On the Design and Fabrication of Chained-Function Waveguide Filters With Reduced Fabrication Sensitivity Using CNC and DMLS

Abstract

In this paper, we present the design and fabrication of a novel class of emerging waveguide filters based on chained-functions at the millimeter-wave band. The derivation of chained-functions by chaining of prescribed generalized Chebyshev seed functions based on the partition theory is presented in details, and the implementation to waveguide technology is proposed and evaluated. The waveguide filter is fabricated through two different technologies, namely the Computer Numerical Control (CNC) milling technology and the Direct Metal Laser Sintering (DMLS) based additive manufacturing technology. The chained-function filters, which lie in between the Butterworth and Chebyshev filters, inherit the salient properties of both Butterworth and Chebyshev filters. Therefore, the chained-function waveguide filter exhibits filtering responses that have a superior rejection property and a lower loss with reduced sensitivity to fabrication tolerance than the standard Chebyshev waveguide filter. The efficiency of the proposed waveguide filter is confirmed both theoretically and empirically, using the CNC and DMLS processes. The issues of a higher manufacturing tolerance and apparent surface roughness associated with the DMLS method are found to be electrically insignificant when the chained-function concept is adopted in waveguide filter design. In general, the measured results of all the realized waveguide filters agree well to those of the simulation models. These results positively demonstrate that the chainedfunction concept has robust properties for rapid, high-performance, low-cost, and sustainable filter design and implementation, particularly for higher millimeter-wave frequency bands and for narrowband applications.

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

“…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.…”

“…Most of the previous CFF papers [13], [25]- [32] focused on theoretical comparisons with the Chebyshev counterpart. However, to the best of our knowledge, no practical comparison has been investigated using the same target specifications, design implementation and manufacturing technology.…”

Design and Synthesis of Parallel-Connected Dielectric Filter Using Chain-Function Polynomial

“…The orthogonal rows can be constructed using the Gram-Schmidt orthogonalization process [3]. The coupling matrix of sub-networks M14 and M23 are formed using the techniques described in [4]. Similarity transformation is used on the sub-network matrix in ( 17) and ( 18) to obtain the coupling combination in (19) and (20).…”

“…This filter often possesses high sensitivity to fabrication tolerance because its design is usually based on Chebyshev polynomial approximation [2], [3]. The chained function, which transverse between Chebyshev and Butterworth polynomials, might be the trade-off and inherit the desired characteristics from both filters, which are studied in this paper to show their benefits in addressing the problem turning and filling in the gap [4], [5]. The Chebyshev filters have high rejection properties and an equal-ripple passband response to a specific filter order, making them the most common filter class in filter design [6], [7].…”

“…The chained function on the other hand can be found to compromise between Butterworth and Chebyshev approximations [10], [11] because it could combine the advantages of both Butterworth functions (lower filter losses, lower sensitivity, and lower resonator unloaded-Q factor) and Chebyshev functions (i.e., higher out-of-band and higher selectivity rejection) [12]. The technique of chained transfer functions can reduce filter complexity, manufacturing tolerance, and, most importantly, post-manufacturing tuning processes [4], [13]. This technique has the potential to extend the state-of-the-art development in a highperformance tuning-less filter toward higher operating frequencies and narrow bandwidth applications [5].…”