## 5 Cma  
The integration of the antenna with the radio frequency front-end transceivers necessitates a design metrics compromise that fulfills the application's need. The CMA is one method for examining such a problem that uses classical electromagnetism to introduce the notion of the CMA [29; 30]. The CMA generates an endless number of distinct current patterns that may be evaluated for the frequency of interest. According to the CMA, the arbitrary conducting plane has multiple distinctive modes, including orthogonal modal currents (J\({}_{i}\)) and weighted eigenvalues (\(\lambda_{i}\)). The cumulative current is given in terms of (J\({}_{i}\)) and the modal weight coefficients (\(\beta_{i}\)) by Equation (6):  
\[\mathrm{J}=\sum_{i=n}^{N}\beta_{i}\,\mathrm{J}_{i}\quad. \tag{6}\]  
\(\beta_{i}\) is used to determine the impact of an individual eigencurrent on the total current and how it affects the overall electric field. The eigenvector signifies the excitation and radiation properties of the antenna while the eigenvalues indicate the magnitude of the capacitive and inductive energy storage, as illustrated in Table 3. The method of moment matrix (\(Z\)) links the eigenvalue and eigencurrent, as depicted in Equations (7) and (8):  
\[[Z]=[R]+j[X],\text{ and } \tag{7}\]  
\[[X]\,\mathrm{J}_{i}\ \ =\lambda_{i}\,[R]\,\ \mathrm{J}_{i}\quad, \tag{8}\]  
where \(X\) and \(R\) represent the imaginary and real components of the impedance \(Z\), respectively. The modal significance (MS) is a key CMA parameter that specifies every mode's optimum normalized current performance and its effects on the radiation characteristics. The characteristic angle (CA) describes the phase difference between the antenna's electric field and the surface current. The MS and CA (\(\alpha_{i}\) ) are computed using Equations (9) and (10), respectively. The proposed UWB antenna is simulated to study the physical insight of the structure through the CMA, as depicted in Figure 15a-c.  
\[MS=\left|\frac{1}{1+j\lambda_{i}}\right|,\text{ and } \tag{9}\]  
\[\alpha_{i}\ =180^{0}-tan^{-1}\lambda_{i}\enspace. \tag{10}\]  
The CMA of the proposed antenna exhibits specific significant modes that contribute to the antenna's radiation. The first four modes are relatively significant and contribute to the antenna performance. The eigencurrents are not affected by any source or excitation, but rather, by the structure and size of the antenna. The optimization of the geometry of the antenna by looking into the individual mode current helps in achieving a broader bandwidth and the required radiation properties. The substantial individual mode current contributes an antenna to achieve bidirectional and omnidirectional radiation patterns at the E- and H-planes, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Eigenvalues (\(\lambda_{i}\))** & **CA (\(\alpha_{i}\))** & **Significance** \\ \hline \(\lambda_{i}\ <0\) & \(180<\alpha_{i}\ <270\) & Capacitive (electric energy) \\ \(\lambda_{i}\ =0\) & \(\alpha_{i}\ =180\) & Resonating point \\ \(\lambda_{i}\ >0\) & \(90<\alpha_{i}\ <180\) & Inductive (magnetic energy) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The relevance of eigenvalues.