The Bode Plot below demonstrates how the EIS instrument interprets the response to an electrical stimulus. It is a Bode Plot of a single Randles Equivalent Circuit Model, ECM, in series with an inductor. Impedance (red, blue and green) is plotted using the right Log y-axis. To present both capacitance and inductance (i.e. negative Zimag) on a positive Log impedance axis, the inductance is mirrored by using the absolute values of Zimag/Zreal and Zimag. The impedance y-axis can be a Log axis for wide dynamic ranges (e.g high impedance barrier films) or can be a linear axis for narrow dynamic ranges (i.e. batteries). The impedance Ratio, Zimag/Zreal, shown as the black dashed line, is plotted using the left y-axis. The Ratio emphasises Zimag or Zreal dominance along a current path rather than more obscure phase angle, ArcTan(Zimag/Zreal).

The Zreal red curve has a maximum, R2, and a minimum, R1, with a negative sloped region in between. The Zimag blue curve for the capacitance response has a peak, R2/2, with a positive and negative sloped region on either side as n*Log(2p*freq*C1). The portion of the Zimag curve for the inductance contribution, at high frequency, has a positive sloped region as Log(2p*freq*L1). The Zmag green curve  shows the impedance response of the overall ECM; R2 at low frequency, a negative sloped region inline with Zimag (i.e. the capacitance dominance), a minimum at mid frequency, and a positive sloped region inline with Zimag (i.e. inductance dominance). The ratio, Zimag/Zreal, essentially shows the transition between Zimag and Zreal dominance as a function of Log frequency; resistance limiting at Log Frequency between -1 and 1.2, capacitive blocking at 1.2 to 3.2, resistance limiting at 3.2 to 5.2, and finally inductive blocking above 5.2.

Traditionally, the Randles ECM form is interpreted as a parallel R2-C1 relaxation response in series with a resistance R1. The relaxation parallel time constant for the response occurs at the maximum of the Zimag curve (i.e. R2/2). However, the EIS instrument interprets the ECM as a series R1-C1 current path in parallel with a bypass resistance, R2. The bypass filter has a series time constant, Fc, where Zimag begins to block current through the filter. For the R-C filter, current is limited above and blocked below Fc. For the R-L filter, current is limited below and blocked above Fc. Thus, characteristic features in the system represent either capacitive (RC) or inductance (RL) current filter paths.

Initial parameter values can be estimated from the position of Fc on the Zimag/Zreal curve, either the leading edge on the high frequency side of a peak (shown), or as in the case of multiple responses an inflection point in the curve (not shown). At Fc, R1 is the value of Zreal, n is the slope of Log(Zimag), and C is calculated from n*Log(2p*freq*C1). Thus, the Zimag/Zreal presentation is useful both in estimating fit parameters and observing fit convergence as a line through data points on a linear y-axis.

The y-axis of the Bode plot can also be changed to line graph ‘SpecView’ presentation using a Gaussian equation. This allows graphically overlaying multiple data sets. The Gaussian peak height can represent capacitance (left) or thickness, d =ee*A/C, (right) , peak position as either Fc (left) or Resistance (right), and peak width proportional to the power law parameter n. Below are shown results for high impedance anodic films on Zirconium; verses Log Freq (left) and Log R (right).