IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 37, NO. 3. JUNE 1989 789 zyx A Free-Space Method for Measurement of Dielectric Constants and Loss Tangents at Microwave Frequencies DEEPAK K. GHODGAONKAR, VASUNDARA V. VARADAN, MEMBER, IEEE, AND VIJAY K. VARADAN, MEMBER, IEEE Abstract-For measurements of dielectric properties of planar slabs of ceramic and composite materials, we have developed a free-space measurement system in the frequencj range of zyxwvutsrq 14.5-17.5 GHz. The key components of the measurement system are a pair of spot-focusing horn lens antennas, the network analyzer, and the computer. Because of the far-field focusing ability of horn lens antennas, the free-space mea- surements can he made at microwave frequencies in a relatively com- pact and simple measurement setup. The inaccuracies in free-space measurements due to diffraction from the sample were minimized by satisfying the condition zyxwvutsrqponml D zyxwvutsrqponm 2 3d, where D and dare the minimum trans- verse dimension of the plate and the heamwidth of the antennas at the focus. The time-domain gating feature of the network analyzer and the thru, reflect, and line (TRL) calibration technique were used to elim- inate the effects of undesirable multiple reflections. The complex re- flection coefficients were measured by inserting a perfectly conducting plate behind the plate of unknown material at the focus of the lens antenna. By implementing an algorithm which finds the zeros of the error function, the dielectric constants and loss tangents were calcu- lated from the reflection coefficients. The dielectric constants and loss tangents were measured for standard materials such as fused quartz, Teflon, and polyvinyl-chloride (PVC). Dielectric properties for Teflon and PVC were also measured in a waveguide medium for purposes of comparison with the free-space method. I. INTRODUCTION N RECENT years, there has been increasing interest in I using free-space techniques for measurement of electri- cal properties of materials and for estimating plasma pa- rameters of magnetoactive plasma zyxwvutsrq [ l]-[3]. In the past, the free-space methods for measurement of complex permit- tivities were used at frequencies above 30 GHz [4]-[6]. Because of the availability of precision horn lens antennas which have far-field focusing ability and recent advances in microwave network analyzers, it is possible to make accurate free-space measurements at microwave frequen- cies. Free-space techniques for electrical property mea- surements are preferred over cavity and waveguide meth- ods for the following reasons. 1) Materials such as ceramics, composites, etc., are in- homogeneous due to variations in manufacturing pro- cesses. Because of inhomogeneity, the unwanted higher Manuscript received February 29, 1988; revised September 3, 1988. The authors are with the Department of Engineering Science and Me- chanics and the Center for the Engineering of Electronic and Acoustic Ma- terials, Pennsylvania State University, University Park, PA 16802. IEEE Log Number 8926909. order modes can be excited at an air dielectric interface in waveguides and cavities. 2) Dielectric measurements using free-space tech- niques are nondestructive and contactless. Because of this feature, these methods are particularly suitable for dielec- tric measurements at high temperature. zyxw 3) In the cavity and waveguide methods, it is necessary to machine the sample so as to fit the waveguide cross section with negligible air gaps. This requirement will limit the accuracy of measurements for materials which cannot be machined precisely. The inaccuracies in dielectric measurements using free- space methods are mainly due to 1) diffraction effects at the edges of the sample and 2) multiple reflections be- tween the two horns via the surface of the sample [2]. The spot-focusing horn lens antennas were used for minimiz- ing diffraction effects due to the edges of the sample. The thru, reflect, and line (TRL) calibration technique and time-domain gating feature of the HP 8510B microwave network analyzer were used to eliminate errors due to multiple reflections. Using this setup, complex reflection coefficients were measured for planar samples of standard materials which are backed by a metal plate. The samples were usually 7 ” x 7’’ x (0.08 to 1)” in dimension. By implementing an algorithm which finds the roots of the error function, the dielectric constants and loss tangents were calculated from the measured reflection coefficients. This novel free-space measurement system is particularly suited for electromagnetic property measurements of chiral composites, ceramic, and polymer samples. Cur- rently, this setup operates in the frequency range of 14.5- 17.5 GHz. However, by changing a few components such as the horn lens antennas, transitions, etc., this free-space measurement setup could be used in the frequency range of 8.2-100 GHz. 11. MEASUREMENT SYSTEM A block diagram of the measurement setup is given in Fig. 1. In this setup, a pair of spot-focusing horn lens antennas have been mounted on a large table (6’ x 6‘) of 1” thick aluminium. For these antennas, the ratio of focal distance to diameter of the lens (F/D) is equal to one and 001 8-9456/89/0600-0789$01 .OO O 1989 IEEE