Filter Group Delay Research Articles

A note on the bandwidth of negative group delay filters

SummaryAn updated definition of group delay bandwidth in analog filters is introduced in this work. Unlike existing definitions, this new definition considers simultaneously the value of the group delay and filter gain, leading to minimized distortion in the filter output. In addition, it offers the capability of handling wide‐band signals without introducing errors in the shape of their envelopes. Selected first‐ and second‐order filters are studied and simulation results are provided to validate the efficiency of the new definition.

Elementary Negative Group Delay Filter Functions

A theoretical study of the behavior of some elementary first- and second-order functions, which are suitable for realizing negative group delay, is performed in this work. As both the gain and phase responses are simultaneously considered, important derivations related to the actual bandwidth of operation are derived accompanied by useful design tips. The presented theory is supported by simulation and experimental results obtained through the utilization of typical active-RC filter structures, as well as from a field-programmable analog array device.

Design Study High Reflectors Graded Index Mirror Dispersive Properties

This paper investigates the dispersive properties of a spectral filter—a quarter-wave (QW) mirror. The study considers the modeling with a smoothly changing refractive index of the applied material (Rugate filter) using Fourier transform analysis of a high and low refractive index. These chirped structures exhibit high reflectivity and low group delay dispersion. The introduced result in this study is in some way better than already existing ones and/or can be used to obtain a meaningful practical effect, because it adopts calculation methods that are characterized by the accuracy and reliability of data using different statistical parameters and can be adopted with all modern and old methods of preparation. These improvements can have significant implications for various applications. Moreover, we investigate different statistical parameters, such as mean, median, mode, and standard deviation (STD), and analyze their impact on the rugate filter group delay (GD) and group delay dispersion (GDD) performance.

Power-Law Negative Group Delay Filters

A study of the behavior of the power-law negative group delay filters, accompanied by a comparison with their integer-order counterparts, is performed in this work. Employing a curve-fitting based approximation technique, the resulting integer-order rational transfer function is versatile in the sense that it has the same form independent of the order and/or the type of the filter. Its implementation is performed by following three alternative approaches, each one offering different advantages. The findings of this work are supported by simulation and experimental results using suitable platforms.

A Robust Algorithm for the Design of Wideband Positive-Slope Linear Group Delay Filters

This article proposes a robust method for the synthesis and design of optimal linear group delay filters with prescribed bandwidth and dispersion properties. The proposed filters are based on a cascade of second-order all-pass filter cells, for which all the parameters are optimized in order to reach the desired wideband linear group delay characteristic with positive slope. Compared to the previously published synthesis method, the proposed approach offers appropriate initialization enabling convergence and aiming for the optimal solution. The method’s convergence and robustness are proved through a 21-cells synthesis, which is the highest number of cascaded cells reported to date, due to the usual convergence problem. Then the electronic feasibility is illustrated through the measurement results of a lumped-elements linear group-delay filter prototype dimensioned with this method. The measured group delay presents a positive slope of 8 ns GHz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> in the frequency range [100–725] MHz. It is, to the best of our knowledge, the highest positive slope reported to date with an electronic implementation (i.e except SAW and waveguide devices).

A linear group delay filter with tunable positive slope for analog signal processing

SummaryThis article describes the design of a tunable positive slope linear group delay filter dedicated to analog signal processing applications. The designed filter is composed of eight second‐order all‐pass cells which have been optimized to obtain a highly linear global group delay characteristic over a specified bandwidth for a specified dispersion. Each of these second‐order cells is designed with a dedicated Gm‐C topology to fit the ideal group delay characteristic with a high efficiency. Based on the sensitivity analysis of the topology, the possibility of tuning the group delay slope is highlighted. The design has been achieved with the ST CMOS 55 nm technology and has a maximum bandwidth of 2.5 GHz, a maximum reachable delay of 5.12 ns, and a group delay maximum variation of 2.5 ns. The positive slope of the group delay can be tuned in the range from 1.48 ns/GHz up to 2.03 ns/GHz. The concept of slope tunability is validated through post‐layout statistical analysis.

Design of integrated all‐pass filters with linear group delay for analog signal processing applications

SummaryThis article describes the design of integrated linear group delay filters for analog signal processing (ASP) applications and their implementation through constant‐resistance lattice and bridged‐T networks. Unlike previously published works, our design method uses a recursive procedure as the basis for the synthesis of a suitable transfer function. Thanks to this method, filters with a more linear group delay characteristic and flat magnitude response can be obtained. Two filters are designed in a 0.13‐μm BiCMOS technology to demonstrate the method: a balanced lattice with a negative slope and an unbalanced bridged‐T of positive slope.

