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In this work, we present a miniaturize power limiter, a device with size smaller than that required by the working frequency, made of coupled self-complementary electric inductive-capacitive (CELC) resonator and original electric inductive-capacitive (ELC) structure. We also make use of Babinet principle to ensure both CELC and ELC are resonating at the same frequency. The CELC structure is loaded with a Schottky diode to achieve the effect of a nonlinear power limiter. The constructive interference of CELC and ELC structure produces a new Fano-type resonance peak at a lower frequency. The Fano peak is sharp and able to concentrate electric field at a region between the inner and outer metallic patch of the metastructure, hence enhancing the nonlinear properties of the loaded diode. The Fano peak enhances the maximum isolation of the power limiter due to the local field enhancement at where the diode is loaded. Numerical simulation and experiment are conducted in the S-band frequency to verify the power limiting effect of the device designed and to discuss the formation of Fano peak. The power limiter designed has a maximum isolation of 8.4 dB and a 3-dB isolation bandwidth of 6%.
© 2016 Optical Society of America
1. Introduction
The function of power limiter is to perform like a noble metal under low power illumination. However, it has ability to attenuate the incoming power to a pre-design threshold value of power under high power illumination. It is based on nonlinear effect and provided by nonlinear medium. In this paper, we follow the proposed structure by Katko to use Complementary Electric Inductive-Capacitive (CELC) structure as a metal patch and power large voltage across the inner metallic patch and outer metallic patch via high power incoming electromagnetic signal [1]. A PIN or Schottky diode is inserted across the inner metallic patch to the outer metallic patch to provide nonlinear properties. What is new in this paper is to add an additional Electric Inductive-Capacitive (ELC) structure at the other side of the substrate to miniaturize the device and to improve its isolation.
Unlike conventional absorber [2] or metamaterial absorber [3–5] that attenuate both high and low power signal, a nonlinear power limiter has the ability to attenuate high power signal only beyond a certain threshold power of the incident signal, while allowing low power signal to transmit. As such, the device covered by the power limiter is still able to function. Metastructure nonlinear power limiter has been studied and realised experimentally by Cummer and Sievenpiper’s group [1,6–8]. Both groups used metal surface embedded with diodes while Sievenpiper’s works had paid specific attention to the high power incoming wave as a pulse.
The power limiter proposed in this paper makes use of self-complementary metasurface [9,10] to create a miniaturize device, a functioning power limiter operating at a lower frequency with a smaller dimension. The miniaturize power limiter consist of two different resonant structure on opposite side of a dielectric substrate. The interaction between this two resonant structure results in an asymmetrical Fano-resonance peak at a lower frequency. The Fano-peak is sharper than the CELC peak, resulting in a power limiter with higher isolation.
2. Design of metasurface
An ELC resonator is an electrically induced metasurface that behaves like a parallel LC circuit [11]. It couples strongly to electric field, resulting in a stop-band at resonant frequency. A CELC resonator, is a pure magnetic resonant structure that couples strongly to magnetic field, resulting in a pass-band at resonant frequency. Babinet principle has been applied to study the duality between the ELC and CELC structures [12,13], hence to excite an ELC structure requires an electric field to be perpendicular to the capacitive gap while a magnetic field perpendicular to the gap complement is required to excite a CELC structure.
As a complement to the ELC structure, the CELC structure can be described by an equivalent circuit of a series LC circuit [14]. As the circuit has minimum impedance at resonance, it results in a pass-band as mentioned earlier. By connecting a resistor across the inner metallic patch to the outer metallic patch as shown in Fig. 1(a), the impedance at resonant frequency will increase with decreasing resistance. A PIN diode or Schottky diode can be used as a circuit element that function like a variable resistor. We call the structure shown in Fig. 1(a) CELC loaded with diode.
Fig. 1 Schematic diagram of (a) front CELC with a lumped element (blue arrow) connected across inner metallic patch to outer metallic patch, (b) back ELC and (c) overall view of miniature power limiter with FR4 substrate. The dimensions are as follow: d = 4 mm, g = 0.5 mm, a = 17 mm, w = 1.1 mm and t = 1.524 mm. (d) equivalent circuit for miniature power limiter (diode not loaded)
The miniature power limiter, as shown in Fig. 1, has a ELC structure patterned on one side of FR4 and CELC structure patterned on the other side of the same FR4 substrate. The ELC structure is rotated by 90° so that they can both be simultaneously excited by the same incident field and resonant at the same frequency. The unit cell is designed to be functioning at the operating frequency of a standard S-band waveguide (2.6 GHz to 3.95 GHz) and the height of the unit cell is fixed at half the height of a standard S-band waveguide so that we can fit two unit cells vertically into the waveguide. The dimensions of the unit cell are given in Fig. 1(a). To describe the response of the proposed structure, an equivalent circuit, which consist of two resonant oscillatory circuit coupled to each other, shown in Fig. 1(d) is proposed.
