Electromagnetic compatibility technologies based on multi-functional spoof surface plasmon polariton channels

High integration of modern microwave circuits and systems puts forward higher requirements for multi-function and electromagnetic compatibility (EMC) performance of transmission channels. In this paper, we propose two EMC technologies including the substrate integrated packaging (SIP) and tuneable wavenumber mismatching (TWM) based on multi-functional spoof surface plasmon polariton (SSPP) channels. The SIP technology can effectively improve the EMC performance of the SSPP channels in the whole frequency band by designing the packaging structure with easy fabrication and compact size; while the TWM technology can significantly suppress crosstalks in desired frequency bands by manipulating the wavenumber difference between two adjacent channels. Simulated and measured results demonstrate excellent multi-function and EMC performance of the integrated multi-functional SSPP channels by employing the two EMC technologies. The integrated multi-functional SSPP channels can realize continuous phase modulation in X-band and continuous amplitude modulation in Ku-band. The coupling coefficient of the integrated channels is about 8–10 dB lower than that of the channels without the package, and is 13–15 dB lower than that of the traditional microstrip channels in the whole X-band and Ku-band. Meanwhile, the coupling coefficient of the integrated multi-functional SSPP channels with a distance of 1/30 λ 0 can be reduced to around −30 dB in the desired narrow bands. Therefore, the proposed EMC technologies may find broad applications in highly integrated microwave circuits and systems.


Introduction
High integration, miniaturization, and reconfigurability are important development trends of modern communication and radar systems, which put forward higher requirements for the electromagnetic compatibility (EMC) and multi-functional performance of microwave circuits and systems [1][2][3][4][5][6][7][8][9]. One of the many solutions is to propose new kinds of transmission channels with both multi-functional ability and excellent EMC performance.
However, the current researches of SSPPs are mainly focused on multi-functional single SSPP channel [14][15][16] and crosstalk suppression between passive SSPP channels [41][42][43]. However, few investigations on EMC improvement for the integrated multi-functional SSPP channels have been reported, which is mainly caused by two reasons. One reason is that reconfigurable systems require tunable low-coupling frequency band, which cannot be realized by passive SSPP channels. The other reason is that the introduction of active components in multi-functional channels makes the coupling properties between adjacent channels different from those of traditional passive transmission arrays, where the EMC problems such as external electromagnetic interference, crosstalk and signal integrity problems become more complicated. Therefore, it is still urgently needed to study EMC technologies of highly integrated multi-functional SSPP channels.
In this work, we propose two EMC technologies based on the multi-functional SSPP channels, including the substrate integrated packaging (SIP) and the tunable wavenumbers mismatching (TWM). This paper is organized as follows. Firstly, a multi-functional SSPP channel which can realize continuous phase modulation in the X-band and continuous amplitude modulation in the Ku-band is designed as the basic prototype. Secondly, two EMC technologies based on the designed multi-functional SSPP channel are proposed. The SIP technology can improve the channels' EMC performance in the whole frequency band by designing the packaging structure with easy fabrication and compact size; while the TWM technology can realize tuneable crosstalk suppression in the desired band by controlling the wavenumber difference between adjacent channels. Thirdly, adopting both SIP and TWM technologies, the integrated multi-functional SSPP channels with excellent EMC performance are realized and measured.

