Nyquist plots complex plane impedance spectra

FIGURE 15.6 Complex plane (or Nyquist) plot of the impedance spectrum for the equivalent circuit shown. An example impedance vector at some arbitrary frequency is illustrated by the dashed arrow. Frequency increases in the direction shown by the solid curved arrow. Circuit elements uncompensated solution resistance J s double layer capacitance Cji polarization resistance Rp and diffiasional (Warburg) impedance Z -... 

Figure 4.5 3. Complex-plane or Nyquist plot for the impedance spectrum of a simple series RC circuit.

The major point to note from this analysis is that an impedance spectrum in its most basic representation is a set of points in the complex plane. A plot of -Z" versus Z is termed a Nyquist plot (see Fig. 1.67). 

The impedance Z[s) represents the state of a Li-ion cell in frequency domain and can be illustrated by an impedance spectrum, e.g. in a Nyquist plot in the complex plane, see Figure 3. The impedance is the system function or the frequency response locus which is in case of a Li-ion cell the complex voltage f/( ), i.e. the system response, divided by the complex current /(, i.e. the excitation signal. In frequency domain s = O jca is the complex frequency with a damping term cr and the angular frequency co=l7rf. 

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