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.

This paper presents, for the first time, the coupling matrix synthesis for the application of a chained-function to waveguide filters. The realization of this filter is carried out by successively adding one resonator at a time by comparing the simulated responses of each stage with those obtained using the coupling matrix synthesized from the chained-function. A sixthorder chained-function waveguide bandpass filter centered at 28 GHz with a fractional bandwidth of 2% is demonstrated. The simulated S-parameter responses and the sensitivity analysis pertaining to the manufacturing errors is included. The chainedfunction waveguide has the lowest percentage changes in terms of the return loss performance given the same amount of distortion as compared with those of the Chebyshev response filters. This results in a lower sensitivity rate with respect to the manufacturing errors, leading to achieving a high-performance filter implementation with a minimum tuning effort.

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