Phase-Coded FMCW Automotive Radar: System Design and Interference Mitigation

A frequency-modulated continuous-wave (FMCW) radar takes advantage of stretch processing (dechirping, deramping) to reduce the sampling requirements of radar systems such as automotive radars. When applying phase coding into FMCW radar systems for interference mitigation or joint communication, preservation of this benefit is not possible, due to the nature of this process. This paper proposes a new phase coded FMCW system as well as a processing strategy based on a group-delay filter to deal with unaligned phase-coded radar return signals. Moreover, this paper proposes an improved interference mitigation method based on a phase-coded linear- frequency-modulated (LFM) continuous waveform and points out the improvements in the signal-to-interference ratio (SIR). In the proposed mitigation technique, unlike the traditional approach where RF spectrum spreads, the beat frequency spectrum of the FMCW radar spreads, thus the bandwidth of RF hardware stays the same as a classical LFM continuous wave radar. The success of the proposed phase coded frequency-modulated continuous-wave (PC-FMCW) radar is illustrated in simulations and increased interference mitigation performance is validated by experiments.

Design of a negative group delay filter via reservoir computing approach: Real-time prediction of chaotic signals

An optimal arbitrary order filter with negative group delay is proposed for a real-time prediction of complex band-limited signals. The filter consists of a set of second-order linear dissipative oscillators and is determined by a rational transfer function with fixed poles and optimized zeros. The filter design and optimization algorithm is based on a reservoir computing approach. The predictive properties of the filter are demonstrated numerically for two chaotic model systems — the finite-dimensional Rössler system and the infinite-dimensional Mackey-Glass system, as well as for the real biological signal of the fingertip photoplethysmogram.

Experimental validation of analog Chebyshev filters with improved group-delay

The strategy of improving the group delay in analog filters through the modification of conventional characteristic polynomials is a concept reported in advanced filter design literature. However, at present, this idea has only been approached from a theoretical perspective, validated by numerical or electrical simulations but not experimentally verified. This paper is precisely devoted to exploring the viability of physically realizing this idea. Because most of the references that deal with this topic consider the case of Chebyshev filters, this type of filters is also considered in our experimental validation. In our proposal, a synthesis based on FDNR topology (frequency-dependent negative resistor) is preferred over other circuit design strategies due to its low sensitivity. In order to verify the physical realization capability of this type of filter, the experimental results of a fifth-order Chebyshev filter implemented by using commercially available JFET op-amps TL082 are reported. In this case study, the frequency (magnitude and group delay) and time (step) responses of the conventional filter are contrasted with those of the modified filter, demonstrating that the experimental results accord with the theoretical background.

Butterworth transfer function with the equalised group delay response in the maximally flat sense

An effective method for the design of the continuous-time all-pass network for the low-pass filter group delay response equalisation is presented in this Letter. Since the method is derived from the maximally flat conditions at the origin of the group delay response's rational function, the cascade connection of the designed all-pass network and low-pass filter exhibits a constant group delay response at the origin in the flat sense. Illustrative examples regarding group delay equalisation of the Butterworth filters are given.

Characterization of Microring Filters for Differential Group Delay Applications

The longitudinal offset technique permits to improve the accuracy of the coupling coefficients of integrated directional couplers and provides designs that can be easily implemented with current fabrication tolerances. In this paper, we address the additional degree of freedom offered by this technology in order to tailor the differential group delay in coupled-resonator optical filters. We present the characterization of several devices exploiting this feature and we discuss their potential applications.

Investigation on microwave photonic filter group delay performance

Investigation on the group delay performance of microwave photonic filters is presented. Analysis and simulation results show symmetrical distribution on the delayed optical signals in the impulse response is required to obtain a constant group delay performance. Experimental results for both symmetrical and asymmetrical tap distribution microwave photonic notch filters are presented showing the group delay response with <±25 ps and around 1 ns ripples, respectively.

Tunable Center Frequency Negative Group Delay Filter Using Coupling Matrix Approach

In this letter, a negative group delay filter (NGDF) with tunable center frequencies is presented. The proposed filter is designed using finite unloaded- $Q_{u}$ resonators based on the coupling matrix approach. The proposed NGDF does not require a lumped resistor to generate a negative group delay and has source-load and inter-resonator couplings. The center frequency of the filter is tuned by varying the bias voltage of the varactor diodes. The design theory for the proposed filter is validated experimentally through fabrication of a second-order NGDF at a center frequency of 2.14 GHz.

Loop coupled resonator optical waveguides.

We propose a novel coupled resonator optical waveguide (CROW) structure that is made up of a waveguide loop. We theoretically investigate the forbidden band and conduction band conditions in an infinite periodic lattice. We also discuss the reflection- and transmission- spectra, group delay in finite periodic structures. Light has a larger group delay at the band edge in a periodic structure. The flat band pass filter and flat-top group delay can be realized in a non-periodic structure. Scattering matrix method is used to calculate the effects of waveguide loss on the optical characteristics of these structures. We also introduce a tunable coupling loop waveguide to compensate for the fabrication variations since the coupling coefficient of the directional coupler in the loop waveguide is a critical factor in determining the characteristics of a loop CROW. The loop CROW structure is suitable for a wide range of applications such as band pass filters, high Q microcavity, and optical buffers and so on.

