Michael Reznikov
The difference is not in the method but in the frequencies range that results in the different measurement cells. LCR method works well up to 1 MHz, when you can use the parallel electrodes cell (capacitor). For higher frequencies, the coaxial measurement cell (in fact, the waveguide) is preferable and correspondingly the data from network analyzer (scattering parameters) are more natural. Depending on your object (as I can see, the microwave ceramics), the LCR method will lead to false spectra due to parasitic capacitances in the probe (measurement cell) for the material sample. But if your object is the real m/w component, LCR is OK because it reveals these parasitic effects in the component.
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