Chained-Function Filter Synthesis Based on the Legendre Polynomials

Stojanović, Nikola; Stamenković, Negovan; Krstić, Ivan

doi:10.1007/s00034-017-0651-1

Cited by 4 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Practical chained-function filters have previously been demonstrated in microstrip transmission line [28] and metalpipe rectangular waveguides [13], [29]- [32]. In 2017, non-Chebyshev seed functions were introduced into CFFs; for example, with Legendre [33], Jacobi [34] and then elliptical [32] polynomials.…”

Section: Chained-function Filtersmentioning

confidence: 99%

3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

et al. 2022

View full text Add to dashboard Cite

This paper investigates physical dimension limits associated with the low-cost, polymer-based masked stereolithography apparatus (MSLA) 3-D printer, with 50 µm pixels defining the minimum print feature size. Based on the discretization properties of our MSLA 3-D printer, multi-step quantization predistortion is introduced to correct for registration errors between the CAD drawing and slicing software. This methodology is applied to G-band 5 th order metal-pipe rectangular waveguide filters, where the pixel pitch has an equivalent electrical length of 8.5 • at center frequency. When compared to the reference Chebyshev filter, our chained-function filter exhibits superior S-parameter measurements, with a low insertion loss of only 0.6 dB at its center frequency of 182 GHz, having a 0.9% frequency shift, and an acceptable worst-case passband return loss of 13 dB. Moreover, with measured dimensions after the 3-D printed parts have been commercially electroplated with a 50 µm thick layer of copper, the re-simulations are in good agreement with the S-parameter measurements. For the first time, systematic (quantization) errors associated with a pixelbased 3-D printer have been characterized and our robust predistortion methodology has been successfully demonstrated with an upper-millimeter-wave circuit. Indeed, we report the first polymer-based 3-D printed filters that operate above W-band. As pixel sizes continue to shrink, more resilient (sub-)THz filters with ever-higher frequencies of operation and more demanding specifications can be 3-D printed. Moreover, our work opens-up new opportunities for any pixel-based technology, which exhibits registration errors, with its application critically dependent on its minimum feature size.

show abstract

Section: Chained-function Filtersmentioning

confidence: 99%

3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

et al. 2022

View full text Add to dashboard Cite

show abstract

“…When all transmission zeros in every seed function approach infinity, the seed functions degenerate to the conventional Chebyshev polynomial [5]. The synthesis of Legendre Chained Function filters was reported in recently published paper [2].…”

Section: Chained Functionsmentioning

confidence: 99%

“…With chained-functions, one may define a new polynomial characteristic function that is given by the product of a combination of low degree classical Chebyshev polynomials, called seed functions. The chained function as product of lower degree Legendre polynomials was recently published in the paper [2].…”

Section: Introductionmentioning

confidence: 99%

Chained-Function Filter Synthesis Based on the Modified Jacobi Polynomials

Perenic¹,

Stamenković²,

Stojanović³

et al. 2018

RADIOENGINEERING

View full text Add to dashboard Cite

A new class of filter functions with pass-band ripple which derives its origin from a method of determining the chained function lowpass filters described by Guglielmi and Connor is introduced. The closed form expressions of the characteristic functions of these filters are derived by using orthogonal Jacobi polynomial. Since the Jacobi polynomials can not be used directly as filtering function, these polynomials have been adapted by using the parity relation for Jacobi polynomials in order to be used as a filter approximating function. The obtained magnitude response of these filters is more general than the magnitude response of published Chebyshev and Legendre chained function filter, because two additional parameters of modified Jacobi polynomials as two additional degrees of freedom are available. It is shown that proposed modified Jacobi chained function filters approximation also includes the Chebyshev chained function filters, the Legendre chained function filter, and many other types of filter approximations, as its special cases.

show abstract

“…The reduction in selectivity and rejection properties will greatly compromise the performance of the filter, especially in narrow-band applications that require high selectivity due to the stringent spectrum utilization. Recent studies on modifying chained-function polynomials have been introduced in [7,8], but the resulting transfer functions are all-pole functions, which limit the selectivity and close-to-band rejection improvement.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Chained-Elliptic Function Waveguide Bandpass Filter With High Rejection

Ng¹,

Cheab²,

Wong³

et al. 2020

PIER C

View full text Add to dashboard Cite

This paper describes the synthesis of a bandpass filter to achieve high selectivity and rejection properties using a new class of filter functions called chained-elliptic function filters. Chainedelliptic filters have higher selectivity than Chebyshev function filters and have the property of sensitivity to manufacturing tolerance reduction in chained-function filters. The proposed design has high selectivity and reduced sensitivity, enabling easier and faster filter fabrication. The characteristic polynomials of chained-elliptic function filters are derived (through chaining elliptic filtering function) and extracted to form a coupling matrix of the bandpass filter. The novel transfer polynomials are given in detail, and a thorough investigation of the filter characteristics is performed. A theoretical comparison with Chebyshev and elliptic filters of the same order is performed to ascertain the demonstrated advantages of this proposed filter class. A high frequency narrow-band fourth-order chained-elliptic function waveguide filter centred at 28 GHz with a fractional bandwidth of 1.61% is fabricated to validate the proposed design concept. A good match among the measured, simulated, and ideal filter responses is shown where the overall responses between measurement and simulation have a difference of approximately 2% which is within the acceptable limit. The chained-elliptic function concept will be useful in designing low-cost high-performance microwave filters with various fabrication technologies for millimetre-wave applications.

show abstract

Chained-Function Filter Synthesis Based on the Legendre Polynomials

Cited by 4 publications

References 19 publications

3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

Chained-Function Filter Synthesis Based on the Modified Jacobi Polynomials

Synthesis of Chained-Elliptic Function Waveguide Bandpass Filter With High Rejection

Contact Info

Product

Resources

About