# A Mayfly-Based Approach for CMOS Inverter Design with Symmetrical Switching
## 5 Results  
In this section, the optimal switching characteristics of the CMOS inverter are obtained using the Mayfly Optimization Algorithm. A total of eight different design sets are considered with the lower and upper bounds for the design parameters of each design set as seen in Tables 1-3 for the three different case studies. TSMC 0.25 \(\upmu\)m CMOS model is used in the LT-Spice simulation to get simulation results. The model parameters are \(\mathrm{V_{DD}}\) = 2.5 V, \(\mathrm{V_{tn}}\) = 0.3655 \(V\), \(\mathrm{V_{tp}}\) = 0.5466 \(V\), \(\mathrm{\mu_{p}C_{ox}}\) = 51.6 \(\upmu\)A/V\({}^{2}\) and \(\mathrm{\mu_{n}C_{ox}}\) = 243.6 \(\upmu\)A/V\({}^{2}\)[25; 26; 27; 28; 29; 30; 32]. For Case I, the MA is implemented using MATLAB to find the design parameters needed to minimize the fall time of the output voltage for the CMOS inverter with an identical size of PMOS and NMOS transistors. For each design set in Table 1, the MA parameters are population size (males and females) equal 20 and number of iterations equal 50. The result of the MA gives the optimal design parameters, i.e., \(\mathrm{C_{L}}\), (W/L) and (t\({}_{t}\)), for the CMOS inverter with the minimum fall time. These results are summarized in Table 4. The results show that the design parameters are within the limits given in Table 1.  
Figure 4 shows the convergence of the objective function, given in 13, with the iterations for the seventh design set. In Figure 4, it can be seen that the objective function reaches an optimal value of 2.7473019 \(\times\) 10\({}^{-20}\) s. The 7 th design set was chosen since it has the lowest value of the cost function. Figures 5-7 show the convergence plots of the inverter design parameters, \(\mathrm{C_{L}}\), (W/L), and (t\({}_{t}\)), for the same design set. In Figure 5, the optimum value for the load capacitance is 0.7122034 pF and it starts to converge after 24 iterations. The aspect ratio (W/L) optimum value for the seventh set is shown in Figure 3 to be equal to 1.8113496. The optimum value for the fall time is equal to 2.1820107 ns as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Set Number** & **C\({}_{\text{L}}\) (pF)** & **W/L** & **T\({}_{\text{f}}\) (ns)** & **CF (s)** \\ \hline
1.0 & 0.6610313 & 3.2691838 & 1.122116 & 8.4500086 \(\times\) 10\({}^{-20}\) \\
2.0 & 0.6817429 & 2.2553382 & 1.6775056 & 8.2739268 \(\times\) 10\({}^{-20}\) \\
3.0 & 0.6 & 2.7507903 & 1.2104557 & 6.3245267 \(\times\) 10\({}^{-20}\) \\
4.0 & 0.7064141 & 2.4468083 & 1.6021919 & 5.3510907 \(\times\) 10\({}^{-20}\) \\
5.0 & 0.8389162 & 3.8796487 & 1.2 & 8.6812836 \(\times\) 10\({}^{-20}\) \\ \hline
6.0 & 0.7272609 & 2.4489382 & 1.6480392 & 9.6705203 \(\times\) 10\({}^{-20}\) \\ \hline
7.0 & 0.7122034 & 1.8113496 & 2.1820107 & 2.7473019 \(\times\) 10\({}^{-20}\) \\ \hline
8.0 & 0.8179995 & 2.3458135 & 1.9351501 & 5.5974648 \(\times\) 10\({}^{-20}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MA results for Case I. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Set Number** & **C\({}_{\text{L}}\) (pF)** & **(W/L\({}_{\text{n}}\)** & **(W/L\({}_{\text{p}}\)** & **t\({}_{\text{f}}\) (ns)** & **t\({}_{\text{f}}\) (ns)** & **t\({}_{\text{PHL}}\) (ns)** & **t\({}_{\text{PLH}}\) (ns)** \\ \hline
1.0 & 0.20–4.0 & 1.10–6.10 & 2.80–19.30 & 1.10–13.0 & 1.10–13.0 & 0.50–10.0 & 0.50–10.0 \\ \hline
2.0 & 0.10–5.10 & 1.60–7.10 & 1.80–18.0 & 1.10–15.0 & 1.10–15.0 & 0.50–8.0 & 0.50–8.0 \\ \hline
3.0 & 0.470–20 & 1.40–6.70 & 3.20–38.0 & 0.50–12.0 & 0.50–12.0 & 0.20–9.0 & 0.20–9.0 \\ \hline
4.0 & 0.10–1.10 & 1.20–7.0 & 1.50–17.50 & 0.50–5.0 & 0.50–5.0 & 0.20–4.0 & 0.20–4.0 \\ \hline
5.0 & 0.20–14.0 & 1.90–50 & 2.70–17.0 & 0.70–6.0 & 0.70–6.0 & 0.40–5.0 & 0.40–5.0 \\ \hline
6.0 & 0.30–3.60 & 1.30–3.50 & 3.50–16.20 & 0.250–7.0 & 0.250–7.0 & 0.30–4.50 & 0.30–4.50 \\ \hline
7.0 & 0.20–4.90 & 1.10–5.80 & 2.20–25.30 & 0.50–6.60 & 0.50–6.60 & 0.20–7.70 & 0.20–7.70 \\ \hline
8.0 & 0.20–3.50 & 0.30–7.60 & 1.30–39.0 & 0.30–6.60 & 0.30–6.60 & 0.10–4.40 & 0.10–4.40 \\ \hline \hline \end{tabular}
\end{table}