Dispersion manipulation of the SSPP unit
Realizing the SSPP unit with the dispersion manipulation ability is the basis to achieve multi-functional SSPP channels. Structural diagram of the proposed tunable SSPP unit is shown in figure 1(a), which is composed of a central metal strip, a rectangular branch, a varactor diode, a via hole and metallic ground plane on the bottom. The via hole connects the branch of tunable SSPP unit with the metallic ground, which makes it convenient to load bias voltage onto the varactor diode [21]. The equivalent circuit of the tunable SSPP unit can be modeled as a microstrip loaded with a tunable short-circuit stub, as shown in figure 1(b). The central metal strip can be modeled as a microstrip (MS) with propagation constant k m and impedance Z m , and the branch can be modeled as admittance Y. According to the circuit topology and Bloch theorem, the dispersion relation can be expressed as [44], where k x is the equivalent wavenumber of the whole structure with period p. The shunt admittance Y can be calculated analytically as, where ω is the operating frequency, k e , Y m , and h e are the wavenumber, impedance, and equivalent length of the shunt branch, respectively, and c v is the tunable capacitance. According to (1) and (2), the relationship between capacitance c v and equivalent wavenumber k x of the tunable SSPP unit can be constructed, which indicates that dispersion curve of the SSPP unit can be controlled in real time by adjusting the bias voltage of the varactor diode, without changing structural parameters of the SSPP unit. On the basis of above analyses, dispersion curves of the proposed tunable SSPP unit with different c v are calculated by Matlab, as shown in figure 1(a), which exhibits their nonlinear property deviating from the light line and low-pass characteristics. Using the eigenmode simulation of the commercial software, CST Microwave Studio, simulated dispersion curves shown in figure 1(a) are also displayed to demonstrate the correctness of theoretical analyses.
Using eigenmode simulation of the commercial software, CST Microwave Studio, simulated dispersion curves of the proposed tunable SSPP unit with different c v are shown in figure 1(a), and they are nonlinear curves deviating from light and exhibit low-pass characteristics.
It is obvious that as c v increases, cutoff frequency of the tunable SSPP unit is gradually decreasing, which leads to larger wavenumber and transmission loss in the passband. Therefore, continuous amplitude modulation can be achieved by tuning the capacitance c v of varactor diodes as well. In addition, the wavenumber difference formed by changing the dispersion curves under different capacitances can realize the continuous phase modulation. In terms of crosstalk suppression, the SSPP unit exhibits stronger field confinement than the traditional MS TL with the same width, demonstrated by simulated electric field distributions, as shown in figures 1(c) and (d). This excellent property is also manifested in nonlinear dispersion curves deviating from the light, in which lays a solid foundation for compact arrangements of multi-functional SSPP channels.

Design of the multi-functional SSPP channel
Based on above analyses, a multi-functional SSPP channel can be constructed as shown in figure 2(a). The whole structure is mainly composed of three parts, including MS TL with 50 Ω, compact transition part and the tunable SSPP TL. For easy fabrication and practical application, the design based on single-layer printed circuit board technology is adopted. The metal is copper with a thickness of 0.036 mm. Rogers RO4003 with a dielectric constant of 3.55 is chosen as the material for the substrate, whose thickness is 0.508 mm.
In order to integrate with traditional microwave circuits and systems, a MS TL with 50 Ω is adopted as the feeding port. Thus, it is necessary to propose a compact stepped groove transition section to achieve broadband and effective mode conversion between MS TL and tunable SSPP TL. The gradual gradient transition reduces the discontinuity of the structure, so that the transmission mode is gradually transformed from the quasi-TEM mode of MS TL to the TM mode of tunable SSPP TL, which realizes broadband impedance matching. In addition, to realize compact circuit arrangement, the transition structure is designed to be only two SSPP units in length, which is only 0.2 λ 0 (Set 10 GHz as the center frequency).
After achieving effective excitation, the tunable SSPP TL is constructed by the tunable SSPP units, whose dispersion curves can be dynamic manipulated, as the main component for realizing various functions. By increasing the applied voltage V dc of varactor diodes, the junction capacitance c v gradually decreases, leading to higher cutoff frequency of the tunable SSPP TL. Therefore, the transmission and reflection coefficients of the SSPP channel can be controlled at the same frequency as shown in figures 2(b) and (c). Especially in the Ku band, the transmission coefficient S21 can be continuously adjusted from −1 dB to −40 dB, which exhibits flexible amplitude modulation. Moreover, with the dynamic regulation of the dispersion curve controlled by varactor diodes, the wavenumber k x of the SSPP channel at the same frequency changes continuously. And transmission phase Φ of the SSPP channel can be tuned according to the relationship between ∆Φ and ∆k x ∆ϕ = ∆k x * L eff (3) where L eff is the effective length of the tunable SSPP TL. Measured results of transmission phase for the SSPP channel are shown in figure 2(d), in which display continuous phase modulation of the SSPP channel, especially in X-band. In the X-band, the proposed SSPP channel can realize the phase shift more than 180 • and even achieve the phase shift of 360 • at 8 GHz.

