# Machine Learning Based Energy-Efficient Design Approach for Interconnects in Circuits and Systems
## 4 Analysis Results
### Stripline with Differential Signal
#### 4.2.2 ANN Model and Optimal Structure in Frequency Domain  
In this example, the ANN model inputs include the differential channel width (W), space ratio (\(K_{S}\)), and the interest frequency range from 0.1 GHz to 10 GHz with a step size of 0.1 GHz. Moreover, the model output contains both the differential S-parameter and \(Z_{0}\). The validation data ensures the model accuracy in frequency-domain. Furthermore, the channel length of 50 mm and thickness of 205 \(\upmu\)m Megtron4 material with a dielectric constant of 3.83 is constant is used. The minimum EH requirement at a 10 GHz data rate is 100 mV with a 1.4 V peak to peak transmitter supply voltage (\(V_{P2P}\)). Table 4 below shows a summary of the training and validation data. In this structure, the proposed approach consumes 606.6 s per structure for the data generation process. The data contains 25 data sets divided into training data and validation data. In addition, the training process and optimization process consume 646.1 s, and 314 s, respectively. The optimization procedure determines the optimal structure among 496 structures by sampling design space with 5 \(\upmu\)m for the channel width and 0.1 for the space ratio. On average, the proposed approach achieves an impressive efficiency with 32.5 s for one structure analysis involved in 31.9 s of data generation and 0.6 s of optimization. The ANN model accuracy with the validation data is illustrated in Table 5. According to the validation results, the ANN model provides reliable data with a slight difference from the simulation results. The significant parameters included \(S_{21}\) and \(S_{41}\) exhibit a negligible error with 0.04 dB and 0.72 dB, respectively. Furthermore, the model produces an accurate \(Z_{0}\) prediction with 1.29 \(\Omega\) in error. On the other hand, the remaining output contained \(S_{11}\) and \(S_{31}\) demonstrate slightly higher errors of 2.87 dB, 1.92 dB, respectively. Nevertheless, these errors mostly originate from the resonance points that are extremely miniature and insignificant in design. While the return loss prediction presents an error of 10.6%, the high accuracy \(Z_{0}\) prediction with 1.22% error assures the impedance matching. Moreover, the other parameters prediction performs an error below 5%. As a consequence, the ANN model is reliable to determine the optimal structure. The differential signal typically demands a 100-\(\Omega\) differential impedance. So, the 95-105 \(\Omega\) is one of the design constraints for this structure. Furthermore, the return loss and crosstalk are smaller than \(-\)20 dB and \(-\)40 dB, respectively. In contrast to the single-ended signal, the channel in one differential signal is immune from the far-end crosstalk caused by the other one. However, the adjacent pair also influences the differential pair referred to as differential crosstalk. Therefore, the differential loss and crosstalk are the source that degrade the signal quality. Hence, the objective function described in Equation (9) can be \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{4}{c}{**Training Data**} & \multicolumn{4}{c}{**Validation Data**} \\ \cline{2-7}  & **Min Value** & **Max Value** & **Step** & **Min Value** & **Max Value** & **Step** \\ \hline Frequency (Ghz) & 0.1 & 10 & 0.1 & 0.1 & 10 & 0.01 \\ \hline W (\(\upmu\)m) & 25 & 100 & 25 & 30 & 90 & 30 \\ \hline \(K_{S}\) & 1 & 4 & 1 & 1.5 & 3.5 & 1 \\ \hline Number of data sets & & 16 & & & 9 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training and validation data information of the stripline structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Metric**} & \(\mathbf{S_{11}}\) & \(\mathbf{S_{21}}\) & \(\mathbf{S_{31}}\) & \(\mathbf{S_{41}}\) & \(\mathbf{Z_{0}}\) \\ \hline Residual (dB) & 2.87 & 0.04 & 1.92 & 0.72 & 1.29 \\ \hline RMSE (dB) & 3.96 & 0.05 & 2.64 & 0.86 & 1.36 \\ \hline Error (\%) & 10.61 & 3.20 & 4.66 & 1.69 & 1.22 \\ \hline \hline \end{tabular}
\end{table}