## 3 Results and Discussion
### Results of Extraction Directional Charge-Transfer Resistance in AC Nyquist Curve
In Figure 14, charge-transfer resistances of both \(FPLC_{ACqu}\) and \(BHL_{ACqu}\) fluctuate during accelerated aging tests. Figure 14: Elements values in linear circuits fitting for EIS: (**a**) \(R_{ct,pc}\); (**b**) \(R_{ct,pd}\); (**c**) \(R_{ct,mc}\); and (**d**) \(R_{ct,nd}\) in \(FPLC_{ACqu}\); (**e**) \(R_{ct,p}\); and (**f**) \(R_{ct,n}\) in \(BHL_{ACqu}\). However, increasing the decibel value of the sum of internal resistances, including contacting resistance and charge-transfer resistances, is relatively stable. Each decibel value of each ascending step in the magnitude bode plot is related to one charge-transfer resistance and one asymptotic line configured by the pole-zero pair in Figure 13a,b. Bode plots change during accelerated aging tests, but orders of \(FPLC_{ACcpu}\) and \(BHLAC_{Acpu}\) are fixed. Therefore, the scale ratio of the decibel value of each ascending step should be stable. Three ratios of decibel value of ascending steps in \(FPLC_{ACcpu}\), as Equations (31)-(33), are stable between 0.2 and 2.5 in Figure 15; these three steps are different and the ratios decrease from \(DelatdB_{F71}\) to \(DelatdB_{F73}\). The ratio of decibel value of ascending steps in \(BHLAC_{Acpu}\), as Equation (34), is stable between one and two in Figure 15.  
Figure 13:0 Figure 13:1 (32) Figure 13:2 (33) Figure 13:3  
In magnitude bode plots of Figure 13, the curves drawing from northwest at low frequency to southeast at high frequency are roughly straight lines. Assuming there is a four-bit analog-to-digital  
Figure 13:4 Ratio of decibel values of ascending steps of the sum of internal resistances: (**a**) E-52\(\#\); (**b**) E-11\(\#\); (**c**) E-02\(\#\); and (**d**) E-20\(\#\). converter for ideal straight-line input, its interpretation steps should be defined as \(2^{0}\): \(2^{1}\): \(2^{2}\): \(2^{3}\). So does a two-bit analog-to-digital converter, as \(2^{0}\): \(2^{1}\). The scale ratios of adjacent steps are two to maximize the measurement range. However, the curves in magnitude bode plots are not ideal straight lines, so the scale ratio of adjacent sums of resistances is not as ideal as two. Figure 15 shows a similar law, as the numbers of steps are strictly limited by \(FPLC_{ACqu}\) and \(BHLC_{ACqu}\). From this perspective, expansions and contractions of magnitude bode plots are reflecting on the sum of internal resistances, and resistances obtained in Nyquist are viable to characterize batteries' SoH. In Figure 16, contacting resistances and stray inductances of both \(FPLC_{ACqu}\) and \(BHLC_{ACqu}\) are very close. High frequency zero points, determined by contacting resistances and stray inductances as Equation (35), are very close in both \(FPLC_{ACqu}\) and \(BHLC_{ACqu}\). Figure 13:5  
The \(FPLC_{ACqu}\) provides DC directional charge-transfer resistances for charging and discharging. Characteristic charge-transfer resistances on the electrode-electrolyte interface are calculated in [29] by \(FPLC_{ACqu}\). During the first four accelerated aging tests rounds, positive characteristic charge-transfer resistances of E-02# are always high, and positive characteristic charge-transfer resistances of E-20# are climbing up in Figure 17a [29]. The positive characteristic charge-transfer resistances of E-52# reach a maximum at the fifth test round in Figure 17a [29]. The increasing of positive characteristic charge-transfer resistances represents non-cohesion of active mass of the positive electrode [4]; all these  
Figure 13:6 Elements values in linear circuits fitting for EIS: (**a**) \(R_{CFP}\) in \(FPLC_{ACqu}\); (**b**) \(R_{CBH}\) in \(BHLC_{ACqu}\); (**c**) \(L_{SFP}\) in \(FPLC_{ACqu}\); (**d**) \(L_{SBH}\) in \(BHLC_{ACqu}\). changes are early warnings of subsequent capacity degradation in Figure 9a. These early warnings are not be interpreted in \(BHL_{ACqu}\); the positive/negative behavioral charge-transfer resistances and contacting resistances of E-20# and E-11# fluctuate close to each other in Figure 14e,\(f\) and Figure 16b.