Chapter 2
Methods and techniques
Course notes
2.1 – Complex impedance spectroscopy
Complex impedance spectroscopy measures the response of an electrochemical system to a small-amplitude ac voltage perturbation of variable frequency
around a steady-state operational point.
2.1.1 – Time domain: principal passive linear dipole devices in sinusoidal regime
We denote voltage and current by v(t) and i(t), respectively. The current-voltage
characteristics of the principal dipole devices in the time domain are
For a resistance R
v(t) = R i(t)
For a capacitance C
( )
( )
v t
C i t dt
1
t
=
#
For an inductance L
( )
( )
v t
L dt
di t
=
2.1.2 – Complex notation
The instantaneous complex expressions for v and i of the voltage v(t) and the
current i(t) respectively derive from the real expressions
v(t) = V sin(ωt + α)
v = V e
jα
e
jωt
i(t) = I sin(ωt + β)
i = I e
jβ
e
jωt
© Springer Nature Switzerland AG 2020
A. Hammou and S. Georges, Solid-State Electrochemistry,
https://doi.org/10.1007/978-3-030-39659-6_2
47