Michael D. Janezic

Complex permittivity determination from propagation constant measurements

The authors present a new transmission line method for measuring the complex permittivity of dielectric materials using propagation constant measurements. In contrast to previous methods, a network analyzer calibration is unnecessary since calibrated scattering parameters are not required. They use measurements in X-band waveguide to show that this technique compares well with the transmission/reflection and cylindrical cavity methods.

Analysis of an open-ended coaxial probe with lift-off for nondestructive testing

The open-ended coaxial probe with lift-off is studied using a full-wave analysis, and an uncertainty analysis is presented. The field equations for the following terminations are worked out: (1) the sample extends to /spl infin/ in the positive axial direction, (2) the sample is backed by a well-characterized material, and (3) the sample is backed by a short-circuit termination. The equations are valid for both dielectric and magnetic materials. The model allows the study of the open-ended coaxial probe as a nondestructive testing tool. The analysis allows a study of the effects of air gaps on probe measurements. The reflection coefficient and phase are studied as a function of lift-off, coaxial line size, permittivity, permeability, and frequency. Numerical results indicate that the probe is very sensitive to lift-off. For medium to high permittivity values and electrically small probes, gaps on the order of fractions of a millimeter strongly influence the reflection coefficient. In order for the field to penetrate through the air gap, larger size coaxial line or higher frequencies need to be used. A comparison of the theory to experiment is presented. The results are in close agreement. A differential uncertainty analysis is also included. >

Dielectric characterization of low-loss materials a comparison of techniques

Measurements on low-loss materials using closed and open cavity resonators, and dielectric resonator methods are presented. Results indicate that consistent measurement results can be obtained with a number of well-characterized fixtures. Uncertainties associated with each method are addressed. Measurements also were performed on materials used in previous intercomparisons.

Full-wave analysis of a split-cylinder resonator for nondestructive permittivity measurements

This paper presents a full-wave analysis of the split-cylinder resonator. We outline a model where the fringing fields are rigorously accounted for and the resonance condition is derived. Using this model, a method for nondestructively measuring the complex permittivity of materials is examined. Measurements of the complex permittivity for low-loss dielectric materials using the split-cylinder resonator agree well with measurements made in a cylindrical cavity. An uncertainty analysis for the complex permittivity is also provided.

Quantitative Permittivity Measurements of Nanoliter Liquid Volumes in Microfluidic Channels to 40 GHz

We describe the design, fabrication, and evaluation of a new on-wafer measurement platform for the rapid and quantitative determination of the complex permittivity of nanoliter fluid volumes over the continuous frequency range from 45 MHz to 40 GHz. Our measurement platform integrates micrometer-scale poly(dimethylsiloxane) (PDMS)-based microfluidic channels with high-frequency coplanar waveguide (CPW) transmission lines to accurately place small fluid volumes at well-defined locations within planar measurement structures. We applied new on-wafer calibration techniques to accurately determine the scattering parameters of our integrated devices, and we developed a transmission-line model to extract the distributed circuit parameters of the fluid-loaded transmission line segment from the response of the overall test structure. All the necessary model parameters were experimentally determined directly from a single set of measurements without requiring a reference fluid of known permittivity. We extracted the complex permittivity of the fluid under test from the distributed capacitance and conductance per unit length of the fluid-loaded transmission line segment using finite-element analysis of the transmission line cross section. Our measurements show excellent agreement with bulk fluid permittivity determinations for methanol at room temperature and yield consistent results for the extracted fluid permittivity for the same microfluidic channel embedded in multiple CPW transmission lines of different dimensions.

Permittivity characterization of low-k thin films from transmission-line measurements

Developed a broad-band technique for measuring the relative permittivity of low-k thin films using microstrip transmission-line measurements. From measurements of the complex microstrip propagation constant and the characteristic impedance, we determined the relative permittivity of thin films incorporated in microstrip lines. We present measurement results to 40 GHz for both an oxide and a bisbenzocyclobutene low-k thin film and show a variability of permittivity of approximately /spl plusmn/5% over the entire frequency range.

High-frequency dielectric measurements

The demands on dielectric material measurements have increased over the years as electrical components have been miniaturized and device frequency bands have increased. Well-characterized dielectric measurements on thin materials are needed for circuit design, minimization of crosstalk, and characterization of signal-propagation speed. Bulk material applications have also increased. For accurate dielectric measurements, each measurement band and material geometry requires specific fixtures. Engineers and researchers must carefully match their material system and uncertainty requirements to the best available measurement system. Broadband measurements require transmission-line methods, and accurate measurements on low-loss materials are performed in resonators. The development of the most accurate methods for each application requires accurate fixture selection in terms of field geometry, accurate field models, and precise measurement apparatus.

Shielded open-circuited sample holder for dielectric measurements of solids and liquids

This paper presents a technique for permittivity measurements that can be used for either liquids or solid coaxial samples from near dc to gigahertz frequencies. The method uses both a full-mode model of a coaxial open-circuited termination and a capacitive method for permittivity determination. The method requires the use of an impedance bridge and a network analyzer. Measurements indicate good accuracy for the permittivity over a very wide band of frequencies. For high permittivity materials the sample surfaces must be metallized. An uncertainty analysis is also presented.

Estimation of Q-factors and resonant frequencies

We estimate the quality factor Q and resonant frequency f/sub 0/ of a microwave cavity based on observations of a resonance curve on an equally spaced frequency grid. The observed resonance curve is the squared magnitude of an observed complex scattering parameter. We characterize the variance of the additive noise in the observed resonance curve parametrically. Based on this noise characterization, we estimate Q and f/sub 0/ and other associated model parameters using the method of weighted least squares (WLS). Based on asymptotic statistical theory, we also estimate the one-sigma uncertainty of Q and f/sub 0/. In a simulation study, the WLS method outperforms the 3-dB method and the Estin method. For the case of measured resonances, we show that the WLS method yields the most precise estimates for the resonant frequency and quality factor, especially for resonances that are undercoupled. Given that the resonance curve is sampled at a fixed number of equally spaced frequencies in the neighborhood of the resonant frequency, we determine the optimal frequency spacing in order to minimize the asymptotic standard deviation of the estimate of either Q or f/sub 0/.

Analysis of a two-port flanged coaxial holder for shielding effectiveness and dielectric measurements of thin films and thin materials

A two-port flanged coaxial probe for measuring the dielectric and magnetic properties of thin material sheets is analyzed. Closed form solutions for the two-port scattering parameters are presented. The solution assumes an incident TEM wave together with evanescent TM/sub 0n/ modes. Numerical results are obtained for both the forward and inverse problem. Computations indicate that at low frequencies the incident waves are almost totally reflected. As the frequency is increased, transmission through the sample increases. Experimental results compare closely with the theory. The inverse solution yielded good permittivity determination for the cases tested. The technique should prove useful for nondestructive testing of circuit boards or substrates.