Another problem arises with the measuring method itself used by certain equipment. In the era of computers it seems easy to change from the traditional analogue scan technique to its digital approximation by a small steps stairs technique. This task can be done by a software controlled D/A converter. The advantage of such a technique is the possibility to easily produce arbitrary wave forms, for instance stable slow signals (slew rate down to zero). The measurement itself too can be performed with the computer using A/D converters. This is the base for flexible and user-friendly CV equipment - but the stair-sweep-approximation idea is too simple to be good! Signals, created by a DA-converter remain discrete. Even if one tries to increase the resolution dramatically, it will stay finite. On the other hand the theories of CV techniques claim steady sweep signals.

Regarding capacitive objects will help to focus on this important difference. If one applies a voltage signal U(t) to a capacitor, the current I(t)=C·dU/dt will flow. A constant slew rate results in a constant current. Discrete steps will cause current pulses with d-pulse shape - that means in theory infinite height for an infinite short time interval but with a well defined integral charge of Q=C·DU. In practice the d-pulse will be distorted to a short pulse of high amplitude. Its shape is determined by the pulse response of the potentiostat and parasitic effects. If the measurement technique samples the response signal after a short time delay relative to the step, the result must be wrong! The only way to get a correct current result is to measure the charge by integrating the total step interval and calculate the mean current. This calculated current value is identical with the measured one with the continuous method.

How can you find out, if your equipment uses this "clean" integrating CV technique? Take an aluminum electrolyte capacitor of 1 mF and perform a test measurement. Choose, for instance, a triangle scan of ±1 V at ±100 mV/s slew rate. The  capacitance of 1 mF should cause a square wave of ±0.1 mA current to flow. Consider the capacity tolerance of -5 % / +25 %. Check the correct capacity using an impedance measurement at low frequency (e.g. 1 Hz): Now the measured current should fit the calculated current exactly.

If not, call the service-hotline of your equipment's manufacturer!

In contrast the minimum measuring time of MS (sine wave) experiments is given by the sum of periods n_e,i of all frequencies w_i to be measured.

A comparison of typical measuring times for both methods is quite difficult as there are some unknown scaling factors. Under the assumption of an ideal measuring object where no ranging processes will occur, the scaling factor f_res in first order depends on the number of measuring points of the lowest decade.
 

The ratio of e.g.

This shows a slight advantage for PS. If, however, at least one ranging process is necessary during measurement, this factor will be reduced to about 1.3. In PS methods ranging processes dominate the measuring time (T, 2T, 3T, etc), while MS can use dynamic ranging. Then the measuring time is extended only by a factor of 1/n, depending on the measuring frequency nw₀. You see clearly, that the simple speculation to save time will not work very good, even neglecting all aspects of accuracy. But in addition, using PS, the total energy of the signal will be spread over all examined frequencies. Only the average fraction E_f » E/n, compared with the monochromatic case will be available for one frequency line. To avoid nonlinear response, the AC amplitude has to be selected sufficiently low. Thus polychromatic stimulation has to be repeated n times to obtain a sufficient signal to noise ratio. This leads to significant longer measuring times than in the case of single sine methods which contradicts the expectations of the user. This fact has been proved by Miloco in 1994 [1]

Nevertheless, regarding non steady state system research, there is a gap, where PS shows clear advantage. In the higher frequency range (>100 Hz) the pure measuring time will no longer dominate the overall time. Most of it is spent by the instrument's microprocessor system analyzing the incoming data after each frequency sample. In the PS case, the sum of all this analysis time appears at the end of a measurement, the measurement itself is much faster. This is an advantage when studying non steady state systems. For this application the PS method was developed further by Schindler and Popkirov [2]. A version of PS can be performed with the IM6, extended by the TR8M transient recorder module.

It must be mentioned, that regarding non steady state behavior, there are several possibilities to increase the reliability of the AC impedance results, if measurement time reduction is impossible:
a) IM6 on-line drift correction: Periodic stimulation offers the detection of non steady state behavior of the investigated system. The IM6 performs an automatic drift correction in the lower frequency mode.
b) LKKT (Logarithmic Kramers Kronig Transform): By means of the LKKT [3] not only violations of the EIS fundamentals of the examined system may be detected. The LKKT version in the THALES analysis software allows the reconstruction of non-affected spectra, if the violations are not too strong.
c) Interpolation of impedance spectra series versus time: Series measurements vs. time offer a further possibility to correct impedance spectra of drifting systems. Under the assumption of slow rates of changes the data may be corrected. The spectra can be transformed by an interpolation routine generating new ones, belonging to unique times. Finally each of those spectra will represent a certain state of the electrode. [4,5] This method is also available in the THALES software package.

[1] Ruben H. Milocco: Minimal measurement time in electrochemical impedance identification. Electrochimica acta, Vol.39, No.10, pp 1433-1439, 1994
[2] G.S. Popkirov and R.N. Schindler: A new impedance spectrometer for the investigation of electrochemical systems. Rev. Sci. Instrum. 63 (11), 1992
[3] H. Göhr, B. Röseler and C.A. Schiller: Advantages of Hilbert Transform compared with Kramers-Kronig Rule when examining the causality of electrochemical impedance spectra. Presented at the 46th ISE Meeting, Xiamen, China, 1995
[4] Z. Stoynov: Nonstationary impedance spectroscopy. Electrochem. Acta 38, no. 14, pp. 1919-1922 (1993)
[5] H. Göhr, H. Bode, A. Burghart and C.A. Schiller: Impedance measurements at electrodes of continuously changing state. Presented at the 2nd EIS Symposium, Santa Barbara, USA, 1992

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