# Portable and Highly Versatile Impedance Meter for Very Low Frequency Measurements
## 3 Results and Discussion
### Preliminary System Testing
Moreover, as we shall discuss in the following, larger ENBs can usually be used without introducing large errors, thus considerably reducing the measurement time. As the test frequency increases, shorter and shorter measurement times are required, and this leads to the conclusion that the overall measurement time is essentially set by the lowest frequency of interest. The results of the measurements on the first test DUT (Figure 6a) are reported in Figure 8 (symbols) and compared to the expected calculated values (continuous lines). As it is apparent, a quite good agreement is obtained with the DUT impedance values changing by a factor of about 1000 over the explored frequency range. A second set of test measurements was performed on the test impedance in Figure 6b. The 200 uF capacitor was obtained as the parallel of 20 10 uF polyester capacitors. The amplitude for the AC signal was still 10 mV, but in this case, a DC bias of 500 mV was also present with the carrier removal block in Figure 3 active to reduce the leakage from the peak at the carrier frequency. As before, as can be noted in Figure 9, a quite good agreement is obtained between measured data (symbols) and expected values (continuous lines). As we have mentioned above, the values of the impedance reported in Figures 8 and 9 were extracted from the spectra estimated with the largest available ENB for which ENB \(<\)\(f_{LF}/5\). It must be noted, however, the QLSA performs the calculation of the spectra corresponding to all the different available ENBs in parallel. This means, for instance, that even if we focus on _ENB_\({}_{10}\) for \(f_{LF}\) = 10 mHz, as in the example discussed above, spectra corresponding _ENB_\({}_{9}\), _ENB_\({}_{8}\), and so on are being calculated as well and, because of Equation (23), estimates corresponding to lower index ENBs become available before the first estimate for a higher index ENB is available. This means that by observing the estimates obtained for lower index ENBs as they become available, if consistent data are obtained for increasing indexes, one can stop the measurement before the estimate for the targeted high index ENB is obtained, thus saving time. This is exemplified in Figure 10 where the estimate of the modulus of the impedance of the DUT in Figure 10 is reported for the three lowest frequencies vs. ENB. The symbols encircled in green  
Figure 8: Result of test measurements on the impedance in Figure 6a. DC bias across the DUT was set to 0 and the AC amplitude of the test voltage was 10 mV at all frequencies. Quite good agreement is obtained between measurements (symbols) and the expected values (solid lines). represent the measurement points reported in Figure 9 and corresponding to \(ENB<f_{LF}/5\). If one had to build the sequence of symbols corresponding to one of the measurement frequencies in Figure 10 in real time during the measurement, the symbols at the right would become available first, followed by the symbol at their left and so on until enough time is elapsed for the estimation corresponding to the leftmost symbols to become available. In observing each sequence of symbols as they become available, it could have been assumed with great confidence that the symbols encircled in blue would have represented the correct value of \(|Z|\) even before the symbols encircled in green (the ones actually used in Figure 9) would have become available, thus saving measurement time. The ability to monitor the progress of the estimation over a number of different ENB settings at the same time is a peculiar feature that is available in QLSA and that, to the best of our knowledge, has no equivalent in other measurement approaches. Proper application software can therefore be developed, based on this unique feature, to optimize measurement time while ensuring the absence of errors due to spectral leakage. Figure 10: Results of the estimation of the modulus of the impedance of the DUT in Figure 6b as a function of the ENB for the three lowest explored frequencies.