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\begin{document}

\title{Design of novel stripline diplexer using frequency dependent couplings}



\author[1]{Jiaxing Song}%
\author[1]{Chuicai Rong}%
\author[2]{Ruilong Zhu}%
\author[2]{Wen Zhang}%
\author[2]{Yiping Zhang}%
\author[1]{Yubo Liao}%
\affil[1]{Gannan Normal University}%
\affil[2]{Xi’an Matrix Wireless Technology Co., Ltd}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\selectlanguage{english}
\begin{abstract}
A novel stripline diplexer design using frequency dependent couplings to
achieve multiple transmission zeros is developed in this paper. The
transmission zeros generated by the frequency dependent couplings are
flexible and controllable, on the basis of the existing cross-coupled,
more transmission zeros are introduced to improve the frequency
selection characteristics. Based on this characteristic, we designed a
2.6G Hz diplexer, its transmitting channel filter is 5 order with 4
transmission zeros, and the receiving channel filter is 4 order with 5
transmission zeros. We fabricated and measured it, the synthesis
results, simulation results, and the tested results are well matched
with each other, which will provide more flexibility in the design of
diplexers for wireless communication system.%
\end{abstract}%



\sloppy


Design of novel stripline diplexer using frequency dependent couplings

\section*{\texorpdfstring{Jiaxing Song\textsuperscript{1}, Chuicai
Rong\textsuperscript{1*}, Ruilong Zhu\textsuperscript{2}, Wen
Zhang\textsuperscript{2}, Yiping Zhang\textsuperscript{2},Yubo
Liao\textsuperscript{1}}{Jiaxing Song1, Chuicai Rong1*, Ruilong Zhu2, Wen Zhang2, Yiping Zhang2,Yubo Liao1}}

{\label{jiaxing-song1-chuicai-rong1-ruilong-zhu2-wen-zhang2-yiping-zhang2yubo-liao1}}

\textsuperscript{1}\emph{School of Physics and Electronic information,
Gannan Normal University. Ganzhou, 341000 China}

\textsuperscript{2}\emph{Xi} \emph{'an Matrix Wireless Technology Co.,
Ltd. Xi'an, 710100 China}

Email: rongchuicai519@gnnu.edu.cn

Abstract:A novel stripline diplexer design using frequency dependent
couplings to achieve multiple transmission zeros is developed in this
paper. The transmission zeros generated by the frequency dependent
couplings are flexible and controllable, on the basis of the existing
cross-coupled, more transmission zeros are introduced to improve the
frequency selection characteristics. Based on this characteristic, we
designed a 2.6G Hz diplexer, its transmitting channel filter is 5 order
with 4 transmission zeros, and the receiving channel filter is 4 order
with 5 transmission zeros. We fabricated and measured it, the synthesis
results, simulation results, and the tested results are well matched
with each other, which will provide more flexibility in the design of
diplexers for wireless communication system.

\emph{Introduction:} With the rapid development and wide application of
modern communication technology, the limited spectrum resources are
becoming more precious, in order to make full use of the electromagnetic
spectrum resources, the operating frequency interval between various
communication systems is getting smaller and smaller, and the
anti-interference requirements between adjacent operating bands are also
put forward higher requirements, the demand for highly selective RF
front-end diplexers is also growing{[}1-2{]}.

The finite transmission zeros are critical for diplexer design to
enhance the rejection ratios, one of the prevalent methods for creating
finite transmission zeros is the basic cross- coupling mechanism, and
another popular mechanism to create finite transmission zeros is based
on the frequency dependent coupling {[}3-5{]}.

Metal stripline resonators have higher \emph{Q} values, better harmonic
suppression characteristics and higher reliability than dielectric
waveguide resonators. Here we introduce a inverted E-type metal
resonator, which can be regarded as an evolution of a 1/4 wavelength
step impedance resonator, and they have similar field distribution and
resonant characteristics. The upper space of the stripline resonator is
mainly electric field distribution, and the lower space is mainly
magnetic field distribution. When two stripline resonators are placed
side by side, the electrical coupling \(E_{c}\) mainly exists
through the upper half space coupling window, while the magnetic
coupling\(M_{c}\) mainly exists through the lower half space
coupling window. When there are coupling windows in the upper and lower
spaces of both stripline resonators, that is, there are both electrical
and magnetic coupling between the two resonators, the total coupling
coefficient\emph{k} is frequency dependent, and the transmission
zero\(f_{\text{tz}}\) produced by the frequency dependent coupling as
follow{[}6-12{]}:

