Reciprocal-Capped Butterworth and Chebyshev NGD Filter Synthesis

The patent transforms the complex multi-parameter optimization problem into a simplified design process by changing the fundamental parameters of the NGD circuit stages. Instead of independently tuning frequency, bandwidth, and attenuation for each stage, the invention uses normalized low-pass transfer functions where only the cutoff frequency and a scaling factor need to be determined. This parameter transformation reduces the design space from multiple independent variables to a minimal set of critical parameters, eliminating the need for cumbersome trial-and-error tweaking while achieving the desired bandwidth and transfer function response.

The patent applies the inversion principle by designing NGD circuits with transfer functions that are reciprocals of conventional low-pass filter transfer functions. This inversion approach allows the circuit to exhibit negative group delay characteristics while maintaining controlled attenuation. By inverting the traditional filter response, the patent achieves high NGD values at the center frequency without the attenuation increasing proportionally, thus breaking the conventional trade-off relationship between time-advancement and signal loss.

The patent implements preliminary action by pre-defining normalized low-pass transfer functions with specific mathematical forms (Butterworth, Chebyshev, elliptic) that inherently possess desirable characteristics such as maximally flat magnitude response or equiripple behavior. These pre-characterized transfer functions serve as templates that can be directly scaled and transformed to achieve the desired NGD circuit response. This preliminary preparation eliminates the need for iterative parameter tweaking during the design phase, as the desired transfer function shape is already embedded in the chosen normalized form.