Microstrip Line Negative Group Delay Filters for Microwave Circuits

This paper presents a novel approach to the design and implementation of a distributed transmission line negative group delay filter (NGDF) with a predefined negative group delay (NGD) time. The newly proposed filter is based on a simple frequency transformation from a low-pass filter to a bandstop filter. The NGD time can be purely controlled by the resistors inserted into the resonators. The performance degradation of the NGD time and signal attenuation (SA) of the proposed NGDF according to the temperature dependent resistance variation is also analyzed. From this analysis, it is shown that the NGD time and SA variations are less sensitive to the resistance variation compared to those of the conventional NGD circuit. For an experimental validation of the proposed NGDF, a two-stage distributed microstrip line NGDF is designed, simulated, and measured at an operating center frequency of 1.962 GHz. These results show a group delay time of -7.3 ns with an SA of 22.65 dB at the center frequency and have good agreement with the simulations. The cascaded response of two NGDFs operating at different center frequencies is also presented in order to obtain broader NGD bandwidth. NGDFs with good reflection characteristics at the operating frequencies are also designed and experimentally verified.

Wavelength-Offset Filtering in Optical OFDM IMDD Systems Using Directly Modulated DFB Lasers

In optical OFDM (OOFDM) intensity-modulation and direct-detection (IMDD) single-mode fibre transmission systems using directly modulated DFB lasers (DMLs), wavelength-offset optical filtering considerably improves extinction ratios of OOFDM signals. However, optical filter-induced group delays bring about OOFDM signal spectrum distortions. Detailed investigations show that group delays associated with super Gaussian optical bandpass filters (OBPFs) significantly reduce both the dispersion tolerance and achievable optical power budget (OPB) of the system. To solve such a challenge, two simple approaches are proposed including combined optical filtering by using a ring resonator filter after a super Gaussian OBPF, and cascaded optical filtering by using multi-stage ring resonator filters. It is shown that, by optimizing ring resonator filter parameters, the proposed approaches can completely eliminate the filter group delay effect and enable 7 dB OPB improvements.

Analogue filter group delay optimization using a stochastic approach

AbstractAn analogue filter group delay response is optimized using an all‐pass network connected in the cascade of the filter. This contribution introduces an original method of all‐pass network correction designing of using a random‐based approach. The main objective of the method is the calculation of an optimal all‐pass network order and optimal coefficients of its transfer function. To realize this objective it is necessary to find minima of so‐called optimization spaces. The spaces definition provides an important generalization of the optimization task. The original stochastic approach is used to find the mentioned minima of the spaces. The minima can be detected using several probability densities. The method combines advantages of a numerical approach with rigorous analytical pre‐processing. Compared to current optimization methods, the described approach provides very good convergence, velocity and especially independence from the initial estimation of the all‐pass network transfer function coefficients. The original objective function ensures absolutely stable convergence in the multidimensional optimization spaces. This objective function was developed with regard to properties of the analogue filters. The designed method is illustrated by a few practical optimizations. A well‐known circuit simulator, Micro‐Cap, is used as a comparative system because of its relatively good optimization algorithm. All the presented original algorithms and functions are debugged in the MATLAB® environment. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Resolving group delay of narrowband optical filters from their transmission characteristics

AbstractIn the paper, the factors affecting the accuracy of calculating the optical filter group delay basing on the measured power transmission characteristic are analyzed. Having the phase characteristic of the filter recovered from its transmission, the group delay is usually calculated via differentiation. The new, direct formula is proposed giving more accurate results when the characteristic of the filter is available in the limited frequency range. Also the limitations arising from the noise of the optical spectrum analyzer are examined.

Impact of the UWB Filter Frequency Domain Non-Idealities on the Filter Transient Response

In this article an approach to the characterization of the behavior of UWB filters in the time domain is presented. In particular, the relationship between the filter frequency domain non-idealities (such as variations of the filter group delay time and ripple in the frequency mask) and their effect on the corresponding filter time domain behavior (transient response) are analyzed. In a novel approach the distortion introduced by a filter with a randomly generated group delay and filter frequency mask are investigated. It is discovered that there is a relatively sharp bound on values of the standard deviation of the filter group delay time and standard deviation of the ripple in the frequency filter mask below which the distortion in the time domain is negligible. The parameters are focused on UWB filters for the European UWB regulations operating in the 6-8.5 GHz frequency range. Index Terms – UWB, Filters, Non-Idealities, Group Delay Time, Ripple, Time Domain.