# A Varactor-Tunable Rasorber Using Tripole and Ring Slot Elements

Authors: Qingxin Guo; Qian Chen; Jianxun Su; Zengrui Li
Journal: International Journal of Antennas and Propagation
 (2021)

---

## Abstract

In this study, a frequency-selective rasorber with a tunable passband and two absorptive bands is presented. It is designed using two active FSSs, an absorptive FSS realized with tripole elements, and a lossless bandpass FSS achieved with ring slots. Both active FSSs embedded with varactors realize the shift of transmission frequency bands by controlling the bias voltage of the feed network. The working principle is briefly investigated according to an equivalent circuit model. A prototype is fabricated and measured to verify the simulated results, which show that a passband is tuned from 3 to 4.78 GHz between two absorptive bands, and the maximum band of |S11| < −10 dB covers from 2.2 to 7.96 GHz.


---

## Body

## 1. Introduction

Frequency-selective surfaces (FSSs) with both absorptive and transmissive bands have attracted much attentions in recent years because they transmit the in-band EM waves and absorb the out-of-band signals [1–3]. They are called as frequency-selective rasorber (FSR) or absorptive/transmissive frequency-selective surface (ATFSS). Some FSRs have been reported by cascading one sheet of lossy FSS which provides an absorptive feature in absorptive bands and another layer of lossless FSS which serves as a passband filter. Different structures have been utilized for designing the lossy FSS, while different slot-shape unit cells have been used for the lossless FSS [4–8]. Most of the published FSRs, including the category that realized using 3D structures [9–11], realized a fixed passband that can be lower or higher than an absorptive band or between two absorptive bands. The radomes used FSRs with fixed passband achieve not only monostatic but also bistatic radar cross-section (RCS) reduction and hence has better defense performance. But for antennas operating in different frequency bands, the radomes lack versatility. Consequently, it is necessary to actively tune the transmission bands.Several articles presented active FSSs, among which only very few has a tunable passband [12–15], and most of them have a switchable passband [16–20]. Some multifunctional active FSSs are also proposed by using PIN diodes in recent years [21, 22]. Figure 1 shows the concept of an FSR with two absorptive bands and one tunable passband. When an electromagnetic (EM) wave is incident onto the surface, the FSR has two different scattering properties versus the frequency of the incident wave. At the absorption bands, the signals are largely absorbed by the structure, while the useful signal between the two absorption bands can freely pass through the structure. It is a challenge to realize a tunable transmission window within two absorption bands. For a tunable or switched frequency-selective rasorber (TFSR) that is realized by using active components such as PIN diodes or varactors, the biasing network should be added into the structure. The additional network might significantly degrade the performances of the initial FSR, and the methods for insulating RF signal and DC power supply must be meticulously designed.Figure 1
The functional diagram of the proposed FSR.In this study, a TFSR with a continuous tunable passband is presented. The operating principle is illustrated with the help of its equivalent circuit model (ECM). The prototype of the proposed TFSR was tested in an anechoic chamber after being manufactured. The TFSR proposed in this study has potential application in many military systems or the protection and interference-mitigation of wireless local area network systems.


## 2. Design and Analysis of the FSR

### 2.1. Structure of the TFSR

Figure2 shows the structure of our tunable FSR, which consists of an absorptive FSS and a bandpass FSS. The permittivity of substrate for both FSSs is εr = 2.2, and the thickness, h1 = 0.508 mm. The space between them is denoted as h2 = 12.5 mm, which approximately equals to λp/4.Figure 2
Configuration of the tunable FSR.On the top layer of the absorptive FSS, three-legged loaded elements are utilized. Within each arm, a branch including two varactorsVC1 and a small patch is added. To provide the necessary reverse biasing for the varactors, the three-legged loaded element on the top layer is also a part of the biasing network, and three additional narrow strips are arranged on the bottom layer of the absorptive FSS. The narrow strips are connected to the small patches on the top layer through vias. To form a return circuit for DC, the three-legged loaded elements are connected to each other by using lumped resistors (Rb) with large resistance. In addition, six resistors are embedded in the narrow strips to mitigate the effects of the biasing network to the performance of the original FSS.Ring slot is etched on the top layer of the bandpass FSS, as shown in Figure2. Three varactors are placed across the slot with 120° angle interval. On the bottom layer, three narrow strips with three lumped resistors are applied for isolating. To mitigate the coupling between the inner and outer conducts induced by the strips, the isolating resistors are situated just beneath the slot.


