Simulation and analysis of unit cells

In the design of SLC_based_ESSs, an SLC resonance circuit is used to generate a stopband for high-power signals. As the stopband moves away for low-power signals, the incident waves are able to propagate. A good example of SLC_based_ESS is provided in [Reference Yang, Liu and Huang4] and is adopted for demonstration in this paper. This proposed structure in [Reference Yang, Liu and Huang4] is composed of metal strips in serial with PIN diodes, seen in Figure 1(a). The ECM of the design is simple where the metal strip is modeled as an inductor L_s, and the diode is modeled as a capacitor C_diode (0.15 pF) in OFF state and an inductor L_ON (0.75 nH) in serial with a resistor R_s (1.5 Ω) in ON state, as shown in Figure 1(b). The metal strips-based ESS (MSESS) works in L band and below.

Figure 1.

Geometry parameters and the ECM of the MSESS. The parameters are set as P = 6 mm, g = 0.8 mm, w = 1 mm.

A commercial software CST MWS (2021) is used for simulations in the paper. The property of MSESS is firstly analyzed with unit cells, which is regarded as infinite arrays. Figure 2(a) reveals the transmission coefficient of the MSESS under different conditions. For low-power signals, the diode is OFF and the SLC circuit resonates at about 6.1 GHz, and the structure is wave-transparent in the working band. By contrast, the structure becomes inductive when diodes are turned on by high-power signals. Therefore, signals are blocked in the working band. Because PIN diodes are voltage-controlled devices, the induced voltage on the diodes could be adopted to evaluate the RT of PLC_based_ESS. However, the SLC resonance is more closely related to the currents. Therefore, the induced currents are used to evaluate the RT of SLC_based_ESS in this paper. Obviously, ESS with larger induced currents are easier to be triggered on and the RT is lower. By contrast, RT would increase if the induced currents are small. As shown in Figure 2(b), the peak of induced currents on the diodes occurs at the resonance frequency of the ECM. This is also valid when the geometry parameters vary. Furthermore, the induced currents are calculated under different geometry parameters, w and g. As seen in Figure 3, the increasing in w and g leads to a rise in the peak of induced currents. The relationship between L_s, w, and g can be indicated in a simple form [Reference Costa, Monorchio and Manara20] as

(1)\begin{equation} {L_s} \propto (P - g)/w. \end{equation}

Figure 2.

(a) The transmission coefficient of the MSESS under different power levels and (b) the induced currents on diodes under low-power signals.

Figure 3.

The induced currents on the diodes under different parameters: (a) w varies from 0.5 mm to 2.5 mm and (b) g varies from 0.4 mm to 1.4 mm.

Obviously, L_s is negatively related to both w and g. A more accurate analytic formula of the structure could be found in [Reference Marcuvitz21], according to which L_s is calculated to be 0.36 nH at this paper. Furthermore, the quality factor is obtained with

(2)\begin{equation} Q_s=\frac{1}{r}\sqrt{\frac{C_{diode}}{L_s}} \end{equation}

where r is the ohmic loss in the circuit (r is not shown in the figure of the ECM for simplicity and can be regarded in serial with L_s). Therefore, the peak of induced currents also rises with Q_s, which is similar to PLC_based_ESS. However, this mechanism is only valid at the resonant frequency range. By contrast, the variation on geometry parameters only causes slight influence on induced currents in the working band of MSESS, which lies on the non-resonant frequency range. Therefore, the design method of RT for PLC_based_ESS, namely by changing the value of quality factor of ECM or geometry parameters of unit cells, may not be applicable at this time.

Simulation and analysis of arrays

Since the induced currents are not sensitive to the variation on Q_s, a possible method is to introduce some additional auxiliary structures (ASs) and enhance the currents on diodes in the non-resonant frequency range. The AS is not required for the design of the electromagnetic (EM) response of ESS, which is added as an extra part of ESS to design RT. However, adding AS to the unit cells of ESS may cause a significant influence on the transmission performance of ESS, hence the AS is introduced to the ESS arrays. The ECM of an ESS array including m × n unit cells could be obtained with simple processes. Shown in Figure 4, there are m rows and n columns in the array. The impedance of each unit cell is represented as $Z_{ESS}=Z_{s}+Z_{c}$, where Z_s and Z_c indicate the self impedance and mutual impedance of each unit cell, respectively. Then the impedance of each column of the array Z_col could be calculated by

(3)\begin{align} Z_{col} &= Z_s+Z_c+\cdots+Z_s+Z_c+Z_s = mZ_s+(m-1)Z_c\nonumber\\ &=(m-1)Z_{ESS}+Z_c. \end{align}

Figure 4.

