NGD Analysis of Turtle-Shape Microstrip Circuit

A negative group delay (NGD) design of a turtle shape circuit topology is developed in this brief. The topology is comprised of two different length transmission lines (TLs) interconnecting two identical coupled lines (CLs). The S-matrix model is established as a function of the TL and CL parameters. The group delay (GD) at the half wave frequency of the short interconnect TL is derived from the transmission coefficient. To verify the relevance of the proposed turtle circuit theory, a microstrip proof of concept was modeled, designed, simulated, fabricated, and tested. The calculated, simulated and measured results are in good agreement and confirm the turtle prototype bandpass NGD function with approximately 1.97 GHz center frequency and NGD level of approximately -1.3 ns. In addition, this passive circuit operates with very low losses less than -2.5 dB over the reflection coefficient better than -14 dB.