Measurement of Axially Inhomogeneous Permittivity Distributions in Resonant Microwave Cavities

5.4.4 Homodyne Vector Network Analysis as a Tool for the Real-Time Measurement of Electrical Material Parameter Distributions in the Field

“…Axially varying material parameters inside a cavity may be resolved by evaluating several cavity resonances [6]. (Note that in many tubular reactors the material parameters are inhomogeneous in the direction of the flow but can be assumed to be homogeneous over the cross-section with little error [1], [2].)…”

“…It looks as if VNA A consistently returns resonance frequencies that are slightly too high, which may be a consequence of an offset error in its frequency base. As the fractional frequency deviation is only about 50 ppm (corresponding to 100 kHz for a 2-GHz resonance), the error may be neglected in practice, as reconstruction algorithms can cope with it [6]. Otherwise the error can be compensated in software by simply adding or subtracting an offset to or from the resonance frequency.…”

“…The frequencies at which resonances occur are influenced by the electrochemical material parameters inside the cavity. We have dealt with several aspects of this method [6], [7], but the availability of low-cost equipment suitable for field (in-process) use remains an open issue. Potentially viable approaches include the use of mobile-phone equipment [8] and of application-specific scalar network analysis [9].…”

Monte-Carlo-Methode zur Verringerung von Messfehlern bei der Materialparameterbestimmung mit Hohlraumresonatoren

“…Ziel ist es, anhand gemessener Resonanzparameter den Segmenten die Materialparameter zuzuordnen. Dazu existieren zwei Verfahren, eines mit [6] und eines ohne Nebenbedingung [5].…”

“…Durch sorgfältiges De-Embedding können unbelastete Resonanzparameter (Resonanzfrequenz werden [4]. Anhand der unbelasteten Parameter mehrerer Resonanzen kann auf die Materialparameterverteilung im Resonator rückgerechnet werden [5]. Dabei wird zunächst unterstellt, dass die Materialparameter nur in longitudinaler Richtung (im Beispiel: in Fließrichtung der Reagenzien) variieren, in transversaler Richtung aber als homogen genähert werden können.…”