The ECM of an ESS array with m × n unit cells.

The impedance of the ESS array Z_ESSA is obtained by

(4)\begin{align} Z_{ESSA} &= Z_{v}||Z_{v}\cdots||Z_{v} = Z_{col}/n=(m-1)Z_{ESS}/n+Z_c/n. \end{align}

Obviously, as m and n increases, Z_ESSA gradually approaches Z_ESS, indicating that an ESS array with finite unit cells could be analyzed with the same ECM as the unit cell (infinite array) approximately.

As for the MESS, four metal strips are introduced to the MSESS array as AS, shown in Figure 5. The AS acts as an inductor L_MS, and thus the ECM of the MSESS array turns to a PLC circuit despite that the ECM of unit cell remains SLC circuits. Because L_MS is much larger than L_s, the PLC resonance of the MSESS array occurs at a much lower frequency range than SLC resonance of the single unit cell. Therefore, the induced currents are greatly enhanced during the operating frequency band due to the AS. Compared to the array without AS, the RT is supposed to be significantly reduced. By introducing AS into ESS design, the circuit topology of SLC_based_ESSs arrays could be changed from SLC to PLC, thus effectively changing the RT.

Figure 5.

The ECM of the MSESS array (a) without and (b) with AS (metal strips).

Demonstration and verification

An MSESS array including 16 × 32 unit cells is investigated with full-wave simulations for verification (although it is better to choose a larger dimension, much more computing resources are required). A plane wave (10 V/m) is used as excitation and open boundary condition is applied at x, y, and z direction. As shown in Figure 6, the induced currents on the diodes of the MEESS array, with and without AS, are calculated for verification at a normal incidence. Apparently, the currents on the array with AS are generally enhanced compared to the one without AS in the operating band as expected. Besides, it can be seen that the induced currents vary with the positions of diodes in the array. This non-uniform distribution of currents is caused by the discontinuity of impedance on the boundary. What’s more, the induced currents also vary with frequency and there are several peaks caused by the resonance of the arrays.

Figure 6.

The induced currents on the diodes of the MSESS arrays (a) without and (b) with AS.

The distribution of electric field is calculated for verification. The distributions of electric field at 1.3 GHz (which is also the frequency for high-power signal measurement) with and without AS are compared, as seen in Figures 7(a) and 7(b). Obviously, the electric field on the MSESS arrays is not uniform due to the impedance discontinuity on the boundary. Specially, the phenomenon is more significant when AS is added. The non-uniform distribution of electric field on the array is supposed to make the diodes easier to be triggered on. Once the diodes at positions with larger induced currents are turned-on, the impedance of diodes become smaller and thus the currents are further enhanced. As a result, the adjacent diodes would also be turned on.

Figure 7.

The distribution of electric field of the MSESS arrays (a) without AS at 1.3 GHz, (b) with AS at 1.3 GHz, (c) with AS at 0.36 GHz, and (d) with AS at 1.1 GHz.

Notably that two peaks of induced currents occur at 0.36 GHz and 1.1 GHz on the MSESS array with AS, the electric field and surface current at these two peaks are investigated, as shown in Figures 7(c) and 7(d). Obviously, strong electric field is excited at the AS and the unit cells near two ends of the array at 0.36 GHz. At the same time, strong surface currents are also excited along AS. The distribution of electric field and surface current indicate that a strong resonance is excited on the AS, which contributes to the rise of the induced currents on diodes. The distribution of electric field and currents at 1.1 GHz is similar to the second-order resonance at 0.36 GHz.

Experimental setup

To verify our analysis, two prototypes are fabricated in which PIN diodes BAP-51-02 from NXP semiconductor are soldered on the F4BME substrate (which has a permittivity of 2.2 and dielectric loss tangent of 0.007) with a thickness of 0.1 mm, as seen in Figure 8 (the AS around the large one are already removed before taking pictures). The dimension of two prototypes is 8 mm × 16 mm (DUT1) and 300 mm × 300 mm (DUT2), respectively. DUT1 is used for a better verification of simulations while the DUT2 for a standard measurement. The geometry parameters of unit cells of both prototypes are the same. To explore the influence of AS on the RT and transmission performance of the prototypes, the experiments are conducted as following steps:

1. (i) Low-power signal measurements with AS;

2. (ii) High-power signal measurements with AS;

3. (iii) Remove the AS and repeat (i) and (ii).

Figure 8.

The two prototypes of MSESS with a dimension of 8 mm × 16 mm (DUT1) and 300 mm × 300 mm (DUT2), respectively.

