## 3 Simulation Results
### Finite Sum of Harmonics Current Excitation
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & & & & & & & & \\ \hline \multirow{6}{*}{**CSCD**} & \multicolumn{4}{c}{**Frequency f\({}_{2}\), _in MHz_**} \\ \cline{2-10}  & & \(\mathbf{-30}\) & \(\mathbf{-20}\) & \(\mathbf{-10}\) & \(\mathbf{0}\) & \(\mathbf{10}\) & \(\mathbf{20}\) & \(\mathbf{30}\) \\ \cline{2-10}  & \(\mathbf{-30}\) & \(18.5\angle\) 1.41 & \(18.5\angle\) \(-2.26\) & \(27.7\angle\) \(-3.04\) & \(36.9\angle\) 2.45 & \(27.7\angle\) 1.67 & \(18.5\angle\) 0.88 & \(18.5\angle\) \(-2.78\) \\ \cline{2-10}  & \(\mathbf{-20}\) & \(31.3\angle\) \(-1.36\) & \(31.3\angle\) 1.26 & \(46.9\angle\) 0.47 & \(62.8\angle\) \(-0.32\) & \(46.9\angle\) \(-1.10\) & \(31.3\angle\) \(-1.89\) & \(31.3\angle\) 0.73 \\ \cline{2-10}  & \(\mathbf{-10}\) & \(99\angle\) \(-1.65\) & \(99\angle\) 0.97 & \(148.5\angle\) 0.18 & \(198\angle\) \(-0.6\) & \(148.5\angle\) \(-1.39\) & \(99\angle\) \(-2.17\) & \(99\angle\) 0.44 \\ \cline{2-10}  & \(\mathbf{0}\) & \(34.5\angle\) \(-1.05\) & \(34.5\angle\) 1.57 & \(51.7\angle\) 0.79 & \(69\angle\) 0 & \(51.7\angle\) \(-0.79\) & \(34.5\angle\) \(-1.57\) & \(34.5\angle\) 1.05 \\ \cline{2-10}  & \(\mathbf{10}\) & \(99\angle\) \(-0.44\) & \(99\angle\) 2.17 & \(148.5\angle\) 1.39 & \(198\angle\) 0.6 & \(148.5\angle\) \(-0.18\) & \(99\angle\) \(-0.97\) & \(99\angle\) 1.65 \\ \cline{2-10}  & \(\mathbf{20}\) & \(31.3\angle\) \(-0.73\) & \(31.3\angle\) 1.89 & \(46.9\angle\) 1.10 & \(62.5\angle\) 0.32 & \(46.9\angle\) \(-0.47\) & \(31.3\angle\) \(-1.26\) & \(31.3\angle\) 1.36 \\ \cline{2-10}  & \(\mathbf{30}\) & \(18.5\angle\) 2.78 & \(18.5\angle\) \(-0.88\) & \(27.7\angle\) \(-1.67\) & \(36.9\angle\) \(-2.45\) & \(27.7\angle\) 3.04 & \(18.5\angle\) 2.26 & \(18.5\angle\) \(-1.41\) \\ \hline \end{tabular}
\end{table} 
Table 1: The amplitudes and phases of the bifrequency spectrum. Figure 5: Diagrams of bifrequency spectrum (**a**) and CSCD (**b**) for the case of finite sum of harmonics current. Figure 7 shows the spectrum of \(p(t)\). The delta functions forming the spectrum of instantaneous power \(p(t)\) are at the same frequencies as the delta functions forming the spectrum of instantaneous current \(i(t)\) and voltage \(v(t)\) because they are periodic functions with the same period. The following quantitative power characteristics were calculated: the average power (33) \(P_{av}=386.5\) uW, apparent power (39) \(P_{app}=541.2\) uVA, power factor (43) \(PF=0.71\). These power quantities can be verified using the traditional method. The periodic voltage \(v(t)\), which is depicted in Figure 1a, can be found analytically using frequency characteristic (57). Its formal representation, which is written with 2-digit precision for the sake of compactness, is as follows:  
\[v(t)=34.5+198\cos(2\pi Ft+0.6)+62.6\cos(4\pi Ft+0.32)+36.9\cos(6\pi Ft-2.45) \ [\text{mV}]. \tag{59}\]  
The effective values of the voltage \(V_{\textit{eff}}\) and current \(I_{\textit{eff}}\), evaluated using (40) and (41), are, respectively, 153.0825 mV and 3.5355 mA, whose product yields the apparent power by definition (39): \(P_{app}=541.2\) uVA. As soon as the voltage and current are known in closed form, the average power \(P_{av}\) can also be evaluated analytically using (32) where the substitution \(p(t)=v(t)i(t)\) is made and the integration limits are chosen from 0 to \(T=1/F\). This yields \(P_{av}=386.5\) uW, which is exactly the same value as found above.