### 2.2. Equivalent Circuit Analysis

Equivalent circuit is an effective method for explaining the working principle of an FSS. The basic procedures for establishing an ECM are [23–25] as follows:(1)
The metallic strips or patches parallel to the incidentE field are equivalent to inductors(2)
The gaps between two conductors and vertical toE field, including the gaps between two elements, are equivalent to capacitors(3)
The inductances and capacitances are obtained using the curve fitting method after the structure has been simulated with a full-wave simulatorThe ECM of Figure2 is established and shown in Figure 3, where ZA represents the equivalent impedance of the absorptive FSS, ZP represents the equivalent impedance of the bandpass FSS, and the impedance Z0 and ZSUB are the characteristic impedance of free space and the substrate, respectively.Figure 3
Equivalent circuit of the FSR.The impedanceZA consists of a series connection of C1L1R1 and a parallel connection of L2C2VC1. The coupling between close cells is regarded as capacitance C1. The arms mostly paralleled to the incident E field are equivalent to the inductance L1, while the arms mainly vertical to the incident E field are equivalent to the parallel circuit of L2C2. The tunable capacitor VC1 is used to tune the frequency. The capacitor C12 denotes the mutual coupling between two arms, which is rather small and can be ignored at low frequency. If C12 is ignored owing to a small value, ZA can be expressed as follows:(1)ZA=R1+jω2L1C1−1ω2L2C2+VC1−1−ω2L2C1ωC1ω2L2C2+VC1−1.The impedanceZP is a parallel circuit of L3, L4, C3, and VC2. The inductors L3 and L4 denote the equivalent capacitances of the conductor inside and outside the ring slot, and C3 is the capacitance of the slot, in which VC2 is a tunable capacitor. The impedance ZP can be expressed as follows:(2)ZP=−j1−ω2L4C3+VC2ωL41−ω2L3C3+VC2.At the resonant frequency,(3)f1=12πL2C2+VC1.The imaginary part ofZA tends to be very large; hence, only a small amount of the incoming signal from port P1 passes through ZA and most transmit forward to port P2. At nonresonant frequencies, part of the incident power traverses R1, and it is inevitably absorbed by the resistor. The circuit of ZP is parallel resonated at frequency(4)f2=12πL3+L4C3+VC2.Iff1 = f2 = fP, a passband is obtained and is altered by tuning VC1 and VC2.The impedanceZB1 consisted of L5, C4, and C5 and ZB2 consisted of L6 and C6 represent the equivalent impedance of the biasing network for the absorptive and the bandpass FSSs, respectively. Both ZB1 and ZB2 resonate at the high frequency far away from the passband because the biasing networks are divided into short strip lines by resistors Rb. They slightly affect the resonate frequencies of ZA and ZP, meanwhile, significantly affecting the match of the FSS at high frequency.


### 2.3. Results of the TFSR

Figures4(a) and 4(b) show the comparison of the results of reflection and transmission coefficients got from the ECM and full-wave simulator, Ansys High Frequency Simulation Software (HFSS). Two results agree reasonably well with each other, especially at low frequencies, which means that the ECM is valid. At high frequencies, the mutual coupling between the FSS and the biasing network becomes stronger and more complex, which cannot be modelled with a simple circuit. Consequently, there is deviation between the two results. Figure 4(c) shows the absorptivity calculated with Abs. = 1–|S11|2–|S21|2, where S11 and S21 represent the reflection and transmission coefficients. Two absorptive bands, whose absorptivity is larger than 80% at 2.16–3.38 GHz and 4.38–7.24 GHz, are achieved. The dimensions for Figure 1 and the values for components in the ECM are given in Table 1. It should be mentioned that the presented structure has very low cross-polarization components, as shown in Figure 4(d), where S11xx and S21xx represent the reflection and transmission of copolarization, and S11yx and S21yx denote the reflection and transmission of cross-polarization. It means that the cross-polarization components hardly contribute to absorptivity.Figure 4
Results got from ECM and HFSS: (a) reflection, (b) transmission, (c) absorptivity, and (d) cross-polarization components.
(a)(b)(c)(d)Table 1
Dimensions for Figure1 and values for components in the ECM.
Symboll1l2l3l4l5l6l7l8l9Value (mm)17.3123.3439111Symbolw1w2w3w4g1r1r2h1h2Value (mm)4.06.00.50.505980.512.5SymbolL1L2L3L4L5L6ZSUBZ0Value (nH)12.4663.4620.5481.8571.5812.645254 Ω377 ΩSymbolC1C2 + VC1C3 + VC2C4C5C6C12R1RbValue (pF)0.1370.3280.3880.0170.2880.1190.001400 Ω10kΩFigure5 shows the simulation results of the TFSR under the normal incidence. The passband is decreased from 4.78 to 3 GHz as the capacitances of VC1 is increased from 0 to 0.68 pF and VC2 from 0.05 to 0.6 pF. Table 2 provides the performances which include the bandwidth of passband, the maximum insertion loss (IL), and the lower and higher absorptive bands of |S11| < −10 dB.Figure 5
The simulatedS parameter of the tunable passband: (a) |S11| and (b) |S21|.
(a)(b)Table 2
Performance of the tunable FSR.
VC1 (pF)VC2 (pF)00.050.30.280.680.6Passband_3 dB (GHz)4.33–5.133.62–4.142.91–3.21Insertion loss (dB)0.520.320.3Lower abs. band (GHz)2.22–3.942.20–3.372.18–2.76Higher abs. band (GHz)5.54–7.964.48–6.943.46–6.41The simulation results of the oblique incidence are shown in Figure6. Both for the lower frequency at 3 GHz and for the high frequency at 4.72 GHz, the performances remain stable as the incident angle rose up to 30°.Figure 6
The simulation results under the oblique incidence: (a) TE at 3 GHz, (b) TM at 3 GHz, (c) TE at 4.72 GHz, and (d) TM at 4.72 GHz.
(a)(b)(c)(d)


