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Title: Asymptotic limits of negative group delay phenomenon in linear causal media
Authors: Kandic, Miodrag
Supervisor: Bridges, Gregory (Electrical and Computer Engineering)
Examining Committee: Oliver, Derek (Electrical and Computer Engineering) Page, John (Physics and Astronomy) Frank, Brian (Queen’s University, Electrical and Computer Engineering)
Graduation Date: February 2012
Keywords: negative group delay
group delay compensation
abnormal propagation
superluminal propagation
group velocity
group delay
Kramers-Kronig relations
causal medium
causal media
constant phase shifter
phased array
feed-forward amplifier
reciprocal circuit
bilateral circuit
delay circuit
distributed parameter circuit
active device
gain compensation
negative refractive index
left handed material
Issue Date: 7-Oct-2011
Abstract: Abnormal 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.
Appears in Collection(s):FGS - Electronic Theses & Dissertations (Public)

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