Dielectric characterization of materials and lossy filter design using reflected group delay
Filters play a significant role in different types of communication systems such as radars, cellular mobile and satellite communication. They are helpful in improving the performance of a communication system by restricting the transmission to the intended frequency band and rejecting the interfering signals from outside. Filters are expected to provide distortion free transmission to the signals in the passband and thus require flat in-band response and an adequate amount of out-of-band rejection. Filter technologies employing coaxial, waveguide and dielectric resonators can meet these requirements but at the cost of large size. Low loss in these filter technologies can be identified by their high quality factor (Q-factor). Higher insertion loss (lower Q-factor) in the filter response is acceptable based on the communication system using that filter and its position in that system. Filter design must deal with the electrical and physical specifications based on the required filter response. The concept of lossy filter is based on the fact that loss in a filter is distributed among the various resonators in a way that helps to achieve flat in-band response. This is achieved at the cost of degraded insertion loss. In this way, lossy filters provide an effective solution to the applications that can afford low Q-factor and higher insertion loss. Resonator is a building block in a filter network and a good understanding of resonators is quite useful in developing an insight of a filter network. Resonators also have a good deal of applications in methods used to perform dielectric characterization of materials. Keeping this connection of resonators and filter in view, the initial research presented in this thesis is focused on lossy resonators. This was helpful in developing some methods for dielectric characterization of materials. In addition to that, the research carried out using lossy resonators has also been helpful in understanding the behavior of resonators in a filter network with the change in amount of loss. The thesis provides a detailed discussion on methods developed to determine the dielectric properties of materials using the reflected group delay of lossy resonators. Methods of dielectric characterization proposed in the thesis can be categorized as methods using an overcoupled coaxial resonator for testing the materials filled inside it and methods using a capacitively coupled microstrip circuit for testing the microstrip substrates. Mathematical models for these methods are based on the reflected group delay of an overcoupled lossy resonator and can be applied in a procedural manner to extract the dielectric constant and loss tangent of the material under test. The errors in extracting dielectric constant and loss tangent are 2%-5% and 30%-100% respectively and depend on the resonator type, material under test, and test setup parameters. The methods are validated through the characterization of various materials using both the coaxial and microstrip resonators. A method of lossy filter design using reflected group delay is also proposed in this thesis. The research presented in this part of thesis describes the effect of decrease in Q-factor on the in-band response in terms of insertion loss and return loss. It also explains the effect of loss on the group delay of a filter network and introduces the use of negative group delay in lossy filter design. The proposed method tends to recover the loss of in-band flatness due to decrease in Q-factor through resistive cross coupling. A circuit model for microstrip coupled line bandpass filter with different specifications are derived using the proposed method to study the improvement in the in-band flatness. The method of group delay is then integrated with Implicit Space Mapping (ISM) technique to derive EM models for the corresponding circuit models. The quantitative analysis of the simulated scenarios using the proposed method shows a significant improvement of 0.5-2.0 dB in the in-band flatness of the filter response. Finally, a microstrip filter is fabricated and tested to validate the method proposed for lossy filter design.
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Faculty of Graduate Studies and Research, University of Regina