## 3 Results and Discussions
### Analysis and Discussions of the Element Parameters
The expansion of the microcrack at a higher strain will certainly result in the reduction of the conductive pathways and the increase of both the RF equivalent resistances and DC resistance, which is consistent with the observations in Figure 6.  
The RF equivalent capacitances \(C_{1}\) are plotted in Figure 8. The capacitance \(C_{1}\) related to the microcracks decreased with the increasing strain as shown in Figure 8. This can be attributed to the enlargement of the crack width as shown in Figure 7. The capacitance can be delivered from the formula \(C=\frac{\epsilon S}{d}\)[25], where \(\epsilon\) is the dielectric constant of PDMS, \(S\) is the cross-sectional area of the microcrack in AgMP/PDMS conductor and d is the width of the microcrack. Thus, the increase of the crack width \(d\) will result in a decrease of the equivalent capacitance. The RF equivalent inductances \(L_{1}\) and \(L_{2}\) were plotted in Figure 9a. The capacitance increased with the increasing strain. With 0% strain, the current directly flowed through the strip conductor as shown in Figure 9b. Once the microcracks formed upon strain, the microcracks will partially block the current and disturb the current distributions as illustrated in Figure 9c. This will increase the equivalent electric length and enlarge the equivalent inductance. Figure 6: (**a**) The change of resistance under strain. (**b**) The relative direct-current (DC) resistance change under strain. Figure 8: The change of capacitance \(C_{1}\) under strain. Figure 7: SEM images of microcracks under different strains: **(a)** 0% strain, **(b)** 5% strain, **(c)** 10% strain. The width distributions of microcracks under different strains: **(d)** 5% strain, **(e)** 10% strain. Figure 5:0 **(a)** The change of the inductance under strain. **(b)** The current path with 0% strain (c). The current path blocked by the microcracks. Generally, the drift of the element parameters in the equivalent circuit model will lead to a change of both the reflection and transmission characteristics of the transmission line. The characteristic impedance \(Z_{0}\) of a short section of the transmission line is calculated by \(Z0=\sqrt{\frac{R+\mu\omega L}{C+\mu\omega L}}\)[26], where \(R\), \(G\), \(L\) and \(C\) are the series resistance, parallel conductance, series inductance and parallel capacitance, respectively, and \(\omega\) is the angular frequency of RF signal. Then the reflection coefficient \(\Gamma\) is calculated by \(\Gamma=\frac{ZL-Z0}{ZL+Z0}\)[26], where \(Z_{L}\) is the load impedance. The characteristic impedance for our microstrip was matched to 50 \(\Omega\), leading to a relatively low reflection. When the microstrip is stretched, the formation and propagation of the microcracks leads to the increase of \(R\) and \(L\), and a decrease of \(G\) and \(C\). This will increase the characteristic impedance \(Z_{0}\), resulting in an impedance mismatch. Thus, the reflection coefficient will certainly increase, which leads to an increase of \(S_{11}\). The \(S_{21}\) implies the total signal eliminating the reflection loss and Ohm loss, and decreases accordingly.