Group Delay Response Research Articles

Group Delay Equalization of Polynomial Recursive Digital Filters in Maximal Flat Sense

The paper presents the development of an algorithm to obtain stable allpass filter, which acts as a group delay equalizer, with the aim to equalize group delay of the polynomial IIR filter in a maximal flat sense. The proposed method relies on a set of nonlinear equations, derived directly from the flatness conditions of the group delay response at the origin in the [Formula: see text]-plane, with the order to obtain the unknown values of the allpass filter coefficients. The algorithm implemented in the MATLAB platform returns the coefficients of allpass filter. In the given example, first we construct a minimum phase polynomial IIR digital filter with a maximally flat magnitude at origin, next we augment the system with cascade connection of nonminimum allpass digital filter with order to equalize the group delay response of the whole filter in a maximally flat sense.

Analysis of a flat-top optical ring resonator

In this paper, a theoretical analysis of a flat-top microring resonator (FTMRR) is undertaken. The intensity and group delay responses of the FTMRR are derived from a transfer matrix formalism, which shows that flat-top resonance is possible in this single-ring cavity by stimulating and manipulating slow light in the counterclockwise (CCW) mode and fast light in the clockwise (CW) mode. The analytical solutions required for achieving the flat-top responses are obtained by assuming that the slope around the resonant wavelength equals zero. In addition, an improvement in the bandwidth of the FTMRR (in comparison with the MRR), the tunable and reconfigurable optical responses for filtering/switching, and the small variation in intensity during the tuning of the flat-top group delay observed in the previous experiments are all proved through theoretical analysis.

A Synthesized Method for Common-Mode Noise Suppression Filters With Specified Common-Mode and Differential Mode Response

In this paper, a synthesized method for broadband lumped-element-based common-mode noise suppression filter (CMNSF) is proposed. Such CMNSF can achieve theoretically lossless performance and controllable dispersive group delay response for differential signals. Besides, the proposed CMNSF can achieve two common-mode transmission zeros, and both frequencies can be arbitrarily assigned to strengthen the suppression ability at certain bands. To validate the synthesized method, a CMNSF with fourth-order equiripple group delay response is demonstrated and validated in an integrated passive device process. The filter can suppress the common-mode noise more than 10 dB from 1.92 to 5.02 GHz or more than 20 dB from 2.20 to 4.20 GHz. At the same time, differential insertion loss is kept less than 3 dB up to 15 GHz and the group delay is kept in a ±5% error up to 12 GHz, which is widest one compared to the published works. In addition, the occupied area with probing pads is 1047 μm × 954 μm, which is compatible to previous works. Therefore, the proposed method is suitable for implementing a lumped-element-based CMNSF with ultraflattened group delay for differential signals based on nonferrite material.

Ultra Wide Band CPW-Fed Circularly Polarized Microstrip Antenna for Wearable Applications

A conformal rigid microstrip ultra-wideband (UWB) circularly polarized wearable antenna is proposed to overcome the behavioural irregularities of flexible body-worn antennas. The design demonstrates the inclusion of two L shaped radiators along with an L shape feed and also a vertically protruded stub embedded with the ground plane for achieving the required ultra-wide bandwidth and circular polarization. Coplanar waveguide (CPW) feed is used to overcome the bandwidth limitation of circular polarization. The proposed low profile antenna with dimensions 75 × 63 × 1.52 mm3 yields a 10 dB impedance bandwidth of 111.4% (1.28–4.5 GHz) and a 3 dB axial ratio bandwidth of 45.61% (2.2–3.5 GHz). On body performance measurement of this planar antenna validates its applicability under body worn condition. Specific absorption rate (SAR) assessment has also been evaluated for this antenna on a hypothetical body model to justify its acceptance for the wearable application. It is observed that the maximum radiation amount absorbed by the body model is restricted to a maximum SAR value of 1.19 W/kg and 1.43 W/kg over 1 g and 10 g average body mass respectively. The time-domain characteristics such as group delay and waveform response, also exhibit satisfactory UWB performance of the proposed antenna. A lumped wideband equivalent circuit model of the antenna is also developed for estimating the broadband matching ability.

