The concept of nonlinear phase shifter and its application to element of sensing RISs

In this study, the concept of the nonlinear phase shifter is proposed to provide a new idea for the hardware architecture of sensing reconfigurable intelligent surfaces (RISs). First, the equivalent circuit of the proposed phase shifter is given to provide theoretical guidance for the design. Then, the nonlinearity analysis of the nonlinear phase shifter is presented. Finally, two simplified sensing RIS elements operating at 4 GHz was fabricated and measured to validate the design. The measured scanning range was from 16° to −18° with the input power increasing from 5 to 23 dBm. The nonlinear phase shifter shows great application potential in sensing RISs.


| INTRODUCTION
Phase shifters [1][2][3][4][5] are important parts of several microwave and millimeter-wave systems, such as phased arrays, smart antennas, modulators, and microwave instruments.In a phased array system, the phase shifter is a key fundamental module that has a huge impact on beamforming quality and steering capability.
[8][9][10][11] It consists of large-scale, low-power, and low-cost units.The parameters such as the phase and/or amplitude of the signal can be changed to realize the intelligent reconstruction of the wireless channel environment and provides a new solution to the challenges in traditional communication scenarios.The advantages of RIS have prompted people to conduct preliminary research on its design and performance in various wireless communication systems.However, it also faces many challenges, such as RIS hardware design and regulation, transmission technology, and system and network architecture design.
As shown in Figure 1, when the incident wave and the interference random field are superimposed at the RIS element, the change of the channel state will cause the power of the signal at the RIS element to change.The waveform of traditional RIS cannot automatically adjust according to the channel state change.Therefore, the sensing RIS [12][13][14] was presented to realize this function.While each sensing RIS element additionally needs a power sensor and an microcontroller unit (MCU).The hardware structure is more complex.
In this study, a nonlinear phase shifter is proposed to realize the sensing RIS with a simple structure.First, the concept, topology, and analysis of the nonlinear phase shifter are given.Second, the nonlinearity analysis of the nonlinear phase shifter is presented.Then we can replace the phase shifter in the traditional RIS circuit with the proposed nonlinear phase shifter to achieve a simplified design of sensing RIS.The detailed circuit of the sensing RIS element using the proposed nonlinear phase shifter is shown in Figure 1.Surface-circuit-surface structure is used to the RIS element design.The circuit of each element contains an amplifier and a nonlinear phase shifter.Finally, to verify that the sensing RIS element using nonlinear phase shifter can realize the beam changing with different power, two simplified sensing RIS elements was fabricated and measured.The topology of the nonlinear phase shifter (π type network) is shown in Figure 2A, which consists of three transmission lines and one shunt Schottky diode.The impedance of three microstrip lines are Z 1 , Z 2 , and Z 3 .The corresponding electrical lengths are defined as θ 1 , θ 2 , and θ 3 , respectively.The power-dependent phase characteristics are produced by Schottky diodes.According to Yamauchi et al. 15 and Bera et al., 16 the large signal equivalent circuit of the diode is shown in Figure 2B.The equivalent susceptance B (P) and conductance G (P) are both function of input power.Figure 2C shows the equivalent circuit of Figure 2A, the admittance of the series transmission line and Schottky diodes can be derived: where . Then, the equivalent G′ (P) and B′ (P) can be calculated: (2) The transmission matrix of the nonlinear phase shifter can be expressed as: BIAN ET AL.
The simulated and measured S parameters of the two nonlinear phase shifters at 5 dBm input power (A) S parameters and (B) phase.The simulated and measured amplitude and phase differences of the two nonlinear phase shifters at 4 GHz (C) amplitude (D) phase.
The S21 of the nonlinear phase shifter is given in a form such as: According to Equations (1-5), we can easily obtain that the phase shift only varies with the input power when the circuit topology and the circuit parameters are determined.Then, the gain conversion ΔG and phase conversion ΔΦ can be further derived as: where S 21h and S 21l are the transmission coefficient of the nonlinear phase shifter at the highest and lowest input power, respectively.The available gain and phase conversion can be tunable by the parameters of three transmission lines.In the design of the nonlinear phase shifter, the insertion loss of the circuit should be as small as possible.Therefore, the design of the nonlinear phase shifter should meet the following conditions: Equation ( 8) is to ensure that the insertion loss of the nonlinear phase shifter at the lowest input power is small.Equation (9) ensures that the gain of the phase shifter basically does not change with the power increase.From the prior analysis, the design procedure of the nonlinear phase shifter can be obtained.First, the required phase conversion ΔΦ is chosen.Second, the impedance of the Schottky diode can be simulated, then the equivalent susceptance B (P) and conductance G (P) can be obtained.Finally, determine the circuit parameters (Z 1 , θ 1 , Z 2 , θ 2 , Z 3 , θ 3 ) according to Equation ( 7) and the insertion loss restrictions Equations (8-9).Therefore, the phase shifter with power-dependent characteristics can be designed.

