# Machine Learning Based Energy-Efficient Design Approach for Interconnects in Circuits and Systems
## 4 Analysis Results
### Single-Ended Microstrip Line
#### 4.1.2 ANN Model and Optimal Structure in Frequency Domain  
In this design, the essential parameters of the structure are ANN model inputs. The space ratio \(K_{D}\) shown in Figure 6 is used as a model input instead of the absolute distance. Hence, the ANN model inputs are the W, \(K_{D}\), and frequency. The constraint of physical  
Figure 6: Cross-section of microstrip line structure with a single-ended signal. dimensions is evenly sampled to produce the training data in which each data set depicts the structure properties over the range of interest frequency from 0.1 GHz to 10 GHz with a step size of 0.1 GHz. Moreover, both S-parameter and \(Z_{0}\) are the model output. The validation data are generated to examine the accuracy of the ANN model. The channel length of 50 mm and FR4 with dielectric thickness of 20 \(\upmu\)m with relative permittivity of 4.4 are used in this design. The minimum EH requirement at a 10 GHz data rate is 250 mV with a 1 V transmitter supply voltage (\(V_{TX}\)). Table 1 below shows a summary of the training and validation data. A sampling design space with W of 5 \(\upmu\)m for W and \(K_{D}\) of 0.1 consists of 496 structures. To generate 28 data sets for training data and validation, it takes 700.8 s per structure. The training process to construct the ANN model takes 1468.9 s. The optimization in the frequency domain takes 248 s to determine the optimal design among 496 structures. The proposed modeling and optimization flow takes a total of only 43.2 s to come up with the optimum design which includes 42.7 s for data generation and 0.5 s for optimization. Hence, the proposed approach is much more efficient than the traditional manual design methods. The accuracy of the ANN model with respect to the validation test data is summarized in Table 2. The errors of \(S_{21}\) and \(Z_{0}\) are 0.11 dB and 0.45 \(\Omega\), respectively, which proves that the ANN model is highly accurate. The residual errors of \(S_{11}\), \(S_{31}\), and \(S_{41}\) are small with values of 0.97 dB, 1.63 dB, and 1.17 dB, respectively. All parameters prediction performs a percentage error below 5%; one of the return loss is a bit higher with 6.73%. However, this higher error is mainly from the resonance points in the return loss and had a small effect on the design. Hence, the ANN model is reliable to predict the optimal structure. The optimal structure needs to satisfy the specifications included characteristic impedance, return loss, and the crosstalk level. Hence, \(Z_{0}\) of 40-60 \(\Omega\) and a maximum \(S_{11}\) of \(-\)15 dB are the design constraints. Furthermore, the \(S_{31}\) and \(S_{41}\) are lower than a maximum of \(-\)20 dB. One notation is that the far-end crosstalk directly influences the receiver signal. Therefore, the EH is more sensitive to this crosstalk due to the induced-noise voltage. Hence, the objective function defined in Equation (8) takes into account the loss and noise for this design. Finally, the design procedure suggests the optimal structure with \(Z_{0}\) of 47.24 \(\Omega\) at 10 Ghz with W=25 \(\upmu\)m and \(K_{D}\) = 2. The S-parameters prediction accuracy is shown in Figure 7.  
\[F_{optimal}=\text{max}\Bigg{[}\frac{1}{N}\sum_{i=1}^{N}(10^{\frac{S_{31}}{20}} -10^{\frac{S_{31}}{20}})\Bigg{]} \tag{8}\]  
where: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{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 & 20 \\ \hline \(K_{D}\) & 1 & 4 & 1 & 1.5 & 3.5 & 1 \\ \hline Number of data sets & \multicolumn{3}{c}{16} & \multicolumn{3}{c}{12} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training and validation data information in microstrip line structure.