3. Simulation and result
Commercial software Computer Simulation Technology (CST) microwave studio is used to simulate the S-parameters of the device. The CELC structure is loaded with lumped element to simulate the response of Schottky diode SMS7621 with varying power incident on the surface. The Schottky diode is modelled as a resistor with decreasing resistance with increasing incident power. The device is designed to work in the operating frequency of S-band waveguide (2.6 GHz to 3.95 GHz).
Firstly, we demonstrate the effect of diode on the CELC S21 characteristic [Fig. 2(a)]. The S21 profile shows that CELC is highly reflective except at the resonant frequency of 4.35 GHz. It can be seen that the S21 value decreases as resistance decreases near the resonant frequency. Therefore, the incident wave with small power will transmit through and wave with high power will be attenuated. A high resistance of 5000 Ω simulating the case of low power incident wave do not affect the S21 profile significantly. When the resistance reduces to 30 Ω representing the case of high power, there is no accumulation of charges across the gap, hence the resonating oscillator is mitigated. As a result, the transmission decreases, causing a depression of S21 peak, demonstrating the function as a power limiter.
Fig. 2 Simulated S21 values for (a) CELC loaded with lumped element and (b) CELC and ELC structure on opposite side of FR4 substrate, loaded with lumped element for various value of resistance to represent diode at various power states.
Secondly, we demonstrate the effect of ELC added to the other side of the FR4 substrate of the original CELC structure [Fig. 2(b)]. There are additional peaks formed at a frequency below and above the original resonant frequency.
The peak we are interested in is that at the frequency of 3.35 GHz shown in Fig. 2(b). Similar to the single CELC structure alone, the S21 value decreases with decreasing resistance (corresponding to higher power incident signal) as well. Hence, we obtain a power limiter with operating frequency that has shifted down by approximately 1 GHz despite the same dimension used, achieving the effect of miniaturization. The effect of miniaturization is dependent on the thickness of the dielectric substrate used.
Simulation was done to investigate the relationship between the shifting of resonant frequency with thickness of dielectric as shown in Fig. 3. As the thickness of the dielectric substrate decreases, the shift increases, indicating greater miniaturization. This is due to stronger coupling between the ELC and CELC structure as the thickness of the dielectric decreases. As such, one can tune the shift accordingly to the thickness the dielectric substrate for application.
Fig. 3 Plot of shift in resonant frequency from original CELC loaded with lumped element to miniaturize power limiter with thickness of dielectric.
Thirdly, we demonstrate the origin of the asymmetrical peak at 3.35 GHz that is sharper than the CELC peak. This is the fingerprint of a Fano-type resonance peak [15–17].
The S21 characteristic curves of ELC and CELC unit cell shows absorption and transmission properties respectively at the same resonance frequency as shown in Fig. 4(a). Figure 4(b) shows the S21 characteristic curves of a unit cell consisting of CELC on one side of the substrate and ELC on the other side of the substrate. The ELC structure interacts with the CELC structure, resulting in an additional Fano-peak at the shoulder of the unperturbed CELC peak at 3.68 GHz, while the unperturbed CELC peak shifts slightly downwards from 7.0 GHz to 5.9 GHz. The ELC and CELC structure can be viewed as two coupled oscillators which interact and produce an asymmetric line shape as a result of a constructive interference between the two oscillator [18, 19]. The equivalent circuit shown in Fig. 1(d) can be used to describe the coupling between the two oscillators as Fano interference can often be simulated using a coupled RLC circuit [20]. The proposed equivalent circuit has been solved and exhibit similar response as the simulated results we got in Fig. 4(b). The CST simulated phase of ELC, CELC and combined ELC and CELC are shown in Fig. 4(c). There is no abrupt phase change across the frequency sweep for ELC and CELC unit cell. However, there is an abrupt phase change of 150° at the Fano resonance frequency peak at 3.68 GHz for the combined ELC and CELC unit cell.
Fig. 4 Magnitude of simulated S21 values for (a) ELC and CELC alone on separate FR4 substrate, (b) CELC and ELC patterned on opposite side of the same FR4 substrate (c) phase of S21 in degrees for the case of substrate with only ELC or CELC and substrate with CELC on one side and ELC on the other side.
Figures 5(a) and 5(b) shows the surface current density of the CELC and ELC surfaces at the Fano-resonance frequency respectively. The surface current density at the CELC surface is generally larger than that at the ELC surface, particularly around the metallic gap of the CELC surface. Therefore, some of the energy has been transferred from the ELC surface to the CELC surface at Fano-frequency of 3.68 GHz. The Fano-peak is a consequence of the path of mutual coupling of constructive interference of CELC (dark mode) and ELC (bright mode) and the path of direct excitation of ELC structure [21–23].
