# Efficient Implementation of Polymer Microwave Fiber Links Employing Non-Galvanic Coupling Mechanism
## 3 PMF-AiP Coupling
### Packaging Technology Characterization  
A key aspect of the coupling's performance is the electromagnetic behavior of the packaging technology. The packaging technology that was used for our design is the eWLB package [28; 29; 30]. In Figure 8, a cross-section of the packaging is shown. The coupling performance is mainly limited by the electromagnetic performance of the dielectric layers and the mold compound (dielectric characteristics), as well as the redistribution metals (conductivity and surface roughness).  
Both the dielectric parameters of the mold compound and the dielectric layers and the surface roughness of the redistribution layer have a complex dependence on the frequency. As a result, the implementation of a simulation model for the complex dielectric constants and the surface roughness becomes a necessity.  
The most suitable model to describe the performance of the eWLB's dielectrics is the Djordjevic-Sarkar model, which assumes frequency-dependent complex relative permittivity [28]:  
\[\varepsilon(\omega) =\varepsilon^{\prime}(\omega)+\mathrm{j}\varepsilon^{\prime\prime }(\omega)\] \[=\varepsilon_{\infty}+\frac{\Delta\varepsilon}{\ln\left(\frac{ \omega_{B}+\mathrm{i}\omega}{\omega_{A}}\right)}\ln\left(\frac{\omega_{B}+ \mathrm{i}\omega}{\omega_{A}+\mathrm{j}\omega}\right)+\frac{\sigma}{\hbar \omega\varepsilon_{0}} \tag{2}\]  
where \(\varepsilon_{\infty}\) is the high-frequency relative permittivity, \(\Delta\varepsilon=\varepsilon_{DC}-\varepsilon_{\infty}\) is the difference between the high-frequency and DC relative permittivity, \(\varepsilon_{0}\) is the free-space permittivity, \(\sigma\) is the bulk conductivity, \(\omega=2\pi f\) is the angular frequency and \(\omega_{A}\) and \(\omega_{B}\) are the lower and higher transition frequencies, respectively. The loss tangent is calculated from complex \(\varepsilon(\omega)\) as [28]  
\[\tan\delta(\omega)=-\frac{\varepsilon^{\prime\prime}(\omega)}{\varepsilon^{ \prime}(\omega)} \tag{3}\]  
After implementing this model in the EM simulator for the dielectric materials of the packaging technology, we simulated a frequency sweep to determine the performance of the packaging in the desired frequency band, i.e., 110 GHz to 170 GHz.  
At high frequencies, the process imperfections of the redistribution layers (RDL) have an impact on the performance. More specifically, the surface roughness of the metal layers adds to the effective impedance of the passive components in the eWLB.  
To illustrate the impact of the frequency dependence of the dielectric and metal layers, three cases of coplanar strip lines were simulated. The first case was simulated with constant dielectric parameters and no surface roughness; the second case used the Djordjevic-Sarkar  
Figure 8: Cross-section of eWLB package [28].  
model for the dielectric layers, but no surface roughness model; and the third case included both the Djordjevic-Sarkar model for the dielectric layers and the Grouse model for the surface roughness of the conductors. The \(|\)S21\(|\) for a 10-mm-long CPS line is shown in Figure 9. As illustrated, the surface roughness has a significant impact on the CPS insertion loss. Regarding the dielectric layers' modeling, the constant dielectric parameter layers exhibit poor performance with the CPS line, which illustrates the importance of a realistic model of the stackup's electrical parameters.