Introduction
With the rapid development of communication technology, the demand for radio frequency (RF) modules with high performance, integration, and multifunction has become an irreversible trend. The design idea of integrating different functional circuits into one component shows great potential in the development of RF modules [Reference Liu, Tian, Liu and Feng1, Reference Psychogiou, Gómez-Garcia and Peroulis2].
The balun is usually composed of an unbalanced input port and two balanced output ports, realizing the conversion between an unbalanced signal to a balanced signal by converting matching input to differential output. Moreover, it is one of the most important components of the RF front-end module. The filtering balun has a frequency selectivity of filtering while realizing signal conversion, so it has received extensive attention. In recent years, coupled lines [Reference Huang, Lin and Tang3–Reference Wang, Huang, Zhu, Cai and Wu5], stepped impedance resonators [Reference Ouyang and Chu6, Reference Kim, Qi, Chaudhary and Jeong7], hybrid cavity-microstrip [Reference Fang, Li, Xue, Wu and Wong8], and other structures [Reference Liu, Wang, Zhu, Zhang and Wu9] have been used to design filtering balun. Based on this, double-sided parallel-strip lines [Reference Feng, Pan, Zhu, Zhou, Che and Xue10, Reference Chen, Wu and Wang11], substrate-integrated defected ground structure [Reference Tang and Luo12], and some other structures [Reference Jia, Zhang and Dong13] have been proposed to design the filtering balun with better performance. However, it is still a major challenge to design the filtering balun with excellent in-band performance, low radiation loss over a wide frequency range, compact size, and flexible integration.
Additionally, due to the continuous increase of application scenarios of communication technology, the performance degradation and abnormal operation of RF modules caused by more and more serious electromagnetic (EM) interference (EMI) occur from time to time. Therefore, it becomes increasingly important to achieve EM compatibility (EMC) when designing high-performance, miniaturized, multifunctional devices.
Low-temperature co-fired ceramic (LTCC) technology is a good choice to achieve various functions in a compact size. Based on the Marchand balun, [Reference Xu, Zhang and Zhao14] achieved filtering performance by using three feeding lines and further reduced the size of the balun filter by LTCC technology and horizontal and vertical folding of the lines. In [Reference Wu, Li, Xue, Feng and Hu15], an LTCC filtering balun and harmonic elimination are achieved by proper coupling between the feeding lines and the resonators in three-dimensional (3D) space. LTCC has excellent high-frequency performance and low loss performance, and multilayer design enables the integration of complex circuits and systems. However, due to the complexity of its manufacturing process and high cost, there are certain limitations in its application. Additionally, the insulating material used in the LTCC technology makes microwave devices using this technology vulnerable to EMI.
The substrate-integrated suspended line (SISL) technology was first proposed in [Reference Ma and Chan16]. This technology uses the shielding structure to shield the influence of EM radiation in the environment on the RF module when reducing the EM wave radiated by the radio frequency module to the environment. It has the advantages of self-packaging, EM shielding, low radiation loss, and low cost and is widely used in RF module design [Reference Xu, Ma and Du17–Reference Liu, Wang, He and Liu19].
In this paper, a filtering balun is designed by applying SISL technology, which realizes the function of EM shielding while retaining wide bandwidth and miniaturization. To improve the efficiency and accuracy of design, this work proposes a filtering balun synthesis design method with filtering characteristics based directly on the entire structure’s equivalent circuit model. It has been verified that this comprehensive design method can effectively guide the design of filtering balun.
Analysis and synthesis
SISL technology
The SISL technology is a transmission line that combines the advantages of suspended and planar structures. While retaining the benefits of traditional suspended lines, it uses standard printed circuit board manufacturing processes to solve the difficulties in grounding and high processing costs associated with traditional suspended line designs. Due to the advantages of SISL technology, such as low loss, high isolation, miniaturization, and easy integration with other planar circuits, it is widely applied in wireless communication systems.
The structure of the filtering balun based on the SISL technology is shown in Figs. 1 and 2. This structure is composed of six substrate layers (from substrate 1 to substrate 6) and 12 metal layers (from G1 to G12).
3D structure of the proposed filtering balun.
Detail layouts of the proposed SISL filtering balun.
The main circuit is designed on substrates 3 and 4, which are using Rogers RO4003C with thickness 
$h_3 = h_4 = 0.813$ mm and 
$\varepsilon_{r1} = 3.55$. Substrates 1, 2, 5, and 6 are using FR-4 with thickness 
$h_1 = h_2 = h_5 = h_6 = 0.6$ mm and 
$\varepsilon_{r2} = 4.4$. Substrates 2 and 5 are hollowed with rectangle shapes, and all the substrates are placed in the order shown in Fig. 3 to form the two air cavities for the main circuit. The EM shielding box consists of air cavities, metal via holes, and mental layers surrounding the air cavity.
