# Portable and Highly Versatile Impedance Meter for Very Low Frequency Measurements
## 1 Introduction  
Electrical Impedance Spectroscopy (EIS) is a non-invasive testing technique that has been extensively used and applied in several research fields. In medicine, for example, EIS (or BIS, Biological Impedance Spectroscopy) has proven to be an effective technique for non-invasive analyses and diagnosis of the healthy condition of subjects in a few medical fields [1, 2, 3, 4, 5, 6, 7, 8] and furthermore, it seems to be appropriate for the characterization of the physicochemical properties of pharmaceutical materials [9] and of bacteria [10, 11, 12] and viruses [13, 14]. The complex impedance of biological tissues exhibits different behaviors as the frequency varies in a very wide range [15] and different phenomena have been recognized, which are responsible for such variations [16]. Although it is well established that these variations of behavior occur from frequencies close to dc up to frequencies in the order of MHz (and, in some cases, GHz), the frequency range of 10 kHz-100 kHz has been considered the most suitable for BIS measurements [17, 18, 19, 20] and the frequency of 50 kHz [21] has often been chosen for data interpretation. Other researchers have lowered the minimum investigation frequency to 100 Hz [22, 23]. This implies that bio-impedance measurements have so far neglected the effects due to the so-called \(\alpha\) dispersion [16], which takes into account the relaxation of ions surrounding the charged cellular membrane and which dominates the impedance behavior from 0 Hz to a few hundred Hertz. Although the results obtained at higher frequencies can be in some cases regarded as reliable and satisfactory, one cannot fail to consider that without measurements in thevery low-frequency range the characterization is incomplete and important, and useful information might be possibly missed [24]. Therefore, having an instrument capable of carrying out very low frequency impedance measurements would be useful in the field of bioengineering. This is however true also in other fields. EIS is also used for the characterization of the electrochemical behavior of energy storage devices and electrode materials for supercapacitors, batteries and fuel cells [25; 26; 27; 28]. As in the case of medical and biological applications, also in these applications the elements to be characterized are modeled by means of multi-element models. As a consequence, the impedance measurements have to be performed in a wide frequency range and, also in these cases, down to very low frequencies, extending in some cases below 1 mHz [29]. In the worldwide market, impedance analyzers with very good performances and capable of performing measurements of this type are available (Solartrton, Novocontrol, Zahner, Hioki, CorrTest) [30; 31; 32; 33; 34], but this kind of general-purpose instrumentation is characterized by high complexity and, inevitably, high costs. On the basis of these considerations, our work has been focused on the realization of a low-cost and yet high versatile hardware platform for the development of low frequency impedance measurement applications. In designing the system, we regarded the ability to easily reproduce it as the most important feature to be achieved, so that any researcher can take advantage of its potentialities in any given field of application. For this reason, we have sacrificed a high degree of automation for simplicity, so that some of the adjustments required for the optimization of the sensitivity depending on the characteristics of the Device Under Test (DUT) have to be done by manually changing a few key components in the system, via a snap-in/snap-out approach. Moreover, the system is highly modular so that one can take advantage of the core components while designing a dedicated front end for specific applications. At the same time, since capacitive parasitic components are not the main concern at very low frequencies, high configurability can be easily implemented by resorting to low-cost switch matrices controlled by a personal computer.