Suitability of passive RC-network-based inductorless bridged-T as a bandpass NGD circuit

Abstract

Purpose The purpose of this paper is to study, a bridged-T topology with inductorless passive network used as a bandpass (BP) negative group delay (NGD) function. Design/methodology/approach The BP NGD topology under study is composed of an inductorless passive resistive capacitive network. The circuit analysis is elaborated from the equivalent impedance matrix. Then, the analytical model of the C-shunt bridged-T topology voltage transfer function is established. The BP NGD analysis of the considered topology is developed in function of the bridged-T parameters. The NGD properties and characterizations of the proposed topology are analytically expressed. Moreover, the relevance of the BP NGD theory is verified with the design and fabrication of surface mounted device components-based proof-of-concept (PoC). Findings From measurement results, the BP NGD network with −151 ns at the center frequency of 1 MHz over −6.6 dB attenuation is in very good agreement with the C-shunt bridged-T PoC. Originality/value This paper develops a mathematical modeling theory and measurement of a C-shunt bridged-T network circuit.

High-pass negative group delay analysis of single capacitor three-port circuit

“…We remind that the NGD analysis (Mitchell and Chiao, 1997, 1998; Nakanishi et al , 2002; Kitano, 2003; Munday and Henderson, 2004; Eleftheriades et al , 2003; Siddiqui et al , 2003; Markley and Eleftheriades, 2010; Monti and Tarricone, 2009; Liu and Xu, 2017; Chaudhary and Jeong, 2017; Shao et al , 2018; Kandic and Bridges, 2011; Wu and Itoh, 2014; Zhang et al , 2017; Ravelo, 2013, 2016, 2017; Randriatsiferana et al , 2021; Wan et al , 2022; Guerin et al , 2021a, 2021b; Du et al , 2021; Ravelo et al , 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a; Lalléchére et al , 2021; Fenni et al , 2021; Guerin et al , 2021b) depends essentially on the elaboration of the transmission coefficient, S mn ( s ), with integer subscript, m ≠ n . By taking the Laplace variable versus angular frequency, s = jω , with angular frequency ω , the transmission coefficient can be expressed as: The basic elements to be explored to pursue the NGD analysis are transmittance, T ( ω ), and phase, φ ( ω ), which are given by, respectively: This last expression can be derived according to the circuit theory-associated group delay (GD) defined by the following equation: The GD at very LF is given by: If GD 0 < 0, the circuit can be classified as LP-NGD topology with cutoff frequency as the root of equation: The basic characteristics of this response are introduced as described in the following paragraph.…”

“…Hence, simpler passive topologies of low-pass (LP) NGD (Ravelo, 2017, 2016; Randriatsiferana et al , 2021; Wan et al , 2022), high-pass (HP) NGD (Guerin et al , 2021a; Du et al , 2021), bandpass (BP) NGD (Ravelo et al , 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a) and stop-band (SB) NGD (Lalléchére et al , 2021; Fenni et al , 2021) lumped cells were investigated and developed. Those identified NGD-lumped topologies (Ravelo, 2017, 2016; Randriatsiferana et al , 2021; Wan et al , 2022; Guerin et al , 2021a; Du et al , 2021; Ravelo et al , 2020a, 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a; Lalléchére et al , 2021; Fenni et al , 2021; Guerin et al , 2021b) constituted by resistive-inductive (RL), resistive-capacitive (RC), inductive-capacitive (LC) and resistive-inductive-capacitive (RLC) networks were identified. The unfamiliar NGD passive circuits (Ravelo, 2013, 2016, 2017; Randriatsiferana et al , 2021; Wan et al , 2022; Guerin et al , 2021a; Du et al , 2021; Ravelo et al , 2020b, 2022a; Lalléchére et al , 2021; Fenni et al , 2021; Guerin et al , 2021b; Jia et al , 2022) were generally designed with two-port topologies.…”

“…Those identified NGD-lumped topologies (Ravelo, 2017(Ravelo, , 2016Randriatsiferana et al, 2021;Wan et al, 2022;Guerin et al, 2021a;Du et al, 2021;Ravelo et al, 2020aRavelo et al, , 2020bNebhen and Ravelo, 2021;Wan et al, 2021;Ravelo et al, 2022a;Lall ech ere et al, 2021;Fenni et al, 2021;Guerin et al, 2021b) constituted by resistive-inductive (RL), resistive-capacitive (RC), inductive-capacitive (LC) and resistive-inductive-capacitive (RLC) networks were identified. The unfamiliar NGD passive circuits (Ravelo, 2013(Ravelo, , 2016(Ravelo, , 2017Randriatsiferana et al, 2021;Wan et al, 2022;Guerin et al, 2021a;Du et al, 2021;Ravelo et al, 2020bRavelo et al, , 2022aLall ech ere et al, 2021;Fenni et al, 2021;Guerin et al, 2021b;Jia et al, 2022) were generally designed with two-port topologies.…”

“…The existence and the diversity of NGD effect generator becomes an attractive topic for few electronic engineering researchers from 1990s to now (Mitchell and Chiao, 1997, 1998; Nakanishi et al , 2002; Kitano, 2003; Munday and Henderson, 2004; Eleftheriades et al , 2003; Siddiqui et al , 2003; Markley and Eleftheriades, 2010; Monti and Tarricone, 2009; Liu and Xu, 2017; Chaudhary and Jeong, 2017; Shao et al , 2018; Kandic and Bridges, 2011; Wu and Itoh, 2014; Zhang et al , 2017; Ravelo, 2013, 2016, 2017; Randriatsiferana et al , 2021; Wan et al , 2022; Guerin et al , 2021a, 2021b; Du et al , 2021; Ravelo et al , 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a; Lalléchére et al , 2021; Fenni et al , 2021; Guerin et al , 2021a, 2021b; Jia et al , 2022; Sambatra et al , 2022; Ravelo et al , 2021c, 2022e). It was found that the NGD effect can be interpreted in the time domain by smoothed pulse signals with output propagating in time-advance compared to the input (Mitchell and Chiao, 1997, 1998; Nakanishi et al , 2002; Kitano, 2003; Munday and Henderson, 2004).…”

“…Some elementary lumped topologies of NGD active circuits using field effect transistor combined with resistors, inductors and capacitors were identified (Ravelo, 2013). Hence, simpler passive topologies of low-pass (LP) NGD (Ravelo, 2017, 2016; Randriatsiferana et al , 2021; Wan et al , 2022), high-pass (HP) NGD (Guerin et al , 2021a; Du et al , 2021), bandpass (BP) NGD (Ravelo et al , 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a) and stop-band (SB) NGD (Lalléchére et al , 2021; Fenni et al , 2021) lumped cells were investigated and developed. Those identified NGD-lumped topologies (Ravelo, 2017, 2016; Randriatsiferana et al , 2021; Wan et al , 2022; Guerin et al , 2021a; Du et al , 2021; Ravelo et al , 2020a, 2020b; Nebhen and Ravelo, 2021; Wan et al , 2021; Ravelo et al , 2022a; Lalléchére et al , 2021; Fenni et al , 2021; Guerin et al , 2021b) constituted by resistive-inductive (RL), resistive-capacitive (RC), inductive-capacitive (LC) and resistive-inductive-capacitive (RLC) networks were identified.…”