Impedance absolute magnitude

Here, Z is the absolute magnitude of the impedance. What allows us to separate different electrochemical processes using EIS is the fact that capacitors have a frequency-dependent ability to be charged or discharged - a property called capacitive reactance. As a consequence, different capacitances within the system will respond at different frequencies, allowing us to separate temporally the electrochemical processes in EIS experiments on the basis of their capacitive reactance. Similarly, diffusion limitations usually also have a characteristic low frequency where they predominantly govern the system response and thus are easily distinguishable. 

The information provided by EIS can be plotted in different graphical representations. Figure 8.2 shows one common representation of EIS data, called a Bode plot. In a Bode plot, the absolute magnitude of the impedance (Fig. 8.2a) and the phase shift (Fig. 8.2b), both of which are experimentally measured, are plotted against... 

A Bode plot (Figure 7.60) displays the impedance Z against the frequency. The absolute value of the amplitude A (o>) and the phase angle rp(co) of the frequency response are separately plotted over the frequency co. A co) and co are usually displayed on a logarithmic scale whereas rp(co) is plotted linearly. The dimension of A(co) is in decibels (dB), and by definition A()dB = 20 log A co). Consequently, the logarithmic representation of A has a linear scale called the magnitude. 

As already described, a magic-tee is a four port device in which two of the ports are isolated, i.e., have infinite impedance between them if the impedances at the other two ports are matched. Thus, the device can be used to match a resonant circuit to 50 Q or, for that matter, to measure the impedance at resonance of the tank circuit. The tank circuit under question will have impedance R at resonance when the output of the magic-tee, easily monitored on an oscilloscope, is an absolute minimum. (See the figure under magic-tee on p. 393.) Unfortunately, this is easier said than done because there are relative minima when the capacitors are adjusted to give an impedance which is, for example, equal to R in magnitude but with an imaginary component. When you play around with a scheme like this for the first time, it will be useful to let R be variable so that it can be adjusted for a... 

The impedance is therefore expressed in terms of a magnitude (absolute value), Za = jZj, and a phase shift, . Impedance is an alternating current (AC) phenomenon that is usually specified at a particular frequency. By measuring impedance across a number of frequencies, a valuable data about an element can be extracted. This is the basis of impedance spectroscopy, and it is the fundamental concept underlying many industrial, instrumentation, and automotive sensors. 

The maximal deviation is 6 mO. (equals 9% at this frequency), whereas the largest relative deviation of the impedance magnitude is at 14%. The reason for the curves drastically different patterns is the vast acquisition range the impedance magnitude is measured in. On the graph in the bottom left corner of Fig. 7 you can see the simulative impedance/phase plot and the average value curves of the measured results for all measurement equipment. The smallest impedance is 1 mQ at 1 kHz and the maximal deviation of 14% refers to an absolute value of 140 pQ. 

---