\(k=\frac{(M_{c}-E_{c})}{(1-\text{M\ }_{c}E_{c})}\) (1)

\(f_{\text{tz}}=f_{0}\sqrt{\frac{M_{c}}{E_{c}}}\)(2)

As can be seen from (1) and (2), when the electric coupling in
\(E_{c}\)is greater than magnetic coupling\(M_{c}\),
the transmission zero \(f_{\text{tz}}\) generated by the frequency
dependent coupling will be at the lower end of the passband. While the
magnetic coupling \(M_{c}\)is greater than the electric
coupling \(E_{c}\), the transmission zero \(f_{\text{tz}}\)
will be at the higher end of the passband.

\emph{Diplexer design and measurement:} Based on the frequency dependent
coupling of the two stripline resonators described above, the frequency
dependent coupling can generate transmission zero at the high frequency
stopband or the low frequency stopband of filter, respectively, which
can effectively improve the selection characteristics of the filter,
while the asymmetric frequency response can greatly improve the
isolation between channels in the diplexer applications. So here, we
designed and fabricated a 2.6G cross-coupled diplexer with frequency
dependent couplings, to verify the feasibility. The following specs have
been assumed (return loss is 22dB for both channels).

Junction: Resonant node.

RX Filter: Band= {[}2495, 2575{]} MHz and \(f_{\text{tz}}\)= {[}2484,
2605, 2679{]} MHz, 4th order.

TX Filter: Band= {[}2615, 2695{]} MHz and \(f_{\text{tz}}\)= {[}2561,
2597, 2717{]} MHz, 5th order.

According to the above technical specifications, we carried out
synthesis, modeling and simulation, the topology with synthesis results
are shown in Fig. 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Fig 1} . Topology schematic of the duplexer with resonating
frequencies, coupling coefficients and the external Q. (Black solid
circle represent the resonators. Numbers next to the lines connecting
the circles represent coupling coefficients or external \emph{Q} . Solid
line segments with arrows: FDC the pair \(\frac{k_{0i,j}}{C_{i,j}}\).)

The diplexer simulation model is shown in Fig. 2, whose dimensions are
55mm\selectlanguage{ngerman}×21mm×19mm, the simulation response and synthesis response are
matched well as shown in Fig. 3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig 2} . The simulation model of the stripline duplexer\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig 3} . The simulation response compared with the synthesis
response of the stripline duplexer\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Fig 4.} Photograph of the fabricated striplinediplexer\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Fig 5} . The narrow band measurement results compared with the
synthesis response of the duplexer\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Fig 6.} The wide band measuremen results compared with
simulation response of the duplexer

The photograph of the fabricated diplexer is shown in Fig. 4, whose
dimensions are 57mm\selectlanguage{ngerman}×23mm×21mm (connector size is not included). In Fig.
6, the wide band response of the diplexer, there is one parasitic
transmission zero of the transmitting channel, while there are two
parasitic transmission zeros of the receiving channel. The parasitic
transmission zeros can further enhance remote suppression. Combined with
Fig. 3 and Fig. 5, we know the synthesis results, simulation results,
and tested results are well matched with each other.

\emph{Conclusion:} In this paper, a novel 2.6G stripline diplexer with
multiple transmission zeros using frequency dependent couplings is
developed. On the basis of the synthesis technique for cross-coupling
filter, by introducing the frequency dependent couplings new
transmission zeros are generated. The diplexer has better frequency
selection characteristics, lower loss, better harmonic suppression
characteristics and higher reliability, and it can be welded and
integrated on the PCB board like the dielectric waveguide diplexer, it
has broad application value.

\emph{Acknowledgments:} This work was supported by science and
technology project of Jiangxi Provincial Department of Education
(GJJ2201211), key research and development plan of
Ganzhou(2022B-GY9645), the natural science foundation of Jiangxi
Province, China (Grant No.20202BABL201022).

\selectlanguage{english}?2021 The Authors. \emph{Electronics Letters} published by John Wiley \&
Sons Ltd on behalf of The Institution of Engineering and Technology

This is an open access article under the terms of the Creative Commons
Attribution License, which permits use, distribution and reproduction in
any medium, provided the original work is properly cited.

\emph{Received:} xx January 2021 \emph{Accepted:} xx March 2021

doi: 10.1049/ell2.10001

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