Bandpass Negative Group Delay Theory of Fully Capacitive Δ-Network

Abstract

A particularly original negative group delay (NGD) theory of $\Delta $ -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 $\Delta $ -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 $\Delta $ -topology is originally elaborated. It is theoretically demonstrated that the passive $\Delta $ -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 $\Delta $ -circuit proof of concept. An electronic circuit board constituted by purely capacitive-network $\Delta $ -circuit is fabricated as an original $\Delta $ -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.

Keywords

• Bandpass (BP) negative group delay (NGD)
• passive topology
• Δ-topology
• three-port circuit
• S-parameter modeling
• NGD theory