1. Introduction

As the development of the fifth generation (5G) mobile communication, Ka-band has gained great interest in many important applications [1], such as base station transceivers [2], satellite communication [3], continuous-wave monostatic radar [4], and deep-space data transmission [5]. Frequency division multiplexing (FDM) is important in these advanced systems to obtain multichannel functionalities and high spectral efficiency, which can be used either as a channel divider or channel combiner [6]. Typically, FDM has four kinds of configurations including hybrid-coupled, circulator-coupled, directional-filter, and manifold-coupled types [7]. Wherein hybrid-coupled multiplexers have large size and require precise machining, circulator-coupled ones suffer from extra loss and high cost, and the directional-filter approach is limited to narrowband applications. In regard to low insertion loss and good electromagnetic compatibility, manifold-coupled FDM is typically considered a promising choice [7–10]. However, most of the manifold-coupled multiplexers are designed in metallic waveguides with bulky profile, large weight, and high cost [11–15]. To achieve miniaturization, ridged substrate integrated waveguides (SIWs) have been investigated for multiplexing at the cost of considerable fabrication complexity [16].

Recently, SIW–spoof surface plasmon polariton (SSPP) hybrid filters have gained great interest by combining the low cut-off response of SIWs and the high cut-off response of SSPPs [17–19]. Due to the cut-off responses, such hybrid filters address broadband out-of-band rejection, which is preferable for FDMs. However, their 3 dB bandwidth is typically larger than 13% [20, 21]. To the best knowledge of the authors, SIW–SSPP hybrid filters have not been applied in FDM.

In our previous work, a novel SIW–SSPP hybrid filter with a narrow bandwidth and microstrip line (MSL) feed has been proposed [21], achieving a 3-dB bandwidth of 3%. In this paper, a manifold-coupled FDM comprising three SIW–SSPP hybrid filters at 28.2, 29.7, and 31.2 GHz is proposed for the first time. Low-loss and compact MSL manifolds are designed to connect the three filter units with phase delay match. The proposed manifold-coupled multiplexer achieves a 3-dB passband of 4.1%, 4.7%, and 4.8% and an insertion loss of 2.10, 2.49, and 2.61 dB at 28.2, 29.7, and 31.2 GHz, respectively, with the benefit of ultrawideband out-of-band rejection, showing good consistency with the simulation.

2. Design and Simulation

Ansys high frequency structure simulator (HFSS) is employed to design the following filters and FDM on a 10-mil thick Rogers 5880 substrate. The substrate has a low loss tangent of 0.0009 and a relative permittivity of 2.2, and the laminated copper layer has a thickness of 18 μm. As aforementioned, SIWs and SSPPs exhibit low and high cut-off responses, respectively, which could be combined for the band-pass function. Typically, complementary SSPPs, that is, periodic rectangular slots, are designed on the SIW broadside to get a high cut-off frequency. However, simple rectangular slots are not long enough to get a narrow passband.

2.1. Filter Design

Figure 1 illustrates the proposed SIW–SSPP hybrid filter with I-shaped SSPP slots, which exhibits much larger effective length and thus achieves a much lower cut-off frequency. As a bandpass filter, the equivalent circuit model of a SIW unit with I-shaped slot is depicted in Figure 1c. Three parallel L-C resonators are cascaded in series, where L₀, L₁, and L₂ are the series inductances along the SIW signal propagation direction. C₀, C₁, and C₂ are the capacitances induced by the lengths L_spp, L_spp1, and L_spp2 in the I-shaped slot, respectively, and L₀₁, L₁₁, and L₂₁ are the corresponding shunt inductances.

To precisely obtain the cut-off frequencies, eigenmode simulation is performed for SIW and SSPP, which are depicted as the inserts in Figure 2. Sweeping W_siw and L_spp can efficiently tune the cut-off frequencies of SIWs and SSPPs, respectively, as shown in Figure 2a. Based on this analysis, three hybrid filters with MSLs feeding are designed at 28.2, 29.7, and 31.2 GHz. The MSLs are suitable for the design of complex and compact manifold networks. To input and output signals, a short taper is designed to connect SIW with large impedance and 50-Ω MSL for low insertion loss and compact profile, which has been widely used for MSL-based interdigital and comb-line filters [22]. The dispersion relations of the three filters are shown in Figure 2b, whose dimensions are depicted in Table 1. To investigate the cut-off response induced by the SSPP slots, hybrid filters with the same size consisting of different numbers of slots are simulated, whose S-parameters are shown in Figure 3. It can be seen that the out-of-band rejection becomes sharper, and the insertion loss increases, as the slot number increases. To compensate for the bandwidth and insertion loss, the slot number is chosen as two. In this case, the insertion loss is 1.82, 1.89, and 2.06 dB at 28.2, 29.7, and 31.2 GHz, respectively, and the 3-dB bandwidth is 4.1%, 3.9%, and 3.5%, respectively.

