# Portable and Highly Versatile Impedance Meter for Very Low Frequency Measurements
## 2 Materials and Methods
### Hardware Configuration
From this point of view, it would be desirable to select a value for \(f_{PAV}\) as low as possible and indeed, one can even select values of \(f_{PAV}\) very close to the maximum frequency of interest since neither the modulus nor the phase of the frequency response contributes to the determination of the DUT impedance (Equation (16)). Note, however, that while the value of \(f_{PAV}\) has no effect on the DC component of \(v_{DUT}\), one must be aware of the fact that it may result, for the higher test frequencies \(f_{LF}\), in a reduction of the amplitude of the AC test signal across the DUT with respect to the intended value. Because of the virtual short at the input of the TIA, the voltage \(v_{DUT}\) is actually the voltage across the DUT. The current through the DUT at the input of the transimpedance amplifier is transformed into a voltage signal through the response \(A_{R}\) of the TIA (Equation (10)). As we have discussed above, unlike the frequency response of the VA, the frequency response of the TIA directly contributes to the measurement results, and it must be known in order to extract the admittance of the DUT according to Equation (16). There are several factors that contribute to the selection of the most proper values for \(R_{R}\) and \(C_{R}\) depending on the nature of the DUT and on the measurement conditions. As a general rule, the gain \(A_{R}\) must be such that we can obtain the largest signal \(v_{ID}\) provided it does not exceed the input dynamic range of the multiplier \(M_{3}\) (\(\pm 1\) V). If we were to set \(C_{R}=0\) in order to obtain a constant transimpedance gain, the fact that the DUT impedance is expected to have a large capacitive component would result in two undesirable effects: (i) the noise and interferences at node \(v_{DUT}\) at higher frequencies would result in large noise components at the output \(v_{ID}\); (ii) for the same AC level, we would obtain a much larger output at the higher end of the explored frequency range with respect to the lower frequency end and it might not be possible, with \(R_{R}\) alone and especially in the presence of a DC component, to ensure linearity and sufficient sensitivity in an extended frequency range. A carefully selected \(C_{R}\) can therefore help in reducing the gain in the higher explored frequency range while ensuring, at the same time, a considerable attenuation of all high frequency disturbances. Clearly, for a proper choice of \(R_{R}\) and \(C_{R}\), one needs some information on the DUT. When such information is not available beforehand, as it is expected to be the case in many situations, one must proceed with preliminary experiments starting with lower values of \(|A_{R}|\) and, once a rough estimate of the impedance of the DUT is obtained, more proper values for \(R_{R}\) and \(C_{R}\) can be selected. Since \(C_{R}\) and \(R_{R}\) are likely to be changed any time a new DUT is changed, in our prototype a ZIF socket is used to hold them in place so that the user can easily select different values. On the other hand, since parasitic capacitance is not a concern at very low frequencies, an automated system for switching among different values of \(C_{R}\) and \(R_{R}\) can be easily obtained by resorting to a relay switch board that can be easily purchased on the market already equipped with an interface for its control by the PC. While in a production environment this may represent a necessity, in a research environment the nuisance of manually changing the values of \(C_{R}\) and \(R_{R}\) from time to time must be weighed against the extremely simple hardware that can be used in this case. We must remark on the fact that we are using the simple front end in Figure 2 as a realistic platform for demonstrating the effectiveness of the approach we propose. For any given class of DUTs, the front-end may change significantly, and we judged that proposing a fully automated system in the context of this work was not really necessary.