Original Theory of NGD Low Pass-High Pass Composite Function for Designing Inductorless BP NGD Lumped Circuit

This paper aims to develop an original circuit theory of inductorless NGD topology. The considered passive cell comprised of resistor and capacitor elements without inductor operates as a bandpass (BP) NGD function. The specifications of NGD functions are defined. Generally, the BP NGD fully lumped circuits available in the literature operate with resonant RLC-network. In the introduced research work, a lumped circuit was first time identified to exhibit the BP behavior without the presence of inductive component. The inductorless BP NGD topology is inspired from the combination of low-pass (LP) and high-pass (HP) NGD passive cells. Therefore, an original LP-HP NGD composite topology is obtained. The identified BP NGD topology is constituted only by passive RC-networks. Then, theoretical development of BP NGD analysis is explored. The inductorless circuit theory starts with the identification of BP NGD canonical form. Then, the expressions of NGD value, center frequency and attenuation in function of RC-network parameters are established. The synthesis equations allowing to determine the resistor and capacitor elements are derived. Proofs-of-concept are designed and prototypes are fabricated to verify the effectiveness of the developed LP-HP NGD composite theory. To validate the developed original circuit theory, two prototypes of RC-network based LP-HP NGD composite were designed, fabricated, simulated and tested. The two prototypes were synthesized with respect to two different NGD center frequencies 13.5 MHz and 22 MHz. As expected, the calculated, simulated and measurement results are in very good agreement with NGD value of about some negative nanoseconds. In the future, the characterized inductorless topology enable to overcome the traditional limitations of RLC-network based BP NGD circuits because of inductance self-effect limitation. INDEX TERMS Bandpass (BP) negative group delay (NGD), low-pass/high-pass (LP-HP) NGD composite, circuit theory, inductorless passive topology.