EMC technologies of multi-functional SSPP channels
Based on the proposed multi-functional SSPP channel, two EMC technologies are proposed to solve the external electromagnetic interference, crosstalk, signal integrity, and other EMC problems in large-scale channels integration. Specifically, the SIP technology can reduce the external electromagnetic interference of multi-functional SSPP channels and improve their electromagnetic susceptibility in the whole frequency band, thereby reducing the overall crosstalk among channels. Moreover, the TWM technology is aimed at tunable desired narrow bands, and achieves targeted coupling suppression by tuning the mismatching degree of wavenumbers between different channels. The two technologies are discussed in detail below.

SIP technology
In order to improve the EMC performance of multi-functional SSPP channels, the SIP technology is proposed with compact size and easy fabrication. The substrate integrated (SI) technology has attracted extensive attention of researchers due to its excellent electromagnetic performance and easy integration with modern planar circuit technology [45][46][47][48]. When electromagnetic waves propagate in the SI waveguide, their electric field distributions are similar with the rectangular waveguide. Upper and lower metal layers and via holes on both sides can effectively resist external electromagnetic interference and avoid affecting surrounding circuits. However, nowadays SI technology is mostly used in designing high-frequency transmission channels and passive devices, and few studies are focus on active multi-functional channels. Taking advantage of SI technology in improving EMC performance, the SIP technology for multi-functional SSPP channels is proposed, which can further enhance the field confinement property of SSPP TLs, leading to overall EMC performance improvement of transmission channels in the whole frequency band.
To analyze influence of the SIP structure introducing in tunable SSPP TLs, the dispersion characteristics and electric field distribution of the packaged SSPP unit are firstly studied. The specific structure and layered representation are shown in figures 3(a) and (b). A single-layer substrate with metallic ground and a layer of defective substrate are laminated on the original structure, and two rows of via holes are respectively designed on both sides. The hollowed-out part in the middle layer is used to make room for varactor diodes welding to the surface of the tunable SSPP TL.
As shown in figure 3(a), eigenmode simulated results demonstrate that the packaged tunable SSPP unit has the same dispersion characteristics as the unpackaged one (as shown in figure 1(a)), and even the cutoff frequencies are almost unchanged. Moreover, observing electric field distributions from the top of the structure shown in figures 3(c) and (d), the SIP technology shows an excellent electric field shielding effect.
Furthermore, overall structure of the packaged multi-functional SSPP channel is shown in figures 4(a) and (b). Rogers RO4003 is chosen as the material for Sub0, Sub1 and Sub2, whose thickness are 0.508 mm, 0.508 mm and 0.203 mm, respectively. To achieve mode conversion between the MS port and the SIP structure, a triangular defect structure is designed for smooth transition. The entire package structure is different from the traditional bulky metal or dielectric shielding boxes, whose width and height are only 0.13λ 0 and 0.043λ 0 respectively (Set 10 GHz as the center frequency). Samples photos of the multi-functional SSPP channel without and with SIP are shown in figures 4(f) and (g).
Electromagnetic properties of the packaged multi-functional SSPP channel are shown in figures 4(c)-(e). Simulated and measured results show that the SIP structure has little effect on functionalities of the original SSPP channel. The packaged tunable SSPP channel still achieves continuous amplitude modulation from −1 dB to −40 dB in Ku band and continuous phase controllable range more than 180 • in X band. After adopting the SIP structure, electric field intensities observed from above are significantly weakened, which proves that the proposed SIP technology has a good electromagnetic shielding effect.
To fabricate the SIP structure, two single-layer circuit boards should be printed separately and assembled with the defective substrate in the middle layer using screws, which is a convenient and low-cost process.

