## The Methods of Establishing RSP Model and RSHARQ  
### Three-Wire Coupling Interconnect Model  
Referring to [10; 42], Section 2.1 establishes the RLC coupling model of interconnects, as Figures 1 and 2 show.  
Figure 1 is the cross-sectional view of the coupling interconnect model. Figure 1a shows the equivalent capacitance model of coupling interconnects. \(\mathrm{C_{g}}\) is the coupling capacitance between an interconnect and the grounding metal layers. \(\mathrm{C_{c}}\) is the coupling capacitance of adjacent interconnects. Figure 1b shows the dimensions of an interconnect.  
Figure 2 shows the distributed RLC spice model of an interconnect, where the interconnect is equivalently divided into n segments. \(\mathrm{V_{in}}\) is the driving voltage source, \(\mathrm{R_{th}}\) is the driving resistance, and \(\mathrm{C_{f}}\) is the equivalent load of the interconnect.  
Figure 1: A coupling interconnect model: (**a**) is the equivalent capacitance model; (**b**) is the dimensions of an interconnect.  
All parameters mentioned above can be calculated from the interconnect dimensions shown in Figure 1b, the material parameters, the working status parameters (called timing constraint parameters as well) and the formulas listed below.  
Dimension parameters of an interconnect include: the length l, width w, thickness t, spacing s and distance h. Material parameters include: the insulating layer relative dielectric constant \(\epsilon_{\mathrm{r}}\) and interconnect resistivity \(\rho\). Working status parameters include: the rising time t\({}_{\mathrm{r}}\) and falling time t\({}_{\mathrm{f}}\).  
Referring to [42; 43; 44; 45], formulas are shown below:  
\[\mathrm{R}=\frac{\rho\cdot 1}{\mathrm{w}\cdot\mathrm{t}} \tag{1}\]  
\[\mathrm{L}=\frac{\mu_{0}\cdot 1}{2\pi}\left[\ln\left(\frac{21}{\mathrm{w}+ \mathrm{t}}\right)+\frac{1}{2}+\frac{0.22(\mathrm{w}+\mathrm{t})}{1}\right] \tag{2}\]  
\[\mathrm{M}=\frac{\mu_{0}\cdot 1}{2\pi}\left[\ln\left(\frac{21}{\mathrm{s}+ \mathrm{w}}\right)-1+\frac{\mathrm{s}+\mathrm{w}}{1}\right] \tag{3}\]  
\[\mathrm{k}_{\mathrm{M}}=\frac{\mathrm{M}}{\mathrm{L}} \tag{4}\]  
\[\mathrm{C}_{\mathrm{g}}=\varepsilon_{0}\varepsilon_{\mathrm{r}}\left[\frac{ \mathrm{w}}{\mathrm{h}}+2.04\left(\frac{\mathrm{s}}{\mathrm{s}+0.54\mathrm{h} }\right)^{1.77}\cdot\left(\frac{\mathrm{t}}{\mathrm{t}+4.53\mathrm{h}}\right)^ {0.07}\right] \tag{5}\]  
\[\mathrm{C}_{\mathrm{c}}=\varepsilon_{0}\varepsilon_{\mathrm{r}}\left[1.41 \frac{\mathrm{t}}{\mathrm{s}}\mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{s}+8 \mathrm{m}}}+2.37\left(\frac{\mathrm{w}}{\mathrm{w}+0.31\mathrm{s}}\right)^{0. 28}\cdot\left(\frac{\mathrm{h}}{\mathrm{h}+8.96\mathrm{s}}\right)^{0.76} \cdot\mathrm{e}^{-\frac{2\mathrm{s}}{\mathrm{s}+8\mathrm{m}}}\right] \tag{6}\]  
\[\mathrm{n}\geq 10\left(\frac{1}{\mathrm{V}\cdot\mathrm{t}_{\mathrm{r}}}\right) \tag{7}\]  
where R is the resistance of the whole interconnect, L is the self-inductance of interconnects, M is the mutual inductance between interconnects, \(\mu_{0}\) is the vacuum permeability, \(\mathrm{k}_{\mathrm{M}}\) is the mutual inductance coefficient, \(\varepsilon_{0}\) is the vacuum dielectric constant, V is the propagation velocity of electromagnetic wave in interconnects, and n is the number of the three-wire distributed RLC spice model's interconnect segments.  
Figure 2: Distributed three-wire RLC spice model.