Abstract
A particularly original negative group delay (NGD) theory of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -topology is developed in the present paper. The NGD three-port topology is a passive circuit purely constituted by capacitors network. The model of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -topology impedance 3-D matrix is analytically established in function of the capacitor elements. Then, the S-matrix model is derived by using the Y-to-S transform. By considering the S-matrix frequency responses, a bandpass (BP) NGD analysis of the capacitive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -topology is originally elaborated. It is theoretically demonstrated that the passive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -topology is susceptible to behave as a BP NGD circuit under an analytical condition between the constituting capacitor values. The design feasibility of the BP NGD function is experimentally verified with lumped capacitor components-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -circuit proof of concept. An electronic circuit board constituted by purely capacitive-network <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -circuit is fabricated as an original <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -circuit prototype. The tested board is constituted by arbitrary chosen capacitors, 100 nF, 10 nF and 0.1 nF. As expected, the calculation, simulation and measurement results, which are in very good agreement, confirm the BP NGD behavior. It is observed from measurement that it generates NGD of about −18.1 ns at a frequency of about 0.55 MHz and, lower and upper cut-off frequencies of about 0.33 MHz and 1.71 MHz. It is noteworthy that the transmission and reflection coefficients at very low frequency are independent of the capacitor values and analytically equal to 2/3 and 1/3, respectively.
Highlights
The first experimentations of the negative group delay (NGD) effect were realized in 1980s with optical system [1], [2]
ON CALCULATED, SIMULATED AND EXPERIMENTED RESULTS OF -TOPOLOGY The relevance of the innovative BP NGD theory associated to our tri-port -topology established in the previous section is verified in the present one
Similar to the two previous paragraphs, the validation is based on the comparisons between the calculated (‘‘Calc.’’), simulated (‘‘Simu.’’), and measured (‘‘Meas.’’) GDs expressed in equation (51)
Summary
The first experimentations of the negative group delay (NGD) effect were realized in 1980s with optical system [1], [2]. These experimentations were initially based on the consideration of negative group velocity (NGV) dispersive media [1]–[4]. It was found that the time-domain signature of the NGD effect manifests with the propagation of the output pulse in time-advance compared to its input [1]–[9]. Thanks to the time-advance behavior, the NGD investigation enables to verify some extraordinary physical effects as superluminal pulse propagation [9].
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