| Nonlinearity analysis of the nonlinear phase shifter
When an antenna element is connected with a nonlinear phase shifter, its radiation field can be expressed as 17 : where p ΔΦ( ) is the phase shift provided by the nonlinear phase shifter, η is the intrinsic impedance, k is the wavenumber, I 0 is the electric current carried by the element, l is the element length, r is the radian distance, θ is the radiation direction.
From the above equation, we can see that the radiation field would have phase distortion.To eliminate nonlinearity, two types of nonlinear phase shifters with opposite phase conversion characteristics and similar gain conversion are used.For a two-element array, the total radiation field can be calculated: where β is the phase difference between the elements.From Equation ( 11), we can obtain that the array factor is a function of input power and the total radiation field would not have distortion.Therefore, in the design of sensing RIS, we should use two types of nonlinear phase shifters with opposite phase change characteristics to avoid distortion.

| TWO SIMPLIFIED SENSING RIS ELEMENTS DESIGN USING THE NONLINEAR PHASE SHIFTER
To verify the proposed nonlinear phase shifter, two nonlinear phase shifters with opposite phase conversion characteristics and similar gain conversion is designed as an example to verify its performance.Through the above analysis, we have given the design method of the nonlinear phase shifter.Then, two nonlinear phase shifters is designed according to the analysis.As shown in Figure 3, the nonlinear phase shifter 1 has positive phase conversion, while the nonlinear phase shifter 2 has negative phase conversion.
The MA4E1318 Schottky diode is used in the circuit.Rogers 5880, with a relative dielectric constant of 2.2 and a thickness of 10 mil, is adopted in this circuit.Figure 3 shows the simulated admittance of the MA4E1318 Schottky diode.S is the unit of admittance.According to the design method of the nonlinear phase shifter in Section 2, the circuit parameters of the two nonlinear phase shifters at 4 GHz are shown in Figure 3.
The fabricated two nonlinear phase shifters is shown in Figure 4.A linear drive power amplifier is cascaded in front of the proposed nonlinear feeding network to make The simulated and measured pattern results for the prototype at different input powers (A) 5, (B) 11, (C) 14.5, (D) 18, and (E) 23 dBm.
sure the Schottky diode working in appropriate power range.The driver PA is a Class AB PA operating in the linear region.Agilent N5244A PNAX vector network analyzer is applied in the measurement.Figure 4 shows the two nonlinear phase shifters' simulated and measured S parameters at 5 dBm input power.The measured insertion loss difference between the phase shifters is less than 1.2 dB.The simulated and measured amplitude difference phase difference between the phase shifters are shown in Figure 4.The measured amplitude difference is less than 1.3 dB at different input power.
The measured phase difference decrease from 59°to −67°as the input power increases from 5 to 23 dBm.
As shown in the right of Figure 5A, two simplified sensing RIS elements can be regarded as two RIS elements with the first layer of patch removed, and its waveform change characteristics can well represent the waveform characteristics of the sensing RIS.Therefore, the fabricated two nonlinear phase shifters can be directly used to verify the performance of the sensing RIS element.As displayed in Figure 5B, the two simplified sensing RIS elements prototype was fabricated.The radiation performance is tested in a microwave anechoic chamber.
Figure 6 displays the simulated and measured pattern results for the prototype at different input powers.The beam points to 16°, 10°, 2°, −8°, and −18°at 5, 11, 14.5, 18, and 23 dBm input power, respectively.It validated that the two simplified sensing RIS elements has realized the power-dependent beam scanning characteristics.From the nonlinearity analysis shown in Section II, it can be seen that two nonlinear phase shifters with opposite phase change characteristics can avoid distortion.Therefore, the two simplified sensing RIS elements can realize the power-dependent beam scanning function without distortion.In Wu and Zhang, 7 intelligent reflecting surface is used to enhance the wireless network.However, the surface does not have the function of sensing power change.In Zhu et al., 13 power sensor and MCU are used to constitute the sensing RIS.Compared with Zhu et al. 13 and Wu and Zhang, 7 our proposed unit structure has the advantages of simple structure, low cost, and the ability to automatically adjust the beam.

| CONCLUSION
This study proposed the concept of the nonlinear phase shifter.First, the structure and equivalent circuit of the nonlinear phase shifter are introduced.Second, the design method for nonlinear phase shifters is demonstrated.Finally, two simplified sensing RIS elements is used to verify the proposed sensing RIS element.The results show great application potential in sensing RISs.In sensing RIS applications, traditional phase shifters can also be combined to achieve more complex functions.

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I G U R E 1 Functionality of the sensing reconfigurable intelligent surface (RIS) and the topology of the element.

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I G U R E 2 (A) The topology of the nonlinear phase shifter.(B) The large signal equivalent circuit of the Schottky diode.(C) The equivalent circuit of (A).THE NONLINEAR PHASE SHIFTER 2.Design method for the nonlinear phase shifter The simulated admittance of the MA4E1318 Schottky diode at 4 GHz (A) G (P) and (B) B (P) .(C) The structure of the two nonlinear phase shifters.

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I G U R E 5 (A) Experimental verification setup.(B) The two simplified sensing reconfigurable intelligent surface (RIS) elements prototype.