Cross-section view of the proposed filtering balun.
For circuits containing dual dielectric substrates, the λg/4 suspended stripline open-circuited stub on G5, and λg/2 suspended stripline resonator on G8 are connected to 50 Ω feeding lines as unbalanced signal input port and balanced signal output port, respectively. As shown in Fig. 3, when a random unbalanced signal is input, the electric field distribution generated by the perpendicular coupling of the suspended stripline resonator and the λg/2 suspended slotline resonators on G6 and G7 can generate a 180∘ phase difference between the two output ports in a wide frequency range [Reference Feng and Zhu20].
Equivalent circuit
Since the balun’s output is balanced, the two output ports can be combined into one port on the circuit [Reference Feng and Zhu21]. Therefore, the three-port network can be equivalent to a two-port network. As shown in Fig. 4(a), the equivalent circuit uses transmission lines and ideal transformers to analyze the frequency response of the model. The λg/2 suspended stripline open-circuited stub and λg/2 suspended slotline resonator are represented by the series open-ended stub, shunt short-ended stub. Moreover, replace the λg/2 suspended stripline resonator for cascading functions with transmission lines. The energy transfer between them is equivalent through ideal transformers N 1, N 2, and N 3. The electrical lengths of the series open-ended stub, shunt short-ended stubs, and cascaded transmission lines are defined as 
$\theta = 90^{\circ}$ at central frequency. Moreover, the characteristic impedance of the 50 Ω feeding lines per port is defined as Z 0. The signal is input into the equivalent circuit network through the feeding line with the input impedance Z 0 and through the series open-ended stub, shunt short-ended stubs, and cascaded transmission line with characteristic impedance Zm, Zs, and 
$Z_{m1}$ and finally output through the feeding line with the output impedance of 2Z 0.
(a) Equivalent circuit with transformer. (b) Simplified equivalent circuit with 
$Z_{\mathrm{m}}^{\prime}=N_1^2 \times Z_{\mathrm{m}},\ Z_{\mathrm{s}}^{\prime}=N_2^2 \times Z_{\mathrm{s}},\ Z_{m1}^{\prime} = N_3^2 \times Z_{m1}$.
Synthesis design
This two-port network can be equivalent to an ideal transmission-line network with 
$N_1 = N_2 = N_3 = 1$. By multiplying the ABCD matrices of all the involved sections [Reference Yang, Zhu, Choi, Tam, Zhang and Wang22], the ABCD matrix of the whole structure can be expressed as
\begin{equation}
M=\left[\begin{array}{ll}
A & B \\
C & D
\end{array}\right]
\end{equation}where
\begin{equation}
A=\left(1+\frac{z_m}{2 z_{m 1}}\right) \frac{\cos \theta}{\sin ^2 \theta}-\left(1+\frac{z_m}{2 z_{m 1}}+\frac{2 z_m}{z_s}\right) \frac{\cos ^3 \theta}{\sin ^2 \theta}, \end{equation}
\begin{equation}
B=j\left[\frac{2 z_{m 1}}{\sin \theta}-\left(2 z_{m 1}+z_m+\frac{4 z_m z_{m 1}}{z_s}\right) \frac{\cos ^2 \theta}{\sin \theta}\right],
\end{equation}
\begin{equation}
C=j\left[\frac{1}{2 z_{m 1}} \frac{1}{\sin \theta}-\left(\frac{1}{2 z_{m 1}}+\frac{2}{z_s}\right) \frac{\cos ^2 \theta}{\sin \theta}\right],
\end{equation}
\begin{equation}
D=\left(1+\frac{4 z_{m 1}}{z_s}\right) \frac{\cos \theta}{\sin ^2 \theta}-\left(1+\frac{4 z_{m 1}}{z_s}\right) \frac{\cos ^3 \theta}{\sin ^2 \theta}.