Asymmetric Reflection-Type All-Pass Equalizer

An asymmetric reflection-type all-pass equalizer (APE) is proposed to realize arbitrarily prescribed group-delay responses. This letter provided its synthesis, including the low-pass prototype for the APE and a new optimization design method of the prototype APE. Finally, a four-order APE with the prescribed group-delay response is designed. Good agreement between the measurement result and the theory verifies the validity of the method.

Experimental demonstration of active phasers based on codirectional coupling for real‐time analog signal processing

AbstractA phaser based on codirectional coupling is proposed and experimentally investigated to achieve a flat transmission magnitude while maintaining strong frequency‐dependent group delay response. This is the first experimental demonstration of such devices for real‐time radio analog signal processing applications, which are readily scalable to mm‐wave frequencies. While shielding improved the transmission performance by mitigating the radiation, a gain element is introduced to achieve a perfectly flat transmission magnitude response. The proposed structure thus forms the fundamental building block of engineering more complex dispersion profiles without compromising transmission magnitude response.

Research on Temporal Cloaked Signal Transmission Based on Time Reversal Technique

Abstract Based on the theory of time reversal technique and through the use of temporal dispersive delay lines, this paper presents a demonstration of temporal cloaked signal transmission at microwave frequencies. When compared with a conventional signal processing system, the related dispersive delay lines are not required to provide linear group delay response. Thus the proposal simplifies the system structure for temporal cloaking, avoids the drawbacks of easy detection, easy decoding and easy analysed brought by linear modulation system, and then strengthen the safety and reliability in signal transmission. Theoretical analysis and experimental results validate the proposed system. The proposed method and achieved results indicate potential application in secure communications and data multiplexing subject to channel bandwidth requirements.

Transition between flat magnitude and flat group delay low pass recursive digital filters

Many a paper has been written on the characteristics of the continuous-time and discrete-time low-pass filters which are designed to have either maximally flat magnitude characteristics or maximally flat group delay responses. The polynomial (all pole) low pass recursive digital filters which are characterised by characterise the transition between a flat magnitude and flat group delay characteristics, named Transitional Butterworth Thiran (TBTh) recursive digital filters, is considered. The characteristics of the resulting filter change gradually from the characteristics of the well known Butterwort's filter to the characteristics of the Thiran's filter with the maximally flat group delay characteristic. Poles of the TBTh filter are obtained by interpolating between poles Butterworth and Thiran's filters by varying a parametar which controls the pole positions that enables a tradeoff between the steepness magnitude characteristic at passband edge and group delay deviation.

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.

Automatic Monitor-Based Tuning of an RF Silicon Photonic 1X4 Asymmetric Binary Tree True-Time-Delay Beamforming Network

Photonic beamforming networks are promising candidates to achieve power-efficient transmission in future cellular communication systems. However, sensitivity to process and temperature variations necessitates an automatic calibration solution to enable robust operation. This paper demonstrates fully automatic monitor-based tuning of an integrated optical ring resonator-based 1X4 asymmetric binary tree optical beamforming network (OBFN). The proposed monitor-based tuning algorithm compensates fabrication variations and thermal crosstalk by controlling micro-heaters individually using information from electrical monitors. This algorithm is demonstrated on an OBFN that operates at 30 GHz with 2 GHz bandwidth and is fabricated in a standard silicon photonics foundry process. Successful calibration of the OBFN from a severely degraded initial response to the well-defined group delay responses required for a targeted radiating angle over 60 $^{\circ }$ (−30 $^{\circ }$ to 30 $^{\circ }$ ) in a linear beamforming antenna array is achieved. This fully automatic tuning approach opens the possibility of employing silicon OBFNs in real wideband mm-wave wireless communication systems.