TWM technology
After improving the overall EMC performance of the multi-functional SSPP channel in the whole frequency band, we try to achieve further crosstalk suppression between different channels in desired frequency bands and realize flexible control of the operating band, so as to be more suitable for the actual demand.
A conventional passive transmission channel has a fixed wavenumber, and wavenumbers of different channels are the same when multiple channels transmit simultaneously. Since the wavenumber k x of the multi-functional SSPP channel can be manipulated in real time by adjusting the applied voltage of varactor diodes, phase constants of channels can be adjusted dynamically, leading to the wavenumber mismatch between adjacent channels and realizing coupling suppression in the desired operating frequency band.
To analyze the coupling property between channels with different wavenumbers in theory, the coupling of two parallel lossless TLs with different wavenumbers can be written as (4) according to coupled-mode theory and the reciprocity of system [49].
where A j (j = 1, 2) expresses the amplitude, β j is the phase constant of TL j, and k 12 is the coupling coefficient, L is the length of TLs. Then the coefficient matrix B of equation (4) can be written as Using the eigenvalue method to solve the differential equations and substituting A 1 (0) = 1, A 2 (0) = 0, then analytical solutions of equations can be indicated by Hence, the coupling power ratio C can be expressed as According to (7), it is obvious that the coupling between two adjacent channels can be controlled by changing the phase constant difference (β 1 -β 2 ) and the coupling coefficient k 12 . Therefore, by changing the applied voltage for varactor diodes of different channels, the wavenumber difference between adjacent channels can be tuned, providing a solution for crosstalk suppression. Moreover, the wavenumber difference can be designed for the specific frequency band, so that the operating frequency band can be flexibly controlled.
Furthermore, if phase constants of the two TLs are equal, i.e. β 1 = β 2 , then (7) can be degenerated into It is the classical coupling power ratio expression of two traditional TLs based on the couple mode theory, which proves the correctness of the above derivation.
Based on above analyses, the coupling between two SSPP TLs is specifically analyzed. Because transmission mode of the SSPP TL is different with the traditional TL such as MS TL, the longitudinal electric field component E jx also needs to be considered, and the coupling coefficient k 12 between two SSPP TLs can be expressed as [50] where E jt is transverse electric field distribution of line j, n is the refractive index of the neighboring medium, n 0 is the refractive index of TLs, ω is the angular frequency, and ε 0 is the vacuum dielectric constant. As indicated in (9), the coupling coefficient is only decided by electric field energy of the overlapping region between coupled TLs when the operating frequency and the surrounding environment are determined. Electric field distribution analyses are proposed for two MS TLs, tunable SSPP TLs and packaged tunable SSPP TLs with the same distance, as shown in figures 5(a)-(d). Simulated results in figures 5(e)-(g) show that compared with MS TLs, the energy of tunable SSPP TLs is strongly enhanced around metal grooves, resulting in better field confinement property. Furthermore, the energy of packaged tunable SSPP TLs is more concentrated than structures without packaging due to the confinement of upper metal and via holes on both sides of the SIP structure. Therefore, the overlap of electric field energy in coupled structures with the packaged tunable SSPP TLs is the smallest among these three structural configurations, which has a smaller coupling coefficient k 12 and is beneficial to crosstalk suppression. Therefore, the proposed TWM technology can effectively suppress crosstalk between adjacent channels in flexible desired narrow frequency bands. Moreover, further crosstalk suppression can be achieved after combining with the above two technologies for compact integrated channels in microwave circuits and systems, which is discussed in details below.

