In this two-parts paper, methods for the quantification of uncertainty in measurement and computational modeling are reviewed, with an emphasis on applications in electromagnetic compatibility (EMC). The current status of international standards relating to measurement uncertainty in EMC is provided (in part I), as well as a review of selected alternative methods and recent developments in the domain of computational modeling and empirical uncertainty quantification (in part II).

This brief introduces an original reduction method of resonance effect dispersion by using bandpass negative group delay (NGD) function. The dispersion transfer function (TF) is model by lumped RLC circuit. The canonical parameters of NGD passive cell are innovatively formulated as a function of the resonance dispersion specifications. The developed method feasibility is validated with commercial tool frequency domain simulations. Proofs-of-concept constituted by passive RLC-resonant and NGD fully passive circuits are considered. The results confirm an obvious peak reduction of resonance magnitudes and GDs from (15-dB, 20-ns) to better than (11.5-dB, 8.6-ns) are realized in the NGD bandwidth of about 20 MHz. The NGD method robustness is also investigated with simultaneous and individual relative variations of the dispersion parameters.

In Part I of this two-part contribution on uncertainty quantification (UQ) in electromagnetic compatibility and electromagnetic interference, the current status of international standards relating to measurement uncertainty is reviewed. Here in Part II, a selection of recent developments in analytical and computational modeling of uncertainty and empirical UQ is reviewed.

This article deals with an original equalization method of 3-D electromagnetic (EM) cavity resonance by using bandpass negative group delay (NGD) function. Based on the equivalent circuit, the S-matrix model of the equalized EM cavity is introduced. The design equations of the NGD function are established in function of the cavity physical parameters. The feasibility of the equalization method is validated with a 42×28×3.8 cm rectangular cavity containing two communicating monopole antennas. By considering the TE110-mode, a significant equalization is realized with improvement of transmission coefficient flatness from 4 dB to less than 0.3 dB. In addition to the magnitude, the NGD equalization method enables to outstandingly reduce spikes of 3-D EM cavity group delay. With the proof of concept, the GD is reduced from more than 4 to 1 ns.

This article introduces an original microcontroller unit (MCU) design of numerical low-pass (LP) negative group delay (NGD) function. The innovative theory of the numerical LP-NGD function is developed based on the first-order analog transfer function discretization. The infinite impulse response (IIR) LP-NGD is fundamentally formulated in function of the desired NGD value, cutoff frequency, gain, and the MCU sampling frequency. A STM32 MCU proof-of-concept (POC) is tested to implement the IIR LP-NGD function. Different real-time tests with visualization of input and output analog signals from the MCU LP-NGD POC were performed. As expected, time-advance demonstration tests with milli-second short- and several hour long-duration time-scale with arbitrary waveform signals from temperature and humidity sensors. The signal time-advance is not in contradiction with the causality. The proposed digital MCU function opens a potential future industrial application of LP-NGD function via sensored signal anticipation.

This paper focuses on the time-domain analysis of bandpass (BP) negative group delay (NGD) function. The innovative NGD investigation is based on the time-domain experimentation of an innovative topology of “lill”-shape passive microstrip circuit. The design principle of the proof of concept (POC) constituted by particular microstrip shapes is described. The NGD circuit is inspired from a recent fully distributed “li”-topology. Before the time-domain investigation, the BP NGD specifications of the circuit under study are academically defined. As practical application of the basic definition, a frequency domain validation of “lill”-circuit is presented in the first section of the paper. The POC circuit is specified by a -8 ns NGD value at 2.31 GHz NGD center frequency and a 27 MHz NGD bandwidth. The “lill”-circuit exhibits an attenuation loss of about -6.2 dB at the NGD center frequency. Then, the two-port black box model of “lill”-NGD-circuit represented by touchstone data of the measured S-parameters is exploited for the transient simulation. The measured group delay (GD) illustrates that the tested “lill”-circuit operates as a BP function regarding the NGD with NGD equal to -8.1 ns at the NGD center frequency. The time-domain demonstration of the BP NGD function was performed using a gaussian pulse modulating sine carrier. The innovative experimental setup with the possibility to plot simultaneously well synchronized input and output signals is explained. The BP NGD time-domain response is understood from commercial tool simulation using the touchstone S-parameters of the measured “lill”-circuit by using a Gaussian up-converted pulse having a 27 MHz frequency bandwidth. It was observed that the output signals are delayed when the sine carrier is out of NGD-band. However, the output signal envelope is in advanced of about -8 ns when the carrier is tuned to be approximately equal to the 2.31 GHz NGD center frequency. To confirm the time-domain typical behavior of BP NGD response, an input pulse signal having Gaussian waveform were considered during the test. However, the input signal spectrum must be determined in function of the NGD bandwidth. After tests, measured output signal envelopes presenting leading edge, trailing edge and peak in time-advance compared to the input ones are observed experimentally. The results of the present feasibility study open a potential microwave communication application of BP NGD function notably for systems operating with ISM and IEEE 802.11 standards.