Topic 5 min read   # ZSim and ZFit as learning tools. III How to detect an inductive behaviour at low frequencies

Latest updated: October 15, 2021

Inductive arc condition for C1/R1/(R2+L2) circuit

Let us consider the C1/R1/(R2+L2) circuit shown in Fig. 1. Figure1: C1/R1/(R2+L2) circuit.

Its impedance diagram in the Nyquist plane does not always have an inductive arc as shown by the change of the Nyquist diagram when $C1$ varies from $10^{-3}$~F to $10^{-2}$~F (Fig. 2). Figure 2: C1/R1/(R2+L2) circuit: change of the Nyquist diagram when $C1$ varies from $10^{-3}$~F to $10^{-2}$~F.

The inductive character is reflected in the Bode plane by a modulus that shows a peak, even when the sign of the phase does not change and the Nyquist graph no longer contains an inductive arc as it is shown in Fig.3.

Plotting the impedance modulus in the Bode representation, therefore, allows a better detection of the presence of an inductance at low frequencies in an equivalent circuit. Figure 3: C1/R1/(R2+L2) circuit: change of modulus and phase plots of the impedance
when $C1$ varies from $10^{-3}$~F to $10^{-2}$~F.

Moreover, it is easy to check in the Nyquist plane, using ZSim, that the impedance diagram of the C1/R1/(R2+L2) circuit shows a low frequency inductive arc when $C1 < L2/R2^2$.

Conclusion

The Nyquist and Bode plots of impedance are complementary: in this case, the presence of a low frequency inductance not detectable in the Nyquist representation can be detected in the Bode plot.

EIS Nyquist plot Bode plot

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