\end{equation}Based on [Reference Wu and Zhu23], the scattering matrix of the two-port ideal transmission line network can be expressed as
\begin{equation}
S_{11}=\frac{A z_L+B-C z_F z_L-D z_F}{A z_L+B+C z_F z_L+D z_F},
\end{equation}
\begin{equation}
S_{21}=\frac{2 \sqrt{z_F z_L}}{A z_L+B+C z_F z_L+D z_F},
\end{equation} where 
$F_M=\mathrm{S}_{11} / \mathrm{S}_{21}$
Based on (1) and (2a) and the ABCD matrix of the whole structure, the mathematical expression of the characteristic function FM can be determined. Due to the introduction of (2a)–(2d), both real and imaginary parts are included in FM, and the Chebyshev polynomial function cannot be directly analyzed and solved. Therefore, ignoring the existence of the imaginary part in FM, FM can be expressed as
\begin{equation}
F_M=K_1 \frac{\cos \theta}{\sin ^2 \theta}+K_2 \frac{\cos ^3 \theta}{\sin ^2 \theta}
\end{equation}and
\begin{equation}
K_1=\frac{1}{2 \sqrt{z_F z_L}}\left[z_L\left(1+\frac{z_m}{2 z_{m 1}}\right)-z_F\left(1+\frac{4 z_{m 1}}{z_s}\right)\right],
\end{equation}
\begin{equation}
K_2=\frac{1}{2 \sqrt{z_F z_L}}\left[-z_L\left(1+\frac{z_m}{2 z_{m 1}}+\frac{2 z_m}{z_s}\right)+z_F\left(1+\frac{4 z_{m 1}}{z_s}\right)\right].
\end{equation} In (2a)–(6a), ZF and ZL are defined as the source and load impedances of this two-port ideal transmission line network, and 
$Z_F = Z_0$, 
$Z_L = 2Z_0$. zm, zS, 
$z_{m1}$, zF, and zL represent the impedance parameters, which are normalized by the source impedance ZF, respectively. The equivalent circuit designed using the quasi-Chebyshev polynomial design method can be expressed as
\begin{equation}
\left|\mathrm{S}_{21}\right|^2=\frac{1}{\left|F_M\right|^2+1}=\frac{1}{\left|F_L\right|^2+1}=\frac{1}{\varepsilon^2 \,\cos ^2(q \xi+n \phi)+1},
\end{equation}
\begin{equation}
\varepsilon=\sqrt{10^{0.1 L_A}-1}, \end{equation}
\begin{equation}
\cos \xi=\cos \phi \sqrt{\frac{\alpha^2-1}{\alpha^2-\cos ^2 \phi}},
\end{equation}
\begin{equation}
\cos \phi=\alpha \cos \theta,
\end{equation}
\begin{equation}
\alpha=1 / \cos \theta_c.\end{equation}In (7)–(11), LA is the ripple-level factor, ɛ is the ripple coefficient, θc is the electrical length at the lower cutoff frequency, and fc is the lower cutoff frequency. Since the equivalent circuit contains a transmission line that functions as a cascade, a filtering balun with a quasi-Chebyshev frequency response with n = 1 and q = 2 is comprehensively designed, and its characteristic impedance FL can be expressed as
\begin{equation}
F_L=K_3 \frac{\cos \theta}{\sin ^2 \theta}+K_4 \frac{\cos ^3 \theta}{\sin ^2 \theta}\end{equation}and
\begin{equation}
K_3=-\varepsilon\left(\alpha+2\left(\alpha^2-1\right)^{1 / 2}\right),\end{equation}
\begin{equation}
K_4=\varepsilon\left(2 \alpha^3+2 \alpha^2\left(\alpha^2-1\right)^{1 / 2}-\alpha\right).\end{equation} When 
$K_1 = - K_3$ and 
$K_2 = - K_4$, the normalized impedance values of Zm and Zs can be determined by calculating LA and θc.
Design and realization
According to the synthesis design method in the section “Analysis and Synthesis”, the original circuit of a three-pole filtering balun is designed according to the design parameters of 
$f_0 = 2.56$ GHz, 
$f_c = 1.72$ GHz, 
$L_A = 0.0436$, 
$\theta_c = 60.5^{\circ}$, and 
$Z_{m1} = 35.36~\Omega$. By theoretical calculation, it can be obtained that impedance 
$Z_m = 112~\Omega$, 
$Z_s = 60 ~\Omega$ or normalized impedance 
$z_m = 2.24$, 
$z_s = 1.2$. However, objective phenomena such as impedance discontinuities can cause deviations between theoretical calculations and full-wave simulations. Therefore, 
$Z_{\mathrm{m}}^{\prime}=N_1^2 \times Z_{\mathrm{m}},\ Z_{\mathrm{s}}^{\prime}=N_2^2 \times Z_{\mathrm{s}},\ Z_{m1}^{\prime} = N_3^2 \times Z_{m1}$ are used in this paper to incorporate this bias into the transformer’s turns ratio of employed transformers shown in Fig. 4, making the recalculated frequency response close to EM simulation result. It can be verified that the selection of 
$Z_m^{\prime} = 119.56~\Omega$, 
$Z_s^{\prime} = 74.76~\Omega$, and 
$Z_{m1}^{\prime} = 36.05~\Omega$ or 
$z_m^{\prime} = 2.39$, 
$z_m^{\prime} = 1.492$, and 
$z_{m1}^{\prime} = 0.73$ is in good agreement with the simulation results, and the turns ratio of the transformer used can be determined as 
$N_1 = 1.03$, 
$N_2 = 1.12$, and 
$N_3 = 1.01$.