Experimental study of CPW‐fed printed UWB antenna with radiation improvement for ground coupling GPR application

AbstractA compact (35 × 30 × 0.8 mm3) coplanar waveguide‐fed circular disk monopole antenna with gain enhancement using dual frequency‐selective surface (FSS) layers, each of dimension 44 × 44 × 1.6 mm3 is proposed in this letter. The proposed antenna added with FSS provides a maximum gain improvement of nearly 5 dBi in the impedance band from 3 to more than 20 GHz. Radiation in the broadside direction is also improved due to the addition of FSS layers. The proposed antenna is also experimentally tested in close proximity of sand and wood made test beds of varying thicknesses with aluminum sheet at the bottom of it. Antenna can cover the 3.1‐10.6 GHz unlicensed band with linear transfer function and nonvarying group delay response in this ground coupling experimental test.

Flat-top optical resonance in a single-ring resonator based on manipulation of fast- and slow-light effects.

Optical single-ring resonance inherently generates Lorentzian-shape magnitude and group-delay responses, leading to critical performance limitation in photonics, cavity quantum electrodynamics, cavity optomechanics, and atomic and optical physics. Here, we propose a new type of microresonator that stimulates flat-top resonance in a single-ring cavity. By manipulating the fast and slow light effects in the microresonator, the flat-top group delay can be tuned with an ignorable magnitude variation. In addition, the bandpass response can be switched to a notch, which can enable function-reconfigurable photonic integrated circuits (PICs) without a physical change in the architecture. Our demonstration provides the possibility of developing microresonator-based PICs with unprecedented high flexibility and capacity.

Neural network‐based design of 2‐channel quadrature mirror filter banks

SummaryTwo‐channel quadrature mirror filter banks can be efficiently established by the combination of real‐valued infinite impulse response all‐pass filters without incurring aliasing and magnitude distortions. The design problem of filter banks is therefore to seek for the phase error minimization of the all‐pass filter coefficients. In this paper, a neural network‐based Lyapunov energy function is used to relate to the objective function of the designed all‐pass filter coefficients. Based on the architecture of neural networks and suitable selection of Hopfield‐related parameters, the all‐pass filter coefficients are obtained when the networks reach convergence. By further using the suitable combination of the designed all‐pass filters, the 2‐channel quadrature mirror filter banks with perfect reconstruction can be efficiently accomplished. Simulation results indicate that the neural network‐based approach has the advantage of satisfactory performance in magnitude and group delay responses in a parallelism manner.

A novel real-time Fourier and inverse Fourier transforming system based on non-uniform coupled-line phaser

A novel real-time Fourier and inverse Fourier transforming (RTFaIFT) system realizing both positive and inverse transformations is designed and verified, using non-uniform coupled-line phaser. Two kinds of Fourier transformations are integrated within one system for the first time. This system can map the spectrum of the input signal into a waveform in time domain whose amplitude mimics the spectrum magnitude, owing to the frequency-varying group delay (GD) response of the phaser. Furthermore, the correspondence between the output waveform and the spectrum of the input signal is given for accurate analysis of the spectrum. This configuration possesses the characteristic of compact structure, simple design procedure, and perfect performance, consisting of a mixer, a phaser with linear group delay, a diode, and a LPF. For experimental demonstration, a RTFaIFT system operating at 6 GHz is designed and fabricated, the bandwidth of which is 4 GHz with −0.5 ns/GHz GD slope. Both single- and double-pulse signals have been chosen as the test signals to verify the performance of the RTFaIFT system, respectively. The experimental results agree well with simulation and theoretical results.

Gain augmentation of a CPW fed printed miniature UWB antenna using frequency selective surface

AbstractA co‐planar waveguide fed compact ultra‐wideband antenna is proposed in this article. The antenna dimension is reduced from 25 × 15 × 0.8 to 17.5 × 14.5 × 0.8 mm3 by lateral half cut of the radiating element. This miniature antenna gives a wide impedance bandwidth from 6 to 20.9 GHz with gain variation of 2‐4 dBi, average radiation efficiency of 85% and monopole like E‐plane and omnidirectional H‐plane pattern as per the experimental study. More than 3 dBi gain enhancement is achieved by adding dual frequency selective surfaces of dimension 17.5 × 17.5 mm2 each at the back side of antenna. The proposed antenna with frequency selective surface package provides more radiation to the broadside direction and an efficiency of >75%, without affecting the impedance band. Linear antenna transfer function and non‐varying group delay response are also reported.

