Flat Group Delay Response Research Articles

Reflective coupled microring resonators for reconfigurable photonic systems: Performance analysis

We propose reflective type triple coupled microring resonators (TCMMRs) for reconfigurable photonic based systems. We have developed an analytical model and analyzed its useful performance characteristics. The TCMMRs based device exhibits a wide range of performance characteristics such as multi-band filtering, optical logical operations, and optical true-time delay lines. Reconfigurable multiple resonances and their splitting features associated with the device provide useful filtering performance characteristics such as high out-of-band rejection, flat-top bandwidth, and near to ideal shape factor. The device can perform multiple functions such as bandpass, bandstop, and notch filtering with a good performance. Unlike two input narrowband logical operations demonstrated in the literature, our proposed device can perform as three-input optical logical operator, and it can switch wideband microwave frequency signals optically. Moreover, the device exhibits wideband flat top group delay response. It carries out delay tuning using a single variable coupling coefficient which simplifies the complexity of the tuning encountered in binary tree-structured optical beamforming networks based on conventional microring resonators.

Maximally Flat IIR Fullband Differentiators with Flat Group Delay Responses

A new design method for maximally flat IIR fullband differentiators with flat group delay responses is derived in this paper. The design method starts from the flatness conditions of magnitude response and group delay response at the origin. After mathematical manipulations it shows that presented design method reduces to solving the system of linear equations. By increasing the orders of polynomials in numerator and denominator, degrees of flatness are increased, that is improvement in magnitude responses and group delay responses in terms of flatness is obtained.

Maximally Flat IIR Fullband Differentiators with Flat Group Delay Responses

A new design method for maximally flat IIR fullband differentiators with flat group delay responses is derived in this paper. The design method starts from the flatness conditions of magnitude response and group delay response at the origin. After mathematical manipulations it shows that presented design method reduces to solving the system of linear equations. By increasing the orders of polynomials in numerator and denominator, degrees of flatness are increased, that is improvement in magnitude responses and group delay responses in terms of flatness is obtained.

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.

Arbitrary Prescribed Wideband Flat Group Delay Circuits Using Coupled Lines

This paper presents the analytical design of transmission-type arbitrary prescribed wideband flat group delay (GD) circuits (type-I and type-II) using $\lambda $ /4 coupled lines. The GD circuit type-I consists of two sections of coupled lines, whereas the GD circuit type-II consists of $\lambda $ /4 transmission lines (TLs) at input and output, in addition to coupled lines. The additional $\lambda $ /4 TLs at input–output ports in GD circuit type-II provide more freedom to obtain larger GD, as compared to type-I, without fabrication difficulties. The analytical analysis shows that the wideband flat GD response can be obtained by selecting the appropriate even- and odd-mode impedances of coupled lines and the characteristic impedance of TLs. To obtain the arbitrary prescribed wideband flat GD response, the closed-form analytical design equations are provided. For experimental validation of the proposed structures, prototypes of GD circuits (type-I and type-II) are designed and fabricated at the center frequency of 2 GHz. The measurement results agree well with the simulation and theoretical predicted results.

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.

Reflection-Type Topologies With Arbitrary Wideband Flat Group Delays Using Coupled Lines

This paper presents the analytical design techniques of several reflection-type group delay (GD) circuits (types-I-III) with arbitrarily prescribed wideband flat GD responses using $\lambda $ /4-coupled lines. The type-I GD circuit consists of the $\lambda $ /4 transmission lines and an open-circuited coupled line with a short-circuited load, whereas type-II consists of a short-circuited coupled line with an open-circuited load. For a compact circuit size, the type-III circuit is realized by a parallel combination of the open-circuited and short-circuited coupled lines. To obtain the arbitrarily prescribed response of wideband flat GD, closed-form analytical design equations are provided. An analytical analysis shows that the wideband flat GD response can be obtained by controlling the appropriate even- and odd-mode impedances of the coupled lines. For an experimental validation of the proposed structures, prototypes of the three GD circuits were designed and fabricated at the center frequency of 2.5 GHz. To realize a higher GD response over a wideband bandwidth, a number of reflection-type GD circuit units are cascaded and measured. The measurement results agree soundly with the simulation and theoretical prediction results.

Use of Phase Delay Analysis for Evaluating Wideband Circuits: An Alternative to Group Delay Analysis

A phase delay analysis is proposed against pursuing a flat group delay response for the design of wideband circuits. While it is believed that a large group delay variation introduces a large data-dependent jitter, this brief reconsiders the effectiveness of the group delay analysis in the evaluation of wideband circuits. Because of its own differentiating nature, the group delay provides a good insight on the delay variation at a vicinity of a certain frequency. However, for certain kind of wideband circuits, the group delay analysis cannot provide a sufficient insight since much of useful information is lost or distorted during the differentiating operation. In this brief, the effectiveness of the phase delay analysis is investigated and comparison with a traditional group delay analysis is presented with a theoretical approach and through a few circuit examples.

