## 3 Results
### Conducted and Radiated Emission: Results and Discussion  
The conducted emission has been measured by using the setup in Figure 6. The measurements have been compared with the simulations in Figure 8, which shows the results for Case 1 defined in Table 2. Specifically, Figure 8a shows the time-domain waveforms of simulated vs. measured currents at one of the pin pairs (data-ground), showing a satisfactorily agreement. Note that the numerical results are affected by ripples corresponding to the transitions across the zero level, which are not present in the measured results, due to low-pass filtering action of the instruments. These oscillations are due to the high-frequency effect of the L-C components in the IC equivalent circuits model, but do not affect the main features of the numerical results (e.g., rms value, frequency, etc.). Indeed, Table 6 provides the rms values of the currents injected into the package pins in the three different conditions of Table 2. The cases with higher frequency (cases 2 and 3) are associated to a higher level of the injected current. The spectrum of the conducted emission noise in terms of voltage across a 50 \(\Omega\) impedance is also reported in Figure 8b, using both simulated and measured results. The agreement is satisfactory in terms of peak values and position. Note that these voltage values cannot be compared to the EMC norm limits [24], since such a norm imposes the use of the so-called \"1 \(\Omega/150\)\(\Omega\) direct coupling method\". A comparison with the norm limits is, however, out of the scope of this paper. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & _Trace Length_ & _Trace Width_ & _Trace Height_ & _Layer Thickness_ & _Dielectric Relative_ \\  & **(mm)** & **(\(\mu\)m)** & **(\(\mu\)m)** & **(\(\mu\)m)** & _Permittivity_ \\ \hline Min & 110 & 1290 & 35 & 200 & 3.92 \\ Max & 210 & 129 & 35 & 200 & 4.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Geometrical and physical parameters for the PCB. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(R_{\text{38}}\) (\(\Omega\)) & \(R_{\text{39}}\) (\(\Omega\)) & \(R_{\text{40}}\) (\(\Omega\)) & \(L_{\text{38}}\) (nH) & \(L_{\text{39}}\) (nH) & \(L_{\text{40}}\) (nH) & \(\mathbf{C_{\text{38-39}}}\) (pP) & \(\mathbf{C_{\text{39-40}}}\) (pP) & \(\mathbf{K_{\text{38-39}}}\) & \(\mathbf{K_{\text{39-40}}}\) \\ \hline
0.070 & 0.068 & 0.071 & 2.91 & 2.81 & 3.10 & 0.32 & 0.35 & 0.55 & 0.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Equivalent electrical parameters for the traces #38–40 of the PCB. Figure 7: Computed scattering parameters for the PCB traces: (**a**) transmission parameters along trace #13; and (**b**) transmission parameters from trace #13 to traces #14 and #15. Figure 9 shows the measured and simulated values of the far-field electric field evaluated at 3 m distance, assuming that the IC injects in the package pins the currents shown in Figure 8. Both the simulated and the measured values refer to the worst case condition, with respect to different polarization and incidence angles. Although the agreement is not as good as for the conducted emission, the results are quite satisfactory, since many of the emission peaks are correctly reproduced. Furthermore, the average level of the emission in the range 30 MHz-1 GHz is satisfactorily taken, as shown in Table 7, referring to the three different operating conditions of the IC defined in Table 2. The lower emission can be found in correspondence to Case 1, which refers to the lower frequency, the higher the rise time (see Table 2) and the lower value of the currents (Table 6). The worst condition is given by Case 3, corresponding to the higher frequency, the lower rise time (see Table 2) and the higher value of the currents (Table 6). As a conclusion, the direct emission is characterized by peak levels that can easily overcome the limits imposed by common EMC international norms for radiated emissions [25,26].