power bus plane impedance

\begin{align}
Z_{ij}(\omega)=\sum_{m=0}^\infty \sum_{n=0}^\infty \frac{N_{mni}N_{mnj}}{\frac{1}{j\omega L_{mn}}+j\omega C_0+G_{mn}} \label{second}
\end{align}

where

\begin{align*}
\omega_{mn}&=\frac{k_{mn}}{\sqrt{\varepsilon\mu}},C_0=\frac{ab\varepsilon}{d},L_{mn}=\frac{1}{C_0\omega_{mn}^2}, \\
G_{mn}&=C_0\omega_{mn}(tan\delta +\frac{r}{d}),
k_{mn}=(\frac{m\pi}{a})^2+(\frac{n\pi}{b})^2 \\
N_{mni}&=c_mc_ncos(\frac{m\pi x_i}{a})cos(\frac{n\pi y_i}{b})sinc(\frac{m\pi W_{xi}}{2a})sinc(\frac{n\pi W_{yi}}{2b})
\end{align*}

\begin{align*}
m=n&=0=>G_{mn}=0,L_{mn}=\infty, N_{00i}=N_{00j}=1 \\
Z_{ij}(\omega )&=\frac{1}{j\omega C_0}+\sum_{m=0,n=0}^\infty \sum_{m,n\neq (0,0)}^\infty \frac{N_{mni}N_{mnj}}{\frac{1}{j\omega L_{mn}}+j\omega C_0+G_{mn}} 
\end{align*}