Synthesis of Reflection-Type Coupled Line All-Pass Circuit With Arbitrary Prescribed Wideband Flat Group Delay

In this letter, the analytical design method of a reflection-type coupled line all-pass circuit with arbitrary predefined wideband flat group delay (GD) is presented. The proposed circuit consists of 90° hybrid and coupled lines with a short-circuited load. The proposed structure is simple and does not require any iterative process to obtain optimum circuit parameters. Theoretical and experimental results are provided for validation of the proposed structure. The prototype circuits were fabricated at a center frequency of 2.5 GHz with 2 and 4 ns flat GD responses. The measurement results agreed well with the simulation and theoretical predicted results.

Design of a Compact UWB Bandpass Filter using Via-Less CRLH TL

A novel compact ultra wideband (UWB) bandpass filter (BPF) based on composite right/left handed transmission line (CRLH TL) is reported in this paper. The proposed UWB BPF is designed and developed by coupling of two unit-cells of via-less CRLH TL, excited by asymmetrical coplanar waveguide (CPW) feed-line. The unit cell of CRLH TL is designed using series interdigital capacitor (IDC) in shunt with the shorted inductive stub. Because of the CPW-fed, no via is required to get the shunt inductance for the realization of CRLH TL, which minimizes the fabrication steps. The filter is compact in size 11.9 x 6 mm 2 . The proposed filter exhibits the return-loss (|S 11 |) more than 11.2 dB and insertion-loss (|S 21 |) less than 0.5 dB and low and flat group delay response throughout the passband, 3.3 GHz to 13.0 GHz. The proposed UWB BPF also shows the good stopband rejection (|S 21 | > 20 dB and |S 11 | < 0.8 dB) from 13.6 GHz to 15 GHz and steep roll-off from passband to stopband. The fractional bandwidth (FBW) of the filter is found to be 119 %. The equivalent lumped circuit model of the filter is obtained through Ansoft Designer. All simulated results are extracted through method of moment based simulator, IE3D. Agilent vector network analyzer (VNA) is used to get the measured results. All measured results are found in close similarity with the simulated results.

Ultra-wideband coaxial-waveguide power divider with flat group delay response

A novel ultra-wideband (UWB) coaxial-waveguide power divider is presented. The design approach for the presented power divider has been developed; and a four-way UWB coaxial-waveguide power divider has been designed, fabricated and measured. The measured results show good agreement with the simulated ones.

Wideband Parallel-Strip Bandpass Filter Using Phase Inverter

A new wideband parallel-strip bandpass filter using phase inverter with stubs is proposed. With the wideband phase inverter in the parallel-strip line structure, the measured fractional passband bandwidth is 123% with a flat group delay response. Also, over 90% impedance bandwidth is obtained for the return loss higher than 20 dB. The theoretical simulation, electromagnetic simulation, and measured results show good agreement with this proposed design.

Group Delay Enhancement in Circular Arrays of Microring Resonators

Circular arrays of microring resonators are proposed for enhancing the group delay of slow-wave microring lattice structures. Large peak delay enhancements can be obtained and dynamically tuned by simply varying the loop coupling coefficient. It is also shown that maximally flat group delay responses can be achieved in these structures for potential application in compact dispersionless optical delay elements.

Synthesis of One-Input M-Output Optical FIR Lattice Circuits

This paper presents a one-input M-output (1 x M)configuration and a synthesis algorithm for realizing an optical finite impulse response (FIR) lattice filter having M output channels (M ges 2). The circuit configuration has a multilayer structure consisting of multiple Mach-Zehnder interferometers with delay time differences of zero or Deltatau. It is a natural extension of the conventional two-port optical FIR lattice circuit (M = 2) . The proposed synthesis algorithm is based on factorizations of the paraunitary total transfer matrix. It realizes output responses having highest orders equal to the number of stages for all output channels. It is shown that such a synthesis algorithm maximizes the degrees of freedom for designing output responses. Two kinds of five-channel interleave filters are demonstrated as synthesized examples: one has a flat group delay response while the other has an inclined group delay response.