## 2.1. Structure of the TFSR

Figure2 shows the structure of our tunable FSR, which consists of an absorptive FSS and a bandpass FSS. The permittivity of substrate for both FSSs is εr = 2.2, and the thickness, h1 = 0.508 mm. The space between them is denoted as h2 = 12.5 mm, which approximately equals to λp/4.Figure 2
Configuration of the tunable FSR.On the top layer of the absorptive FSS, three-legged loaded elements are utilized. Within each arm, a branch including two varactorsVC1 and a small patch is added. To provide the necessary reverse biasing for the varactors, the three-legged loaded element on the top layer is also a part of the biasing network, and three additional narrow strips are arranged on the bottom layer of the absorptive FSS. The narrow strips are connected to the small patches on the top layer through vias. To form a return circuit for DC, the three-legged loaded elements are connected to each other by using lumped resistors (Rb) with large resistance. In addition, six resistors are embedded in the narrow strips to mitigate the effects of the biasing network to the performance of the original FSS.Ring slot is etched on the top layer of the bandpass FSS, as shown in Figure2. Three varactors are placed across the slot with 120° angle interval. On the bottom layer, three narrow strips with three lumped resistors are applied for isolating. To mitigate the coupling between the inner and outer conducts induced by the strips, the isolating resistors are situated just beneath the slot.


## 2.2. Equivalent Circuit Analysis

Equivalent circuit is an effective method for explaining the working principle of an FSS. The basic procedures for establishing an ECM are [23–25] as follows:(1)
The metallic strips or patches parallel to the incidentE field are equivalent to inductors(2)
The gaps between two conductors and vertical toE field, including the gaps between two elements, are equivalent to capacitors(3)
The inductances and capacitances are obtained using the curve fitting method after the structure has been simulated with a full-wave simulatorThe ECM of Figure2 is established and shown in Figure 3, where ZA represents the equivalent impedance of the absorptive FSS, ZP represents the equivalent impedance of the bandpass FSS, and the impedance Z0 and ZSUB are the characteristic impedance of free space and the substrate, respectively.Figure 3
Equivalent circuit of the FSR.The impedanceZA consists of a series connection of C1L1R1 and a parallel connection of L2C2VC1. The coupling between close cells is regarded as capacitance C1. The arms mostly paralleled to the incident E field are equivalent to the inductance L1, while the arms mainly vertical to the incident E field are equivalent to the parallel circuit of L2C2. The tunable capacitor VC1 is used to tune the frequency. The capacitor C12 denotes the mutual coupling between two arms, which is rather small and can be ignored at low frequency. If C12 is ignored owing to a small value, ZA can be expressed as follows:(1)ZA=R1+jω2L1C1−1ω2L2C2+VC1−1−ω2L2C1ωC1ω2L2C2+VC1−1.The impedanceZP is a parallel circuit of L3, L4, C3, and VC2. The inductors L3 and L4 denote the equivalent capacitances of the conductor inside and outside the ring slot, and C3 is the capacitance of the slot, in which VC2 is a tunable capacitor. The impedance ZP can be expressed as follows:(2)ZP=−j1−ω2L4C3+VC2ωL41−ω2L3C3+VC2.At the resonant frequency,(3)f1=12πL2C2+VC1.The imaginary part ofZA tends to be very large; hence, only a small amount of the incoming signal from port P1 passes through ZA and most transmit forward to port P2. At nonresonant frequencies, part of the incident power traverses R1, and it is inevitably absorbed by the resistor. The circuit of ZP is parallel resonated at frequency(4)f2=12πL3+L4C3+VC2.Iff1 = f2 = fP, a passband is obtained and is altered by tuning VC1 and VC2.The impedanceZB1 consisted of L5, C4, and C5 and ZB2 consisted of L6 and C6 represent the equivalent impedance of the biasing network for the absorptive and the bandpass FSSs, respectively. Both ZB1 and ZB2 resonate at the high frequency far away from the passband because the biasing networks are divided into short strip lines by resistors Rb. They slightly affect the resonate frequencies of ZA and ZP, meanwhile, significantly affecting the match of the FSS at high frequency.


