## 4 Experimental Results and Comparative Analysis  
For this study, an equivalent experimental setup with PSPICE(r) simulations was used. The methodology was based on a network analyzer to measure the resonant frequency in equivalent RL shunt damping [12] experiments. Based on Equations (4) and (6), the value of the VCSI inductance is a function of \(RC_{g}\), and in practice, can be easily modified using a new value for the capacitor. Some adjustments are also possible using new values for resistors \(R_{1}\), \(R_{2}\), and \(R_{3}\), or only \(R_{3}\) to ensure very simple tuning facilities. The static capacitance of the PZT patch and VCSI value of inductance are responsible for the resonance frequency of the electrical circuit \(\omega_{e}=1/\sqrt{LC_{PZT}}\) and the static capacitance of the PZT patch is the first element that has to be identified before starting the VCSI design. A schematic of the experimental configuration is shown in Figure 5. The measurement system is built around a virtual vector network analyzer (SpectraPLUS-SC(r), version 5.3.0.2, Pioneer Hill Software LLC, Poulsbo, WA 98370, USA) to investigate a VCSI in parallel with a capacitor with an equivalent value of the static capacitance of the PZT patch (26 nF) used in the RL shunt vibration damping experiments. The virtual vector network analyzer was configured to measure a complex transfer function in 24 bits sampling format with a 0.732 Hz spectral line resolution. A white noise excitation signal is generated by software using a DDS (direct digital synthesis) algorithm. The USB interface used for data acquisition contained a performant coder-decoder circuit (CA0187-IAQ) boosted with a high impedance and very low noise amplifiers for both input channels. The excitation signal from the output of the coder-decoder circuit was passed through a power amplifier with a standard 50 \(\Omega\) output impedance. An external power supply (\(+/-\) 24 V, HP-6236B) was used and voltage control was derived from it in a \(-10\) V to 10 V range based on a precision voltage reference (AD584) and op-amps (OP27) in a voltage follower configuration. The simulation and experimental results for both versions of the VCSIs are shown in Figure 6a. To ensure a realistic comparison for both versions of the VCSI, an equal range for the voltage control was considered. For VCSI implemented with an AD633 analog multiplier as a V  
Figure 5: Experimental setup based on virtual vector network analyzer. to keep the error less than 0.5 Hz was obtained for the voltage control from \(-\)10 V to 2 V. In the case of a VCSI implemented with OTA LM13700 as a VCR, in the condition aforementioned, the linear response was obtained for the voltage control between \(-\)2 V to 10 V. For particular implementations presented in this paper, the frequency range was 8.4 Hz for the VCSI based on LM13700 and 8.9 Hz for the version with AD633. It can be considered that both VCSIs covered equal linear frequency domains for an equivalent voltage control range with a medium resolution of 0.72 Hz/V. With the experimentally validated linearity and its unique very high resolution, the new VCSIs analyzed in this paper outperformed the previous analog circuits [11; 12] presented up until now in literature. From analysis of the residuals, for the identical voltage control range presented in Figure 6b, it can be concluded that the VCSI based on AD633 had a better linearity in comparison with the LM13700 version. Both VCSIs had an equivalent frequency domain for identical linear voltage control ranges and met the condition of having a frequency deviation less than 0.5 Hz to produce with linear behavior. From the experimental point of view, the VCSI based on an analog multiplier (AD633) was more easily implemented using only a resistor mounted external to the integrated circuit. Figure 6: Voltage-controlled synthetic inductor: (**a**) simulation, experimental results, and linear fitting; and (**b**) comparative residuals analysis for equal voltage control ranges.