Negative Group Delay Filters  NGD designs, tradeoffs and optimization
Interpretation of Negative Group Delay (NGD) phenomenon in both the time and frequency domains, is demonstrated
in the plots above.
The first plot is in the timedomain, for an input Gaussian pulse. The plot demonstrates the timeadvancement
of the output pulse peak relative to the input pulse peak (NGD effect) for two different NGD media (more details in the references
at the bottom of the page). It also demostrates the effect of transients in the NGD output waveform, for pulses with
defined turnon/off times (an undesired tradeoff of NGD, proportional to frequency domain outofband gain).
The second two plots show frequency domain magnitude and group delay (negative derivative of phase) characteristics of an
NGD medium from a reference at the bottom of the page, based on a rational transfer function of order N.
In the time domain, the peak of an analytical pulse propagated through an NGD medium will
appear at the output of the medium before it enters the input, given that the pulse frequency spectrum is mostly located
within the NGD frequency band. This seemingly abnormal propagation does not violate
causality, since the pulse turnon and turnoff parts propagate normally, with a delay (at the speed of light or slower).
It is only the steady state part of the pulse (for example a Gaussian pulse) that gets reshaped by the NGD medium in such
manner that the pulse peak at the output precedes the input pulse peak.
Timedomain NGD tradeoffs include:
 Amplitude of transients associated with turnon and turnoff (tail) parts of the pulse
 Distortion of steadystate part of the pulse, due to reshaping
In the frequency domain, amplitude characteristic has its minimum at the center frequency, and phase
characteristic has a postive slope within the NGD band (group delay, as a negative derivative of the phase characteristic,
is therefore negative).
Frequencydomain NGD tradeoffs include:
 Outofband gain (amplitude characteristic has a minimum at the center frequency), equivalent to
timedomain pulse turnon/off parts transient amplitudes
 Amplitude and/or phase distortion, equivalent to timedomain distortion of the pulse steadystate
part
Optimized designs attempt to maximize the timedomain relative NGD (pulse advancement relative to pulse
duration), or NGDbandwidth product in the frequency domain, while keeping the above listed tradeoffs below some
predefined acceptable levels.
Applications of NGD filters and devices include:
 delay compensation (or even advancement) in signal transmission involving pulse waveforms
 beamsquint minimization in phasedarray antennas, by the virtue of flattening the phase
characteristic slopes
of delay lines between array elements, so the delay in electrical degrees is virtually
constant for all frequencies within the bandwidth
 wideband delay compensation in electromagnetic cloaking media
Several pertinent publications based (and expanding) on the work found in the
Ph.D. thesis by Miodrag Kandic are listed
below:
• M. Kandic and G.E. Bridges, "Negative Group Delay Prototype Filter Based on the Ratio of Two Classical Chebyshev Filter Transfer Functions", Progress in Electromagnetics Research (PIER B), 2024
• M. Kandic and G.E. Bridges, "Negative Group Delay Prototype Filter Based on the Reciprocal Transfer Function of a LowPass Butterworth Filter Capped at Finite OutofBand Gain", Progress in Electromagnetics Research (PIER B), 2024
• M. Kandic and G.E. Bridges, "Negative Group Delay Prototype Filter Based on Cascaded Second Order Stages Implemented with SallenKey Topology", Progress in Electromagnetics Research (PIER B), 2021
• M. Kandic and G.E. Bridges, "Limits of Negative Group Delay Phenomenon in Linear Causal Media", Progress in Electromagnetics Research (PIER), 2013
• M. Kandic and G.E. Bridges, "Asymptotic Limits of Negative Group Delay in Active ResonatorBased Distributed Circuits", IEEE Transactions on Circuits and Systems I (TCAS), 2011
• M. Kandic and G.E. Bridges, "Bilateral GainCompensated Negative Group Delay Circuit", IEEE Microwave and Wireless Components Letters (MWCL), 2011
For any comments, questions or inquiries, you can email Miodrag Kandic by clicking here.
