into the TES $$\begin{split}
\frac{\partial I_{t}}{\partial P_{t}}   &=  \frac{ - I_{to} R_{to}}{R_{l} \! + \! R_{to}(1 \! + \! \beta)} 
                                \frac{\alpha}{C_{t}T_{t}} 
                                M_{2D (1,1)}^{-1}(\omega) \\
                                                                                                                &\sim       \frac{- I_{to} R_{to}}{R_{l} \! + \! R_{so}(1 \! + \!\beta)}
                                            \frac{\alpha}{\left( {\mathcal{L}_{2D}}\!+\! 1 \right)}
                                            \frac{1}{\left( G_{tb} \! + \! G_{ta} \right)T_{t}} \frac{1}{1+j\omega/\omega_\mathit{eff}}\\
                            &\sim   \frac{-1}{I_{to}(R_{to} \! - \! R_{l})} \frac{{\mathcal{L}_{2D}}}{{\mathcal{L}_{2D}}\! + \!1 } \frac{1}{1+j\omega/\omega_\mathit{eff}}
\end{split}
\label{eq:dIdPt}$$ and into the absorber $$\begin{split}           
\frac{\partial I_{t}}{\partial P_{a}}   &=              \frac{- I_{to} R_{to}}{R_{l} \! + \! R_{to}(1 \! + \! \beta)}
                                            \frac{\alpha}{C_{a}T_{t}}
                                            M_{2D (1,2)}^{-1}(\omega) \\
                                                                                                                                                                                                                                &\sim    \frac{\partial I_{t}}{\partial P_{t}}
                                    \left(\frac{G_{ta,a}}{G_{ta,a} \!+ \!G_{ab}}\right)
                                    \left(\frac{1}{1+j\omega/\omega_{ta}}\right)                                                
\end{split}
\label{eq:dIdPa}$$ where $$\begin{split}
    \omega_\mathit{eff} \! &=   \left({\mathcal{L}_{2D}}\! + \! 1 \right) \frac{G_{ta} \! + \! G_{tb}}{C_{t}} \! + \!  
                    \frac{1}{{\mathcal{L}_{2D}}\! + \! 1} \frac{G_{ta,a}}{G_{ta} \! + \! G_{tb}} \frac{G_{ta}}{C_{a}} \! + \! \dots\\
    \omega_{ta} \! &=   \frac{G_{tb} \! + \! G_{ta,a}}{C_{a}}  \! -\! 
                    \frac{1}{{\mathcal{L}_{2D}}\! + \! 1} \frac{G_{ta,a}}{G_{ta}+G_{tb}} \frac{G_{ta}}{C_{a}} \! + \! \dots
\end{split}
\label{eq:omega}$$ All of the approximations shown are valid only for the pertinent limiting case where $G_{ta}$ and $G_{ab} \ll G_{tb}$ ([*c*f.]{} Table \[tab:PhononDet\]).

Qualitatively, the last term of Eq. \[eq:dIdPa\], which is an additional pole that surpresses the bandwidth of $\frac{\partial I}{\partial P_{a}}$ relative to $\frac{\partial I}{\partial P_{t}}$, is due to the fact 