This oval is known as a "Lissajous Figure". If we plot the applied sinusoidal signal E(t) on the X-axis of a graph and the sinusoidal response signal I(t) on the Y-axis, the result is an oval (see Figure 2). The impedance is therefore expressed in terms of a magnitude, Z o, and a phase shift, Φ. In a linear system, the response signal, I t, is shifted in phase (Φ) and has a different amplitude than I 0.Īn expression analogous to Ohm's Law allows us to calculate the impedance of the system as: The relationship between radial frequency ω (expressed in radians/second) and frequency f (expressed in hertz) is: Where E t is the potential at time t, E 0 is the amplitude of the signal, and ω is the radial frequency. The excitation signal, expressed as a function of time, has the form Sinusoidal Current Response in a Linear System Linearity is described in more detail in the following section.įigure 1. In a linear (or pseudo-linear) system, the current response to a sinusoidal potential will be a sinusoid at the same frequency but shifted in phase (see Figure 1). This is done so that the cell's response is pseudo-linear. This current signal can be analyzed as a sum of sinusoidal functions (a Fourier series).Įlectrochemical impedance is normally measured using a small excitation signal. The response to this potential is an AC current signal. Assume that we apply a sinusoidal potential excitation. Like resistance, impedance is a measure of the ability of a circuit to resist the flow of electrical current, but unlike resistance, it is not limited by the simplifying properties listed above.Įlectrochemical impedance is usually measured by applying an AC potential to an electrochemical cell and then measuring the current through the cell. These elements force us to abandon the simple concept of resistance, and in its place we use impedance, a more general circuit parameter. However, the real world contains circuit elements that exhibit much more complex behavior.
AC current and voltage signals though a resistor are in phase with each other.Its resistance value is independent of frequency.It follows Ohm's Law at all current and voltage levels.An ideal resistor has several simplifying properties: While this is a well known relationship, its use is limited to only one circuit element - the ideal resistor. Ohm's law (Equation 1) defines resistance in terms of the ratio between voltage, E, and current, I. It is the ability of a circuit element to resist the flow of electrical current. AC Circuit Theory and Representation of Complex Impedance Values Impedance Definition: Concept of Complex ImpedanceĪlmost everyone knows about the concept of electrical resistance. Each topic starts out at a quite elementary level, then proceeds to cover more advanced material. No prior knowledge of electrical circuit theory or electrochemistry is assumed. Extracting Model Parameters from Impedance Data.Physical Electrochemistry and Circuit Elements.AC Circuit Theory and Representation of Complex Impedance Values.You will get useful information from this application note, even if you don't follow all of the discussions.įour major topics are covered in this Application Note. If you still find the material presented here difficult to understand, don't stop reading.
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This tutorial presents an introduction to Electrochemical Impedance Spectroscopy (EIS) theory and has been kept as free from mathematics and electrical theory as possible. Basics of Electrochemical Impedance Spectroscopy
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