Based on the results of theoretical calculations, a prototype circuit is fabricated on the Rogers RO4003C substrate. The details of the structure are shown in Figs. 2, 3, 5, and 6. The center frequency of the processed filtering balun is 2.56 GHz and the fractional bandwidth (FBW) is 65.6%. The measured return loss is better than 11.3 dB, but the simulated return loss is better than 20 dB. Insufficient machining accuracy is the main reason for this deviation. The magnitude imbalance is better than 1.7 dB, the phase imbalance between the two balanced ports is better than 4∘ (Fig. 7).
Top view of the filtering balun (unit: millimeters): mar1 = 8, mar2 = 43.5, mar3 = 4.75, W1 = 1.763, W2 = 4.6, W3 = 1.6, W4 = 4, W5 = 3.2, W6 = 1.763, L1 = 13.4, L2 = 4.85, L3 = 13.637, L4 = 18.6, L5 = 19.4.
The actual structure diagram of the proposed filtering balun: (a) Top-view of the first layer. (b) Top-view of layers other than the first layer. (c) Bottom-view of layers other than the sixth layer. (d) Bottom-view of the sixth layer.
Theoretical, EM-simulated, and measured frequency responses of the proposed filtering balun: (a) Comparison of theoretical, EM-simulated, and measured results. (b) Phase imbalance and magnitude imbalance.
Table 1 shows the performance comparison between the proposed wideband filtering balun and the related works. It can be analyzed that the proposed filtering balun has good insertion loss, phase imbalance, and wide FBW. Moreover, the integrated design method proposed in this paper can improve the design efficiency accurately and effectively. The use of SISL technology makes the filtering balun has a good EMC and good integration.
Comparison with some related work
1MI, magnitude imbalance; PI, phase imbalance; IL, insertion loss; -, not given.
Conclusion
In this brief, a wideband filtering balun is proposed, which is based on SISL technology. Because of balun’s output balance, its circuit can be equivalent to a two-port network. Based on the two-port network theory and Chebyshev polynomials, the characteristic functions FM and FL can be solved. By setting the characteristic functions FM and FL equal, the characteristic impedances Zm and Zs of the equivalent circuit can be obtained. According to the equivalent circuit whose parameters are solved, a filtering balun with 2.56 GHz as the center frequency is designed. The results show that the theoretical analysis, EM simulation, and measurement are in good agreement.
Funding Statement
This work was supported by Guangdong Basic and Applied Basic Research Funding—Regional Joint Fund for Youth Project under grant 2019A1515110417; National Natural Science Foundation of China under grant no (61761032, 62161032, and 62001170); Nature Science Foundation of Inner Mongolia under contract no. 2019MS06006; Joint Foundation of Key Laboratory of Shanghai Jiao Tong University-Xidian University, Ministry of Education, State Key Laboratory of Millimeter Waves, and China Postdoctoral Science Foundation under grant 2022M712513.
Competing interests
The author(s) declare none.
Yongliang Zhang received the B.S. and Ph.D. degrees in electrical engineering from Xidian University, Xi’an, China, in 2009 and 2014, respectively. He is currently with the College of Transportation, Inner Mongolia University, Hohhot, China. His research interests include passive microwave/millimeter-wave device, filtering antenna, smart antennas, reconfigurable antennas, and frequency selective surfaces, electromagnetic compatibility.
Huan Zhou received the B.E. degree from the Nanchang University, Nanchang, China, in 2020. He is currently pursuing the M.E. degree. His current research interests include filter, antennas, balun, and butler matrix.
Linping Feng received the M.S. degree from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2015 and the Ph.D. degree in electrical and computer engineering from the University of Macau, Macau, China, in 2018. From 2019 to 2021, he was a Post-Doctoral Research Fellow with the Guangdong Provincial Key Laboratory of Millimeter-Wave and Terahertz, School of Electronics and Information Engineering, South China University of Technology, Guangzhou, China. Since 2022, he has been an Assistant Professor with the School of Electronics and Information Engineering and the School of Microelectronics, Xi’an Jiaotong University, Xi’an, China. His current research interests include synthesis microwave circuits, high-temperature superconducting microwave circuits, cryogenics monolithic microwave integrated circuit (MMIC) low noise amplifier (LNA), and receivers.
