Lissajous analysis

Lissajous analysis, as an experimental approach for impedance measurement, is obsolete and has been replaced by methods using automated instrumentation. Lissajous plots, however, have great pedagogical value as a means of learning impedance spectroscopy. In addition, as discussed in Section 8.2, use of oscilloscopes is recommended for monitoring the progress of impedance measurements, and oscilloscopes capable of displaying Lissajous plots are particularly useful. 

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Fourier analysis and phase-sensitive detection are conunonly used to convert time-domain signals into the frequency domain. For contextual purposes, the mathematical transformations used by Fourier analysis and phase-sensitive detection instruments are reviewed in the following subsections. Such systems have replaced the Lissajous analysis described in Section 7.3.1. The Lissajous analysis is useful. 

Example 7.1 Lissajous Analysis Use a Lissajous plot to find the impedance at a frequency of 100 Hz for a linear system with capacity Qi = 31 pP/cm, charge-transfer resistance Rt = 51.34 dcm, and a potential perturbation AV = 0.01 V. 

Lissajous analysis is another method of presenting MTDSC data that allow the operator to monitor whether the sample is in steady state or otherwise. In the case of MTDSC, the Lissajous figure is obtained by plotting the derivative of the mod-... 

Figure 4.79. Reversing heat flow rate and Lissajous figure of the quasi-isothermal analysis at...

Analysis of Lissajous figures on oscilloscope screens was the accepted method of impedance measurement prior to the availability of lock-in amplifiers and frequency response analyzers. Modern equipment allows automation in applying the voltage input with variable frequencies and collecting the output impedance (and current) responses as the frequency is scanned from very high (MHz-GHz) values where timescale of the signal is in micro- and nanoseconds to very low frequencies (pHz) with timescales of the order of hours. 

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