Integration of multi-functional SSPP channels with excellent EMC performance
Combining the above two technologies, integrated packaged multi-functional SSPP channels with excellent EMC performance are realized and fabricated. Moreover, samples of MS channels and unpackaged multi-functional SSPP channels with the same distance are also fabricated for comparison, as shown in figure 6(a). In order to mimic the scenario of compact highly integrated channels arrangement in practical applications, the distance between two adjacent channels is chosen as 1 mm, which is only 1/30 λ 0 (Set 10 GHz as the center frequency). Input and output ports of the upper channel are marked as port #1 and port #2. Input and output ports of the lower channel are marked as port #4 and port #3, respectively. A four-port vector network analyzer is utilized to measure the S-parameters of three samples. We introduce a wideband Bias-Tee between the DC power supply and the sample to isolate the RF signals and the DC signals during the measurement.
Simulated and measured S-parameters of MS channels, unpackaged multi-functional SSPP channels and packaged multi-functional SSPP channels with the same distance are displayed in figures 6(b)-(d), where capacitance c v for varactor diodes of two adjacent channels are tuned to be the same: c v1 = c v2 = 0.04 pF. It is obvious that the coupling coefficient of the integrated channels is about 8-10 dB lower than that of the channels without the package, and is 13-15 dB lower than that of the traditional microstrip channels in the whole X-band and Ku-band. From the perspective of time domain, when the same Gaussian pulse of 0-18 GHz is input, peak values of the pulse received by the transmission port and coupling port of three kinds of channels are shown in figures 6(e) and (f). It is obvious that coupling port of the packaged multi-functional SSPP channel receives the smallest pulse peak. Therefore, the field confinement property of tunable SSPP channels and the effectiveness of the SIP technology are demonstrated from both frequency and time domains.
In order to further prove the crosstalk suppression capability in the desired frequency bands and operating frequency variation ability of packaged multi-functional SSPP channels, the capacitance value for varactor diodes of one channel is fixed as c v2 = 0.04 pF, and c v1 of the other channel is changed. Simulated  and measured results of S-parameters in four states while c v1 is changing are selected to display, where reflection coefficients S11, S33 and transmission coefficients S21 and S43 of the two channels are shown in figure 7, and the coupling coefficients S31 and S41 are shown in figure 8. According to results, as the c v of one channel increases, its cutoff frequency decreases. Meanwhile, wavenumber difference of the two channels is changed, leading to a valley value of the coupling coefficient S31, which gradually moves to the lower frequency as c v increases. Thus, coupling coefficient of the desired frequency bands can be reduced to around −30 dB, which is difficult to achieve in such a close distance (1/30 λ 0 ), as shown in figure 8, and the effectiveness of TWM technology is proved.
In addition to factors such as dielectric loss and radiation loss, because it is difficult to obtain the exact relationship between the actual capacitance value of varactor diodes and the applied voltage, there is a slight exhibition error between measured and simulated results. But it is worth noting that the exhibition error has no influence on practical applications, because through continuous voltage regulation, samples can still achieve the same functions as simulated results.

Conclusion
We proposed a multi-functional SSPP channel and the SIP and TWM EMC technologies. By tuning the applied voltage of varactor diodes in real time, we have achieved continuous amplitude modulations in the Ku-band and continuous phase modulations in the X-band by manipulating the dispersion properties of the multi-functional SSPP channels. Moreover, the SIP and TWM technologies are proposed to realize the crosstalk suppression and other EMC improvements for the overall frequency band and the desired frequency band, respectively. Integrated multi-functional SSPP channels are simulated and measured, which demonstrate the effectiveness of the two proposed technologies. Therefore, the proposed novel transmission channel and two EMC technologies are promising candidates to solve external electromagnetic interference, crosstalk and signal integrity problems for compact integrated microwave circuits and can be extended to other active systems.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).