Asymptotic limits of negative group delay phenomenon in linear causal media

dc.contributor.authorKandic, Miodrag
dc.contributor.examiningcommitteeOliver, Derek (Electrical and Computer Engineering) Page, John (Physics and Astronomy) Frank, Brian (Queen’s University, Electrical and Computer Engineering)en_US
dc.contributor.supervisorBridges, Gregory (Electrical and Computer Engineering)en_US and Computer Engineeringen_US of Philosophy (Ph.D.)en_US
dc.description.abstractAbnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.en_US
dc.description.noteFebruary 2012en_US
dc.rightsopen accessen_US
dc.subjectnegative group delayen_US
dc.subjectgroup delay compensationen_US
dc.subjectabnormal propagationen_US
dc.subjectsuperluminal propagationen_US
dc.subjectgroup velocityen_US
dc.subjectgroup delayen_US
dc.subjectKramers-Kronig relationsen_US
dc.subjectcausal mediumen_US
dc.subjectcausal mediaen_US
dc.subjectconstant phase shifteren_US
dc.subjectphased arrayen_US
dc.subjectfeed-forward amplifieren_US
dc.subjectreciprocal circuiten_US
dc.subjectbilateral circuiten_US
dc.subjectdelay circuiten_US
dc.subjectdistributed parameter circuiten_US
dc.subjectactive deviceen_US
dc.subjectgain compensationen_US
dc.subjectnegative refractive indexen_US
dc.subjectleft handed materialen_US
dc.titleAsymptotic limits of negative group delay phenomenon in linear causal mediaen_US
dc.typedoctoral thesisen_US
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