## 2.3. Results of the TFSR

Figures4(a) and 4(b) show the comparison of the results of reflection and transmission coefficients got from the ECM and full-wave simulator, Ansys High Frequency Simulation Software (HFSS). Two results agree reasonably well with each other, especially at low frequencies, which means that the ECM is valid. At high frequencies, the mutual coupling between the FSS and the biasing network becomes stronger and more complex, which cannot be modelled with a simple circuit. Consequently, there is deviation between the two results. Figure 4(c) shows the absorptivity calculated with Abs. = 1–|S11|2–|S21|2, where S11 and S21 represent the reflection and transmission coefficients. Two absorptive bands, whose absorptivity is larger than 80% at 2.16–3.38 GHz and 4.38–7.24 GHz, are achieved. The dimensions for Figure 1 and the values for components in the ECM are given in Table 1. It should be mentioned that the presented structure has very low cross-polarization components, as shown in Figure 4(d), where S11xx and S21xx represent the reflection and transmission of copolarization, and S11yx and S21yx denote the reflection and transmission of cross-polarization. It means that the cross-polarization components hardly contribute to absorptivity.Figure 4
Results got from ECM and HFSS: (a) reflection, (b) transmission, (c) absorptivity, and (d) cross-polarization components.
(a)(b)(c)(d)Table 1
Dimensions for Figure1 and values for components in the ECM.
Symboll1l2l3l4l5l6l7l8l9Value (mm)17.3123.3439111Symbolw1w2w3w4g1r1r2h1h2Value (mm)4.06.00.50.505980.512.5SymbolL1L2L3L4L5L6ZSUBZ0Value (nH)12.4663.4620.5481.8571.5812.645254 Ω377 ΩSymbolC1C2 + VC1C3 + VC2C4C5C6C12R1RbValue (pF)0.1370.3280.3880.0170.2880.1190.001400 Ω10kΩFigure5 shows the simulation results of the TFSR under the normal incidence. The passband is decreased from 4.78 to 3 GHz as the capacitances of VC1 is increased from 0 to 0.68 pF and VC2 from 0.05 to 0.6 pF. Table 2 provides the performances which include the bandwidth of passband, the maximum insertion loss (IL), and the lower and higher absorptive bands of |S11| < −10 dB.Figure 5
The simulatedS parameter of the tunable passband: (a) |S11| and (b) |S21|.
(a)(b)Table 2
Performance of the tunable FSR.
VC1 (pF)VC2 (pF)00.050.30.280.680.6Passband_3 dB (GHz)4.33–5.133.62–4.142.91–3.21Insertion loss (dB)0.520.320.3Lower abs. band (GHz)2.22–3.942.20–3.372.18–2.76Higher abs. band (GHz)5.54–7.964.48–6.943.46–6.41The simulation results of the oblique incidence are shown in Figure6. Both for the lower frequency at 3 GHz and for the high frequency at 4.72 GHz, the performances remain stable as the incident angle rose up to 30°.Figure 6
The simulation results under the oblique incidence: (a) TE at 3 GHz, (b) TM at 3 GHz, (c) TE at 4.72 GHz, and (d) TM at 4.72 GHz.
(a)(b)(c)(d)


