Summary

EIS measures the impedance of a system by applying a small sinusoidal voltage (or current) over a range of frequencies and recording the corresponding current (or voltage).

Experiment

• Sinusoidal voltage of ~ 10mV over a frequency range is applied
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• Current response is recorded and the impedance calculated
• Bode plot and Nyquist plots constructed

Theory

• Impedance: $Z(\omega )=\frac{V(\omega )}{I(\omega )}$
  • $Z(\omega )$ Impedance (complex)
    $V(\omega )$ Applied voltage
    $I(\omega )$ Measured current
    $\omega$ Angular frequency $\omega =2\pi f$
• $Z(\omega )=Z^{\prime }-j{Z}^{\prime \prime }$
  • $Z^{\prime }$ Real part, resistor like behaviour
    $Z^{\prime \prime }$ Imaginary part, capacitive and inductive
    $i$ Imaginary unit where $i^2=-1$
• Resistor: $|Z|=R$
• Capacitor: $|Z|=\sqrt{\frac{-j}{\omega C}}$

Spectrum

• Nyquist Plot
  • Real (X) vs. Imaginary (Y)
• Warburg Impedance
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  • Due to the movement of ions
• Bode Plots are $\log |Z(\omega )|$ vs $\log f$ and $\varphi$ vs $\log f$:
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• Resistor in series with capacitor
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• Resistor parallel with Capacitor
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• Randles equivalent circuit
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