Design of maximally flat IIR filters with flat group delay responses

Digital filters with linear phase responses, that is, constant group delay responses are needed in many applications for signal and image processing. In this paper, a novel method is proposed for designing maximally flat IIR filters with flat group delay responses in the passband. First, a system of linear equations are derived from the flatness conditions of IIR filters given in the passband and stopband, respectively. Then, a set of filter coefficients can be easily obtained by simply solving this system of linear equations. In the proposed design method, the flatness of the frequency response can be specified arbitrarily. The design of lowpass filters are described in detail, and bandpass and bandstop filters are given also. Moreover, the causality and stability of the proposed maximally flat IIR filters are examined by designing various IIR filters with different group delays. It is shown from the experimental results that the obtained maximally flat IIR filters are causal stable if the group delay is set to be larger than a specific value. Finally, some design examples are presented to demonstrate the effectiveness of the proposed maximally flat IIR filters.

Design of microstrip quadruplet filters with source-load coupling

Quadruplet microstrip filters with source-load coupling are proposed to achieve similar skirt selectivity and/or in-band flat group delay as that of a sixth-order canonical form or an extracted pole microstrip filter. The diagnosis method of unwanted effects such as asynchronous resonant frequencies and unwanted couplings, which often occurs in the microstrip's open environment, is described in detail. A systematic design flow to implement a quadruplet microstrip source-load coupled filter with proper filter response is also provided. Two trial filters exhibited quasi-elliptical and flat group-delay response are designed and fabricated. Both theoretical and experimental results are presented.

Results on Maximally Flat Fractional-Delay Systems

The two classes of maximally flat finite-impulse response (FIR) and all-pass infinite-impulse response (IIR) fractional-sample delay systems are thoroughly studied. New expressions for the transfer functions are derived and mathematical properties revealed. Our contributions to the FIR case include a closed-form formula for the Farrow structure, a three-term recurrence relation based on the interpolation algorithm of Neville, a concise operator-based formula using the forward shift operator, and a continued fraction representation. Three types of structures are developed based on these formulas. Our formula for the Farrow structure enhances the existing contributions by Valimaki, and by Vesma and Sarama/spl uml/ki on the subsystems of the structure. For the IIR case, it is rigorously proved, using the theory of Pade approximants, that the continued fraction formulation of Tassart and Depalle yields all-pass fractional delay systems. It is also proved that the maximally flat all-pass fractional-delay systems are closely related to the Lagrange interpolation. It is shown that these IIR systems can be characterized using Thiele's rational interpolation algorithm. A new formula for the transfer function is derived based on the Thiele continued fractions. Finally, a new class of maximally flat FIR fractional-sample delay systems that exhibit an almost all-pass magnitude response is proposed. The systems possess a maximally flat group-delay response at the end frequencies 0 and /spl pi/, and are characterized by a closed-form formula. Their main advantage over the classical FIR Lagrange interpolators is the improved magnitude response characteristics.

Miniaturized microstrip cross-coupled filters using quarter-wave or quasi-quarter-wave resonators

Miniaturized microstrip filters using quarter-wave or quasi-quarter-wave resonators with cross-coupling are presented. The quarter-wavelength resonators enable very compact positively or negatively cross-coupled filters to be realized. The combination of quarter-wave and quasi-quarter-wave resonators facilitates the cross-coupling with a proper coupling phase. A new explanation for the coupling phase between the main-coupling and cross-coupling paths is proposed. Different filters that use the proposed resonators are realized and may have either quasi-elliptical or flat group-delay responses. Measurement results correlate well with theoretical predictions.

Universal maximally flat lowpass FIR systems

The family of FIR digital filters with maximally flat magnitude and group delay response is considered. The filters were proposed by Baher (1982), who furnished them with an analytic procedure for derivation of their transfer function. The contributions of this paper are the following. A simplified formula is presented for the transfer function of the filters. The equivalence of the novel formula with a formula that is derived from Baher's analytical procedure is proved using a modern method for automatic proof of identities involving binomial coefficients. The universality of Baher's filters is then established by proving that they include linear-phase filters, generalized half-band filters, and fractional delay systems. In this way, several classes of maximally flat filters are unified under a single formula. The generating function of the filters is also derived. This enables us to develop multiplierless cellular array structures for exact realization of a subset of the filters. The subset that enjoys such multiplierless realizations includes linear-phase filters, some nonsymmetric filters, and generalized halfband filters. A procedure for designing the cellular array structures is also presented.

Optimised square passband fibre Bragg grating filterwith in-band flat group delay response

Through a controlled apodised sinc-shaped refractive index profile, an optimised square reflection band Bragg grating filter is demonstrated. The filter is 5 cm long and has a flat dispersion profile within the photonic bandgap and an edge steepness of 7.9 dB/GHz.