Use of Network Analyzer and Coaxial Probe to Determine Complex Permittivity
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USE OF NETWORK ANALYZER AND COAXIAL PROBE TO DETERMINE COMPLEX PERMITrIVITY DAVID BLACKHAM
Hewlett-Packard Company, Santa Rosa, CA.
ABSTRACT A vector network analyzer combined with an open ended coaxial probe provides a way to make non-destructive measurements of complex permittivity. These measurements can be made on both solids and liquids. Many authors have done work on using an open ended coaxial line for making these measurements[1][2][3]. They have presented different techniques for modelling the coaxial probe. This paper does not focus on the area of modelling, but deals instead with the use of a vector network analyzer and coaxial probe in making measurements. To enhance measurement accuracy, the technique described adapts a calibration technique currently in use in vector network analysis. An HP 8720B vector network analyzer was used for the development and measurements presented in this paper.
DESCRIPTION OF MEASUREMENT SYSTEM A vector network analyzer system with a coaxial probe provides a stimulus response system that allows permittivity to be measured over multiple decades of
microwave frequency. A simple blockdiagram of the measurement is included in
NETWORK ANALYZER SYSTEM NETWORK-ANALYZER- SYSTEM Incident wave Detectori
I
Relce wave w Reflected
Detector 0 Figure 1. A vector network analyzer ------------------------------- JI consists of a frequency source, signal separation devices and detectors. The Figure 1 frequency source provides the stimulus for the incident signal. Since the incident and reflected waves travel along the same coaxial structure the signal separation devices are required to separate the incident wave and the reflected wave prior to detection. The detectors sense the magnitude and phase of the incident and reflected waves. In this application the vector network analyzer is used to measure the reflection coefficient ( r.) at the open end of the coax probe. r. is a complex number defined as the ratio of the reflected wave over the incident wave. The magnitude and phase of the reflection coefficient depend on the material properties of the sample in contact with the open end of the coax probe. The interrelationship between r. and the complex permittivity
Mat. Res. Soc. Symp. Proc. Vol. 189. ©1991 Materials Research Society
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is established by a model for the coax probe. This model depends on the physical geometry of the coax probe and is derived from a boundary value problem using Maxwell's equations. A polar coordinate system is frequently used to plot r8 . Since the magnitude of the 2.45 GHz reflected wave is always less than or equal to that of the incident wave, the radius of the polar system is unity. The model can be thought of as a bidirectional mapping of permittivity to 2 TEFLON reflection coefficient. The 1 mapping is a function of ` frequency as can be seen in figures 2, 3, and 4. Lines of tan 6 j2 constant real part of permittivity 100 (C,') are plotted for a real part 80 40 60 WATER equal to 1, 5 and increments of 5 up to 100. Lines of constant loss Figure
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