Table 1. Dimensions of the proposed hybrid filters.

Wsiw(f1)	Wsiw(f2)	Wsiw(f3)	d	Psiw
3.77 mm	3.94 mm	3.56 mm	0.4 mm	0.91 mm
Lspp(f1)	Lspp(f2)	Lspp(f3)	Wspp1	Wspp2
2.3 mm	2.36 mm	2.22 mm	0.16 mm	0.10 mm
Lspp1(f1)	Lspp1(f2)	Lspp1(f3)	Lspp2	Pspp
0.51 mm	0.4 mm	0.38 mm	0.58 mm	0.70 mm
Wt	Lt
0.1 mm	0.2 mm

2.2. FDM Unit Design

Figure 4a depicts the manifold FDM unit consisting of one H-plane junction and two filters at f₁ and f₂. Due to the intrinsic properties being independent of frequency optimization, these junctions are commonly characterized by three-port S-parameters. Due to the H-plane symmetry of a microstrip junction shown in the insert of Figure 4a, S₂₂ = S₁₁ and S₃₂ = S₃₁, and thus only four S-parameters, that is, S₁₁, S₂₁, S₃₁, and S₃₃ should be considered. Assume Y₁ = 1, Y₂ = 1, and Y₃ = 1 are the admittances at Ports 1, 2, and 3, respectively. If a given port is terminated with an arbitrary admittance, the S-parameters between the other two ports need to be modified accordingly. When Port 2 is terminated with an admittance Y₂ ≠ 1, the modified two-port S-parameters between Ports 1 and 3 can be expressed as follows:

$$ ()

where Γ₂ = (1 − Y₂)/(1 + Y₂). This S-matrix also applies if an admittance Y₁ ≠ 1 at Port 1 due to the H-plane symmetry. When Y₃ ≠ 1 at Port 3, the S-parameters between Ports 1 and 2 should be modified as follows:

$$ ()

where Γ₃ = (1 − Y₃)/(1 + Y₃) [7]. These S-matrices can be readily converted to ABCD matrices using standard transformation formulas, which allows for seamless cascading with channel filters and transmission lines in the manifold. The designed dual-channel FDM is illustrated in Figure 4b, which consists of one microstrip junction and two hybrid filters at f₁ = 29.7 GHz and f₂ = 28.2 GHz. The characteristic impedance of each channel is set to be 50 Ω, and the lengths of branches L_ms1 and L_ms2 are chosen as mλ_g/4 (m is an integer, and λ_g is the effective wavelength at the center frequency of the passband) to obtain a good phase match and minimize the reflectivity of the two-port junction. The input impedances of the two FDM channels are

$$ ()

$$ ()

See Figure 4a. In this case, signal f₁ will transmit through Filter 1 and largely reflect at Filter 2, and signal f₂ will transmit through Filter 2 and largely reflect at Filter 1, as shown in Figure 4c. The final return loss at the common port can be calculated from the final input conductance Y_in as follows:

$$ ()

and the isolation between channels can be calculated from the S- and ABCD matrices [7].

Due to the phase error induced by the transitions of the filters, such as the short tapers, the distributed manifold arms should be optimized. The pitches between the T-junction and filters, that is, L_ms1 and L_ms2, are investigated in Figure 5a,5b. Due to the shift of the transmission zero, the passband of S₂₁ becomes a little wider as L_ms1 increases and gets narrow as L_ms2 increases. In contrast, it shows little impact on S₃₁. This phenomenon reveals that the end-fed filter is more sensitive to the pitch variation. Finally, L_ms1 = 4.6 mm and L_ms2 = 3.4 mm are chosen to optimize the bandwidth and out-of-band rejection, whose S-parameters are illustrated in Figure 5c. The return loss is less than −10 dB from 27.8 to 30.1 GHz, the insertion loss is 1.96 and 2.2 dB at 28.2 and 29.7 GHz, respectively, and the corresponding passbands have a 3-dB bandwidth of 4.85% and 5.15%, respectively. In this case, the insertion loss of the manifold is 0.14 and 0.31 dB at 28.2 and 29.7 GHz, respectively, which is mainly due to the conductive and radiation losses of the MSLs and is not significant with respect to the total loss. Figure 4c shows the simulated electric field distributions at 28.2 and 29.7 GHz, revealing good spectral division and weak parasitic coupling at different output ports. The dimensions of the proposed dual-channel FDM are as small as 2.07 λ × 2.07λ at 28.2 GHz and 2.17λ × 2.17λ at 29.7 GHz.