Obviously, only two prototypes are required and each prototype is tested repeatedly under different conditions. The results with and without AS from the same prototypes are compared to eliminate the measurement errors. For low-power signals, the transmission coefficient is measured in an anechoic chamber with a vector network analyzer (from Ceyear AV3672E). The DUTs are placed in the central of an absorbing wall with two broadband horn antennas on the front and back, respectively. For high-power signals, a high-power source is used to generate high-power illumination, and an oscilloscope is applied to monitor the field intensity. The experiments are conducted at a microwave anechoic chamber and the ESS prototype is mounted on the window of a shielding box. The detailed experimental setup is illustrated in our previous works [Reference Hu, Wang, Zhang, Zha, Wu, Liu and Liu9, Reference Hu, Liu, Xu and Costa12] and not illustrated in this paper.

Low-power signal measurements

For the low-power signals, the two prototypes are measured under a normally incident plane wave and the transmission coefficient is shown in Figure 9. Interestingly, there are obvious fluctuations with frequencies on the transmission coefficient for DUT1 with and without AS. The fluctuations mainly contribute to the small dimension of DUT1 and unexpected resonance occurs at the test window. However, such a fluctuation is smaller than 1 dB and could be ignored in the measurements for high power signals. Regarding the size of the DUT1 , which is too small to be considered as an infinite array in the experimental frequency range, the measurement results of transmission coefficient for DUT1 is not reliable. Since the focus of this paper is the RT of ESS, DUT1 is fabricated and measured to explore the relationship between the size of AS and RT. There is a better agreement on the results of measurements and simulations for DUT2. The measured transmission coefficient is almost 1 dB smaller than the simulations, and the difference becomes larger with frequency. There are two main reasons. Firstly, the equivalent capacitor C_diode used in the simulations is 0.15 pF (which is a typical value for reference). However, C_diode varies in a certain range, which introduces errors and this kind of error would increase with frequency, shown in Figure 10(a). Secondly, the equivalent model of the diode is a simplified model, which does not take the ohmic loss into consideration. As the ECM of the diode is further improved by considering ohmic loss and optimizing the value of C_diode, the measurements and simulations reach a good agreement ($R_d = 10\,\Omega $, $R_{OFF} = 2000\,\Omega$), shown in Figure 10(b).

Figure 9.

The transmission coefficient of two MSESS prototypes with and without AS for low power signals (Sim: simulation results, Mea: measured results).

Figure 10.

The analysis of the causes of errors. (a) The effects of capacitance and (b) the effects of the ECM of the diode.

It is interesting to see that the AS does not cause any fluctuations in the transmission coefficient this time. Specifically, the S ₂₁ of the DUT2 with AS is larger than that without AS when the frequency is lower than 1.5 GHz while in the higher frequency range, the trend is opposite. Since the resonance mode of the AS varies with frequency, the S ₂₁ may be increased in some band but decreased in others.

In summary, the influence caused by AS on the transmission coefficient is not significant and less than 1 dB according to the measured results of DUT2. In addition, as the dimension of AS changed, the influence on transmission coefficient also varies when comparing the measured results of DUT1 and DUT2 together.

High-power signal measurements

The transmission coefficient of MSESS with and without AS for high-power signals are measured at 1.3 GHz, shown in Figure 11. For DUT1, the RT of the prototype with AS is about 1.2 kV/m while that without AS does not appear when the field intensity is less than 4.2 kV/m. For DUT2, the RT of the prototype with and without AS is about 1.2 kV/m and 6.5 kV/m, respectively. The results of both DUTs prove that the AS plays a critical role in the design of RT and the proposed method is useful in the MSESS design.

Figure 11.

The transmission coefficient of two MSESS prototypes with and without AS for high-power signals (a) DUT1 and (b) DUT2.

Comparison

To illustrate the advantages of the proposed method, the results of this paper are compared with the previous works, shown in the Table 1. In [Reference Hu, Liu, Tian, Xu and Liu19], the RT is designed by changing the geometry parameters of the unit cells, the RT of ESS becomes 1.3 times the initial value. In [Reference Yang, Torbe, De Marco, Marc and Christian18], the RT is designed by changing the types of diodes, and the variation range of RT is up to 10 times theoretically (no experiments in [Reference Yang, Torbe, De Marco, Marc and Christian18]). However, the change of diodes may significantly increase the cost and makes negative impacts on other indicators of ESS. For instance, if the diode of ESS is changed from a PIN diode to a Schottky diode, the power capacity will be reduced. Besides, the operating frequency, and the response time of ESS may also be changed with the diodes. On the contrary, the proposed method in this paper makes a noticeable design effect on the RT of ESS without introducing extra cost or negative impacts.

Table 1.

Comparison of different methods