Self-Apodization Effect in Tapered Fiber Bragg Gratings

A novel self-apodization effect that occurs in tapered fiber Bragg gratings (TFBG) is presented. The detailed theoretical analysis and experimental results show that only by feeding the electromagnetic wave into the grating from the taper waist side, the significant reduction of oscillations in a group delay response of TFBG is achieved. Thus, the apodization effect is achieved without any additional technological processes during the grating inscription. Moreover, a counterdirectionally written tapered and chirped fiber Bragg grating that has a negative slope of the group delay response and exhibits self-apodization effect is proposed.

Gain enhancement of a printed leaf shaped UWB antenna using dual FSS layers and experimental study for ground coupling GPR applications

AbstractA printed leaf shaped compact (40 mm × 30 mm × 0.8 mm) UWB antenna added with dual frequency selective surfaces (FSS) of dimension 44 mm × 44 mm × 1.6 mm is proposed. The FSS layers having 4 × 4 array in each can provide maximum gain of 8.7 dBi and gain enhancement by 2–4.5 dBi in the antenna bandwidth of 3–14.64 GHz. The proposed design also ensures maximum radiation in the broadside direction with average radiation efficiency of 85%. The antenna bandwidth and group delay responses were measured in close proximity of soil test bed for varying test bed thicknesses. Relative bandwidth of more than 114% with non‐varying group delay response ensure the ability of proposed antenna to work for ground coupling ground penetrating radar applications.

Leaf‐shaped CPW‐fed UWB antenna with triple notch bands for ground penetrating radar applications

AbstractA compact (38.31 mm × 34.52 mm × 0.8 mm) leaf shaped CPW fed ultra‐wideband antenna is proposed. The antenna gives wide impedance bandwidth from 2.58 GHz to 11.62 GHz with sharp triple notch bands (3.28 GHz–3.82 GHz, 5.12 GHz–5.4 GHz, and 5.7 GHz–6 GHz) to eliminate interference from co‐existing IEEE 802.16 WiMAX (3.3 GHz–3.8 GHz), IEEE 802.11y (3.65 GHz–3.69 GHz), IEEE 802.11a WLAN (5.15 GHz–5.35 GHz and 5.725 GHz–5.825 GHz), and IEEE 802.11p DSRC (5.85 GHz–5.925 GHz) bands. The antenna provides minimal gain variation (2–5 dBi), flat group delay response and non‐varying transfer function with high average efficiency of 88% in the pass band. Significant drop in gain and efficiency, nonlinearity in transfer function, and high variation in group delay are observed at notch bands. Antenna VSWR, and efficiency are measured in close proximity of sand, wood, and glass. Satisfactory results ensure its ability to work as Ground penetrating radar antenna.

Lossy Coupling Matrix Synthesis Approach for the Realization of Negative Group Delay Response

In this paper, a systematic synthesis approach is proposed for achieving negative group delay responses using lossy coupling matrix. It is mathematically proved that, for a passive and reciprocal network, loss is the necessary condition to realize a negative group delay. Also, the optimum strategy is to place zeros and poles of the transfer function on the left complex plane. A closed-form relation between the group delay and magnitude is then derived based on this strategy, and followed by a complete synthesis approach using coupling matrix. Two numerical and one experimental examples are finally given to illustrate the proposed synthesis method.

Apodized Spiral Bragg Grating Waveguides in Silicon-on-Insulator

We demonstrate an apodization technique by tapering the corrugations of spiral Bragg grating waveguides on the silicon-on-insulator platform, for the fundamental transverse magnetic mode. The transmission and reflection responses of uniform and apodized spiral Bragg grating waveguides are experimentally compared to show higher sidelobe suppression ratios by the proposed apodization scheme. We also present an apodized, period-chirped spiral Bragg grating waveguide, and the group delay of the proposed device has been measured; the results show an efficient suppression in the ripples of the group delay response.