Bandpass Negative Group Delay Demonstration on a VHF RLC Parallel Passive Lumped Circuit

This paper demonstrates the bandpass (BP) negative group delay (NGD) behavior of a passive RLC-parallel lumped network at very high frequencies (VHFs). After topological description, the BP NGD analysis is introduced. The BP NGD circuit is theoretically modelled by means of voltage transfer function (VTF) expression. The analytical equations illustrating the BP NGD specifications as the NGD center frequency, NGD value, NGD bandwidth and VTF attenuation are established in function of the R, L and C component parameters. To verify the relevance of the BP NGD analysis, a lumped circuit proof of concept (POC) is synthesized and designed. As prototype, the corresponding BP NGD circuit prototype of printed circuit board (PCB) is implemented in hybrid technology with SMD components. Then, quite innovated testing method allowing to extract the VTF is developed. As expected, the calculated, simulated and measured results are very well-correlated and showing BP NGD behavior of the POC. The calculated and simulated results with NGD value of -8 ns (resp.-12 ns), attenuation of -10 dB (resp.-8 dB) and bandwidth around 225 MHz (resp. 240 MHz) NGD center frequency are obtained. In addition to the experimental validation, uncertainty analysis (UA) with respect to the BP NGD specifications is also studied in order to show the influence of quality and tolerance of lumped components. The theoretical formulas of NGD specification UAs in function of R, L and C tolerances are derived. The UAs with respect to 1%, 2% and 5% relative tolerances of R, L and C components constituting the BP NGD circuit POC are discussed.