Robust Tolerance Design of Bandpass Filter With Improved Frequency Response for Q-Band Satellite Applications

Abstract

A rectangular waveguide bandpass filter for Q-band with simple fabrication is proposed in this letter. The design is based on the use of the first passband replica of commensurateline stepped-impedance structures and achieves the suppression of their inherent low-pass response. In order to do it, the filter is implemented by rectangular waveguide sections with different widths and heights that can be analytically calculated. The technique is validated by a 9 th order Chebyshev filter with passband between 40 and 43 GHz and fabrication yield equal to 84 % for a manufacturing error of ± 20 μm. The measured results of the prototype fabricated with CNC milling are in good agreement with the simulated ones.

Integrating multiple stubs in stepped‐impedance filter aiming for high selectivity

“…Then, the characteristic impedance values are modelled with waveguide sections where both the width, a n , and height, b n , can be varied. Assuming TE 10 ‐mode propagation, a n and b n are related through () [6] $$\begin{equation}{b_n} = {Z_n}\ \sqrt {{{\left( {\frac{{2\ \times \ \pi \ \times \ \ {f_\pi }}}{c}} \right)}^2} - \ {{\left( {\frac{{\pi \ }}{{{a_n}}}} \right)}^2}} \end{equation}$$where c is the speed of light in vacuum and f π is the central frequency of the passband calculated as in [7]. As the BPF is based on commensurate lines, the electrical length $$\pi -{\theta}_{c}$$ and $$\pi +{\theta}_{c}$$ of the commensurate lines correspond to f 1 and f 2 , respectively, where π is the electrical length that corresponds to the middle frequency of the passband and θ c is given by () [7] $$\begin{equation}{\theta _{\rm{c}}} = \pi \ \times \ \frac{{{\lambda _{f1}} - {\lambda _{f2}}}}{{{\lambda _{f1}} + {\lambda _{f2}}}}\end{equation}$$being λ fi the wavelength related to frequency f i .…”

“…Rectangular waveguide stepped-impedance filters based on commensurate lines are typically employed to obtain low-pass waveguide filters [4]. In [5,6], the first passband replica of these structures was used to design bandpass filters (BPFs), significantly increasing the fabrication tolerances compared with the classical inductive iris filters. These BPFs are implemented with stepped-impedance waveguide sections and allow novel topologies, such as the meandered filters proposed in [7] to reduce their overall footprint.…”

“…Design method: As it is detailed in [5,6], in order to design a steppedimpedance BPF based on commensurate lines, the order of the filter N, the in-band return loss level, the type of filtering function, and the lower and upper cut-off frequencies (f 1 and f 2 ) of the device must be specified to calculate the impedances Z n of the N + 2 commensurate lines of the prototype that satisfy the specified frequency response. Then, the characteristic impedance values are modelled with waveguide sections where both the width, a n , and height, b n , can be varied.…”

“…Then, the characteristic impedance values are modelled with waveguide sections where both the width, a n , and height, b n , can be varied. Assuming TE 10 -mode propagation, a n and b n are related through (1) [6] where c is the speed of light in vacuum and f π is the central frequency of the passband calculated as in [7]. As the BPF is based on commensurate lines, the electrical length π − θ c and π + θ c of the commensurate lines correspond to f 1 and f 2 , respectively, where π is the electrical length that corresponds to the middle frequency of the passband and θ c is given by (2) [7]…”

“…Design example: According to the design method explained in the last section, the first step is to design a stepped-impedance BPF based on commensurate lines. For instance, for Ku-band applications [5,6], seventh-order (N = 7) Chebyshev bandpass response can be achieved between f 1 = 10.70 GHz and f 2 = 12.75 GHz with in-band return losses better than 20 dB using the following normalized impedances Z n : Z 0 = Z 8 = 1, Z 1 = Z 7 = 1.84, Z 2 = Z 6 = 0.40, Z 3 = Z 5 = 3.32, Z 4 = 0.32, assuming a constant width equal to a = 19.05 mm and an initial height b 0 = 3.8 mm. Afterwards, the heights of the sections, b n , for the corresponding Z n are calculated using (1) and l n is adjusted satisfying the phase conditions given in [7].…”