## 4 Design and Measurement
The circuit simulation was performed by considering and realizing the equivalent lumped elements of the DGS section, as shown in Figure 10. The S-parameters results of the circuit simulations for the proposed circuit, i.e., \(S_{11}\), \(S_{21}\), \(S_{31}\) and \(S_{32}\), are illustrated as dotted lines in Figure 11a,b, which were designed at 3 and 2 GHz, respectively. It is clear from the results that the designed circuits and their parameters fulfill the requirements for the proposed Wilkinson power dividers, as they achieved good return losses \(S_{11}\) and isolations \(S_{32}\) of the order of \(-55.84\) and \(-55.02\) dB, respectively, for the WPD designed at 3 GHz and \(-60.61\) and \(-40.64\) dB, respectively, for the WPD designed at 2 GHz. ANSYS HFSS Software package (ANSYS Electronics Desktop 2020 R2) was utilized to extract the final layout of the proposed WPD. Figure 11a,b shows the S-parameters results, i.e., \(S_{11}\), \(S_{21}\), \(S_{31}\) and \(S_{32}\), of an EM simulation for the respective WPDs as solid lines. The calculated values and their respective dimensions are given in Tables 2 and 3. To achieve an acceptable result, the circuits were tuned slightly. Therefore, the final layouts of the circuits were adjusted slightly, as compared to its initial dimensions. From the simulation results, the proposed circuits achieved almost equal power division, i.e., \(S_{21}\approx S_{31}\approx-3\) dB. Figure 10: Circuit schematic analysis of WPD designed at 3 GHz with physical dimensions and equivalent DGS circuit. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Operating** & **C** & **L** & **a** & **b** & **g** \\
**Frequency** & **(pF)** & **(nH)** & **(mm)** & **(mm)** & **(mm)** \\ \hline
3 GHz & 0.267 & 10.54 & 5 & 13 & 0.2 \\
2 GHz & 0.3789 & 16.71 & 6 & 21 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Lumped values and physical dimensions of DGS sections (\(\varepsilon_{r}=2.97\), H = 0.76 mm). Figure 11: Simulation results of the proposed WPD circuit. Most importantly, they show very good isolations between the output ports, i.e., about \(S_{32}=-29.36\) dB and about \(S_{32}=-35.42\) dB for the WPDs designed at 3 and 2 GHz, respectively. The results shown in Figure 11a,b also demonstrate good return losses of about \(S_{11}=-28.18\) and \(-20\) dB for the WPDs designed at 3 and 2 GHz, respectively. The comparison between the circuit and EM simulation illustrate that the isolation and the return loss are reported to be decreased slightly in case of EM simulation as compared to the results achieved in the circuit simulation. The difference of isolation and return loss are \(-25.66\) and \(-27.66\) dB, respectively, in the case of the WPD designed at the resonant frequency of 3 GHz and approximately \(-5.22\) and \(-40.61\) dB, respectively, in case of the WPD designed at the resonant frequency of 2 GHz. The proposed Wilkinson power dividers were fabricated on a specified substrate using a special technique called photolithography. Figures 12 and 13 show the pictures of the fabricated circuits designed at the operating frequencies 3 and 2 GHz, respectively. The simulated (EM simulation) and measured results of both circuits are illustrated in Figure 14 and compared in Table 4. In the case of the measured results, Table 4 shows that, due to attenuation and signal distortion in the microstrip line, the return loss and isolation at the resonating frequencies of 3 and 2 GHz in the fabricated WPDs are decreased to a small degree as compared with the simulation results. The return loss \(S_{11}\) of the simulated circuit designed at 2 GHz is about \(-20\) dB, which is less preferable. Therefore, the fabricated circuit is tuned slightly by the trial-and-error method to get the preferred measured return loss. Hence, the measured return loss of the divider at 2 GHz is better than the simulated circuit. Moreover, the attenuation pole in both WPDs is shifted slightly to higher frequencies with better dips as compared with the simulation results.