## 3. Experiment Results and Discussion

To verify the design, a prototype was fabricated and measured. Considering the power of the full-wave simulator and the experimental cost, only parts of performances are measured. Figure7(a) shows the prototype which is composed of 7 × 7 unit cells within a total size of 220 mm × 220 mm. Between two FSSs, plastic nuts and screws are used to support the space of 12.5 mm. The free space measurement system consisting of one vector network analyzer (Keysight N5234A) and two antennas in an anechoic chamber is used to measure the reflection and transmission coefficients of the tunable FSR, as shown in Figure 7(b). The tunable range of the passband largely depends upon the capacitance tuning range of the used varactors. Varactors modelled SMV2019-079LF [26] are chosen to change the capacitance from 0.3 to 2.22 pF as their reverse bias voltage decreased from 20 to 0 V. For lower capacitance, MAVR-011020-1411 produced by MACOM is a choice [27].Figure 7
Prototype and measurement system. (a) Photo of the TFSR and (b) measurement system.
(a)(b)Figure8 shows the measured |S11|, |S21|, and absorptivity under the normal incidence. Three different bias voltages of 5, 7, and 19 V for VC1 and 4, 6 and 18 V for VC2, respectively, are plotted. As the reversed voltage increased, the passband increases from 2.6 to 3.77 GHz. The measured insertion losses shown in Figure 8 are larger than the simulated results shown in Figure 5, especially at the low frequencies. High insertion loss results in large absorptivity at the passband, as shown in Figure 8(c). The main reason is that the series resistance (RS) of varactors is voltage dependent, and it is higher at low reversed bias voltage [28, 29]. Figure 9(a) shows the comparison of the simulated insertion losses of different series resistances. The IL is increased from 0.32 to 2.5 dB as RS is increased from 0 to 10 Ω. A typical equivalent circuit for a varactor is also shown in the figure, where Ls is the parasitic inductance associated with the package and bonding wires of the diode, CP is the package capacitance, and CJ is the varactor junction capacitance. The second reason is the truncation of the structure, namely, only a finite array of 2λ × 2λ at 3 GHz has been fabricated and measured, but an infinite periodic array was simulated.Figure 8
Measured results of the presented TFSR with different bias voltage under the normal incidence. (a) |S11|. (b) |S21|. (c) Absorptivity.
(a)(b)(c)Figure 9
Comparisons of the simulated and measuredS-parameters. (a) Effect of series resistance on insertion loss, (b) |S11|, and (c) |S21|.
(a)(b)(c)Figures9(b) and 9(c) show the comparison of the simulation results of VC1 = 0.3 pF, VC2 = 0.28 pF, and experiment results of the bias voltage of 18 and 20 V. The measured band of |S21| ≥ −3 dB covers from 3.50 to 4.09 GHz and the band of |S11| ≤ −10 dB covers from 2.2 to 7.86 GHz. Almost same minimum insertion loss of 1.5 dB is obtained for two results at 3.77 GHz, owing to the consideration of the series resistance of varactors. Some discrepancies exist between the two results, particularly at high frequency. Besides the aforementioned reasons, another might be because some distribution parameters such as the package and soldered dot of the varactor diodes were not taken into account during the simulations.Table3 provides the comparison of the performances of the presented TFSR and some published designs with continuously tunable passband. For the bandwidth of |S11| ≤ −10 dB (BWS11), this work is wider than the others. The minimum insertion loss of this work is lower than [12, 14]. The thickness of the design, corresponding to the longest absorptive wavelength (λL), is slightly thicker than [12] but thinner than [13, 14].Table 3
Comparisons between this work and some published results.
RefSimulationMeasurementThickness (λL)Pol.Cap. (pF)Tunable (GHz)Voltage (V)Tunable (GHz)IL (dB)BWS11 (GHz)[12]0.12–0.522.7–3.40–221.6–3.33.4–9.31.9–5.40.092Dual[13]0.12–0.383.8–5.24–163.8–5.20.59–2.52.4–6.580.107Single[14]0.15–0.53.33∼5.134–182.8–4.21.7–6.52.67–7.890.134DualThis work0–0.683.0–4.785–202.6–3.771.5–52.2–7.860.099Dual


## 4. Conclusion

A tunable frequency-selective rasorber has been successfully designed, and some performances have been measured for verification. The tunability is achieved by integrating the varactors and biasing network on both the absorptive FSS realized with tripole elements and the bandpass FSS realized with slot ring elements. Measured results show that designed TFSR has a continuous tuning range from 2.6 to 3.77 GHz for the center transmission frequency as the reverse biasing voltage of the varactors are decreased from 20 to 5 V. The proposed TFSR has potential applications in reconfigurable stealthy antenna-radome systems owing to the tunable transmission band in wide absorptive bands.



---

*Source: 9766379-2021-12-16.xml*