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


#### **Table 10.**

*Statistical data of magnitude error for design-2 SOMI.*


#### **Table 11.**

*Qualitatively data of magnitude error for design-2 SOMI.*


#### **Table 12.**

*Convergence profile for design-2 SOMI.*


#### **Table 13.**

*Percentage improvement in magnitude and phase error for design-2 SOMI.*

**Figure 7** depicts the comparison of the designed SOMIs with the existing second order microwave integrator. **Figure 7(a)** and **(b)**, respectively, display the comparative magnitude response and AME of the designed SOMI GSA-based optimization with an existing integrator. The corresponding qualitative and statistical magnitude error analysis of the existing SOMIs and the designed integrator is shown in **Table 14**. **Figure 7** and **Table 14** confirm that GSA-based designed SOMIs are more suitable in terms of magnitude, minimal magnitude error, and wide bandwidth, especially for high-frequency ranges.

The results of the proposed-2 SOMI GSA-based leads in performance to the proposed-1 SOMI counterpart. All simulation results of the design-2 SOMI approximates with the ideal one and have linear phase response in its frequency range 3.0– 15 GHz. Therefore, the designed-2 SOMI is simulated on ADS by using microstrip lines. To simulate the designed-2 SOMI on ADS, RT/duroid substrate is selected with dielectric constant *ϵr*=2.2, height of substrate ð Þ¼ *H* 30 *mil* ð Þ 0*:*762 *mm* , loss tangent tan ð Þ¼ *δ* 0*:*001, and copper cladding is 35 um. The magnitude and phase response of the designed-2 SOMI GSA-based is illustrated in **Figure 8(a)** and **(b)** respectively.

The Design-2 SOMI GSA-based magnitude response closely matches that of the ideal one in the 3.0–15 GHz frequency range. Based on the observations, compared to PSO and CSA, GSA has the least magnitude error and highest convergence speed.

*Profile of the design-2 SOMI (a) Magnitude response, (b) Magnitude error response, (c) Phase response,*

**Algorithm Total magnitude error Phase error** PSO 3.9217 0.9861 CSA 3.6920 1.0968 GSA 3.6573 1.0595

*(d) Pole-zero plot, (e) Convergence profile, and (f) Improvement bar graph.*

*Innovations in Ultra-WideBand Technologies*

*Comparison summary of total magnitude and phase error for design-2 SOMI.*

**Figure 6.**

**Table 9.**

**142**

elements i.e. transmission line sections, open-circuited stub and short-circuited stub. The optimum values of line elements are obtained by applying the PSO, CSA and GSA by which the magnitude response of designed integrators approximate the ideal magnitude response. The results are simulated statistically on MATLAB, which affirms that GSA outperforms the PSO and CSA in all state-of-the-art in terms of magnitude response. Furthermore, the designed-2 SOMI GSA-based is also simulated on ADS using microstrip lines. With the exception of lower frequency range (under 3 GHz), the simulated magnitude response of integrator has consistency over the frequency range from 3 to 15 GHz with ideal one in both MATLAB and ADS environment, which makes it appropriate for ultra-wideband applications.

*Analysis of Wideband Second-Order Microwave Integrators*

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

**Author details**

**145**

Technology, Delhi, India

Usha Gautam\* and Tarun Kumar Rawat

provided the original work is properly cited.

\*Address all correspondence to: usha.aitpg@gmail.com

Division of Electronics and Communication, Netaji Subhash Institute of

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

#### **Figure 7.**

*Comparison of the designed SOMI-GSA with existing integrator (a) Magnitude reponse and (b) Error response.*


#### **Table 14.**

*Comparison of magnitude error of the designed SOMIs with existing design method.*

**Figure 8.** *Using ADS software (a) Magnitude response and (b) Phase response.*

## **5. Conclusion**

The study focused on the design and analysis of compact, stable and wideband second order microwave integrators. The designs are obtained by cascading the line
