Asymptotic Limits of Negative Group Delay in Active Resonator-Based Distributed Circuits

• Published in: IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2011-08, Vol.58 (8), p.1727-1735
• Main Authors: Kandic, Miodrag, Bridges, Greg E.
• Format: Article
• Language: English
• Subjects: Compensation; Delay; delay circuits; distributed parameter circuits; Frequency measurement; Gain; gain compensation; group delay compensation; Integrated circuit modeling; metamaterial; Resonant frequency; RLC circuits; Transient analysis
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2011.2107251

In this paper the asymptotic limits of negative group delay (NGD) phenomena in multi-stage RLC resonator-based circuits are discussed. A NGD-bandwidth-product limit is derived as a function of the number of stages and the out-of-band gain, which is independent of the circuit topology and can include active gain compensation. The limit is verified experimentally at microwave frequencies using a gain-compensated NGD circuit employing a parallel RLC resonator in the feedback path of a high-frequency op-amp. It is shown that, in the asymptotic limit, the NGD-bandwidth-product is proportional to the square root of the number of stages, and also to the square root of the logarithm of the out-of-band gain. The relation between the time-domain transient amplitude and the out-of-band gain is analyzed for finite-duration modulated signals, indicating an exponential increase in transient amplitudes with the square of NGD. Analysis shows that any attempt to increase the NGD of a finite-duration modulating waveform, by cascading more stages, is thwarted by the transients.