2.3. Three-Channel FDM Design

To show the diversity of the proposed techniques, a three-channel frequency division multiplexer is designed in this section. Figure 6a shows the configuration of the manifold multiplexer consisting of two T-junctions and three filters, and Figure 6b illustrates the proposed FDM with SIW–SSPP hybrid filters 28.2, 29.7, and 31.2 GHz. For simplification, the dual-channel FDM can be considered as an end-fed filter. Similarly, Z_T (f₃) = 50 Ω and Z_R (f₁/f₂) = ∞ in channel 3, and Z_T (f₃) = ∞ and Z_T (f₁/f₂) = 50 Ω at the common port of Channels 1 and 2. In this case, L_ms3 and L₁ should be optimized as discussed in the last subsection. First, L_ms3 and L₁ are chosen as 5λ_F3/4 and λ_F3/4, respectively, to minimize the device profile. Then, L_ms3 and L₁ are slightly swept to obtain a good phase match and low reflection. L_ms3 and L₁ are optimized as 4.54 and 1.7 mm, respectively. The S-parameters of the three-channel FDM with optimization are shown in Figure 6c. The three passbands are centered at 28.2, 29.7, and 31.2 GHz, respectively, and the corresponding 3-dB bandwidth of the passbands is 5.10%, 4.68%, and 4.68%, respectively. The insertion loss is 1.95, 2.42, and 2.54 dB at 28.2, 29.7, and 31.2 GHz, respectively, and the loss induced by the manifolds is 0.14, 0.53, and 0.48 dB for each channel, respectively. Figure 7 shows its simulated electric field distributions and good spectral division. The size of the proposed three-channel FDM is just 2.4λ × 3.2λ at 29.7 GHz. The proposed FDM shows good electromagnetic compatibility due to the SIWs and potential for large channel numbers due to the nonresonant function of the hybrid filters.

3. Experiment and Results

A prototype was fabricated with the optimized dimensions in Table 1, as shown in Figure 8a. Long MSLs are designed to provide enough space for integrating end-launch connectors. Figure 8b illustrates the measurement system set-up. The three-channel FDM is integrated with four end-launch connectors from Southwest Microwave Inc. Two ports are connected to a vector network analyzer (VNA) Ceyear 3672E for passband characterization, and the other two ports are integrated with 50-Ω loads to minimize the reflection. The insertion loss of the connector is about 3 dB at 30 GHz. Before measurement, the VNA was calibrated with the calibration kit 85058E using the standard short-load-open-through (SLOT) method.

Figure 8c,d shows the measured S-parameters of the proposed FDM, which are in good agreement with the simulated data. The reflectivity is less than −10 dB from 27.8 to 31.4 GHz, and the absolute insertion loss is about 2.10, 2.49, and 2.61 dB at 28.2, 29.7, and 31.2 GHz, respectively, which are calculated by excluding the connector loss. The 3-dB bandwidth of the three channels is 4.1%, 4.7%, and 4.8% at 28.2, 29.7, and 31.2 GHz, respectively. Table 2 compares the proposed manifold-coupled FDM with other reported devices [8–16]. It should be noted that the proposed FDM addresses small profile, low insertion loss, and ease of fabrication.

4. Conclusion

In sum, a Ka-band FDM with SIW–SSPP hybrid filters is demonstrated with a compact profile, low insertion loss, and good out-of-band rejection. Theoretical analysis and simulation of the manifold FDMs are discussed. Dual-channel and three-channel FDMs have been investigated at 28.2, 29.7, and 31.2 GHz, whose insertion loss is less than 2.61 dB in each channel. The proposed approach is suitable for compact multichannel FDM at millimeter wave frequencies.

Conflicts of Interest

The authors declare no conflicts of interest.

Author Contributions

Y.W. and Z.L. contributed equally to this work.

Funding

This research is supported by the National Key Research and Development Program of China (10.13039/501100012166) (2022YFA1400025), the National Natural Science Foundation of China (10.13039/501100001809) (62371272), the Shandong Provincial Natural Science Foundation (ZR2023ZD08, ZR2024LLZ006), and the Key Technology Program of Qingdao City (23-1-2-qljh-5-gx).