster than PSO and CSA with less execution time is shown in **Figure 6(e)**, which is also summarized in **Table 12**. The percentage improvement comparison in magnitude error for the design-2 SOMI as CSA to PSO, GSA to PSO, and GSA to CSA and the percentage improvement comparison in process error, summarized in **Table 13**, are shown in **Figure 6(f)**.

**Characteristic impedance PSO CSA GSA** *ZOC* 116 26.87 141 *ZTL*<sup>1</sup> 30.5 142.6 33 *ZTL*<sup>2</sup> 145 84 138 *ZTL*<sup>3</sup> 9.5 19 10 *ZSC* 110 138.09 116.89


#### **Table 4.**

*Statistical data of magnitude error for design-1 SOMI.*


#### **Table 5.**

*Qualitatively data of magnitude error for design-1 SOMI.*


#### **Table 6.**

*Convergence profile for design-1 SOMI.*

*Analysis of Wideband Second-Order Microwave Integrators DOI: http://dx.doi.org/10.5772/intechopen.94843*


**Table 7.**

records the overall magnitude error and the phase error. **Table 4** and **Table 5** summarize the statistical analysis and the qualitatively analyzed data of magnitude error of the design-1 SOMI. It is observed that GSA-based results have least values in all aspects with respect to PSO and CSA. The pole-zero plot of the Design-1 SOMI for stability analysis in which all the poles and zeros lie inside the unit circle is shown in **Figure 4(d)**. This plot asserts that the SOMI design-1 is stable. The convergence profile of all three algorithms in which GSA is clearly demonstrated to be faster than PSO and CSA in less execution time is shown in **Figure 4(e)**, which is also summarized in **Table 6**. The percentage improvement comparison in magnitude error for the design-1 SOMI as CSA to PSO, GSA to PSO, and GSA to CSA and the percentage improvement comparison in phase errors summarized in **Table 7** are shown in **Figure 4(f)**. The design-1 SOMI GSA-based magnitude response closely matches that of the ideal one in the 2.5–16 GHz frequency range. On the basis of these observations, compared to the PSO and CSA, GSA has the lowest magnitude

**Algorithm Mean Variance Standard deviation** PSO 0.0410 0.0035 0.0588 CSA 0.0393 0.0036 0.0603 GSA 0.0354 0.0024 0.0494

**Algorithm Maximum Minimum Average** PSO 0.2642 <sup>4</sup>*:*<sup>8442</sup> <sup>10</sup><sup>4</sup> 0.0410 CSA 0.3762 <sup>9</sup>*:*<sup>2306</sup> <sup>10</sup><sup>4</sup> 0.0393 GSA 0.2384 <sup>4</sup>*:*<sup>2118</sup> <sup>10</sup><sup>4</sup> 0.0354

PSO 400 313.2654 0.6132 CSA 400 291.3719 0.5547 GSA 400 269.6370 0.4950

**per iteration**

**Execution time (s) per cycle**

*Comparison summary of total magnitude and phase error for design-1 SOMI.*

**Algorithm Total magnitude error Phase error** PSO 5.7746 1.0403 CSA 5.5353 1.0031 GSA 4.9954 1.0030

error and the highest convergence speed.

*Innovations in Ultra-WideBand Technologies*

*Statistical data of magnitude error for design-1 SOMI.*

*Qualitatively data of magnitude error for design-1 SOMI.*

**Algorithm Iteration cycle Execution time (s)**

**Table 3.**

**Table 4.**

**Table 5.**

**Table 6.**

**140**

*Convergence profile for design-1 SOMI.*

*Percentage improvement in magnitude and phase error for design-1 SOMI.*