Fig. 5 The surface current distribution of (a) front CELC and (b) back ELC surface at Fano-frequency and contour plot of y-component of local electric field Ey (direction of E-field indicated by arrows) at frequency (c) 3.68 GHz and (d) 5.9 GHz for CELC and ELC patterned on opposite of same FR4 substrate, with no lumped element loaded.
Fourthly, we discuss the simulated figure of merit of single CELC loaded with diode and the miniature power limiter. The first figure of merit is the maximum isolation of the miniature power limiter. The maximum isolation is defined as the difference in S21 between the high power state and low power state, .It was noted from CST simulation that the Fano-peak at 3.35 GHz [Fig. 2(b)] has a larger maximum isolation, 20.4 dB, as compared to the maximum isolation, 17.3 dB, of a single CELC loaded with lumped element [Fig. 2(a)]. This is the result of strong local field enhancement between the inner metallic patch and outer metallic patch in which the diode will be loaded at the Fano-resonance frequency. Figures 5(c) and 5(d) shows the local electric field at the Fano-frequency and the unperturbed CELC resonant frequency respectively. The electric field is oscillating and the electric field strength is as shown in the inserted scale, with negative value representing an opposite direction. Comparing Fig. 5(c) and 5(d), it can be seen that the local electric field at the Fano-resonance frequency is significantly stronger than the local electric field at the unperturbed CELC resonant frequency, another significant characteristics of Fano-type resonance [24, 25]. As shown in Fig. 5(c) and 5(d), the electric field at Fano-frequency 3.68 GHz and 5.9 GHz are out of phase, supporting the result of Fig. 4(c). The second figure of merit is the 3-dB isolation bandwidth, , where f1 and f2 is the frequency in which the isolation between high power and lower power state is more than 3 dB and fR is the resonance frequency. The 3-dB isolation bandwidth, however, is compromised due to the formation of Fano-peak that is sharper. The simulated isolation bandwidth for the single CELC loaded with diode is 40.5% (1.79 GHz) while the simulated isolation bandwidth for the miniature power limiter is 19.5% (650 MHz).
4. Experiment and results
The miniature power limiter consists of 8 unit cells, fabricated with standard PCB technology. The diode SMS7621 is soldered across the inner metallic patch to the outer metallic patch of the CELC pattern as shown in Fig. 6(a). The sample is placed in a S-band waveguide, with direction of propagation of wave to be perpendicular to the sample surface. Agilent Technologies N5230A PNA is used to measure the S-parameter according to the schematic diagram shown in Fig. 6(b).
Fig. 6 (a) Picture of the fabricated sample (front) with diode soldered, (b)schematic diagram and (c) actual set-up for experiment. The insert in (c) shows how the sample is placed inside the waveguide.
To verify that the device is functioning as a power limiter, a spectrum analyser (Keysight CXA Signal Analyzer N9000A) is connected to port 2 to measure the output power as the input power vary. The PNA, therefore, acts as a signal generator. The measured S21 values and output power in shown in Fig. 7.
Fig. 7 (a) Experimental S21 measurement and (b) plot of output power against input power of miniature power limiter.
Comparing the experimentally measured S21 values in Fig. 7(a) and simulated values in Fig. 2(b), the Fano-peak is approximately at the same frequency while the unperturbed CELC peak is shifted downwards to approximately 3.70 GHz. Similar to the simulated results, the Fano-peak is more sensitive to varying power of incoming signal, again, indicating the enhancement of local field. The maximum isolation, compared to the simulation results, are very much lower. This is likely to be due to the surface being more lossy as compared to the ideal condition in simulation.
The experimental result has a slightly different shape as the simulated results presented earlier as the simulation uses incident plane wave while experiment uses TE10 mode of the waveguide. To verify that the experimental results can be matched with the simulation results, a simulation with 8 units with boundary conditions closer to the actual experiment set-up is performed. The observed frequency range of the experiment measurement is then expanded beyond the operating frequency of the S-band waveguide. As shown in Fig. 8, we can observe similarity between the shape of the S21 measurement for the simulation and experiment. There are parasitic characteristics of the diode that may not have been considered in the simulation as well. Hence, there is a shift in the peak position.
Fig. 8 S21 values measured in a S-band waveguide for miniature power limiter extended beyond operating frequency. (Insert) simulated results for 8 unit cells.
From −30 dBm to 0 dBm, the output power varies linearly with input power. Beyond 0 dBm, the device exhibits some insertion loss, the characteristic of a limiter. Hence, we can determine that the threshold power is approximately 0 dBm. This can also be observed from the S21 measurement as the S21 value only decreases when input power is increased beyond the threshold. The Schottky diode used in this experiment has a linear I-V characteristic beyond 15 dBm, hence it cannot function as a power limiter beyond 15 dBm. Therefore, the threshold power and maximum power can be adjusted by applying bias to the diode or by changing another more suitable diode such as a PIN diode.
The proposed miniature power limiter has a maximum isolation of approximately 8.4 dB and isolation bandwidth of 6% (200 MHz).
5. Conclusion
In conclusion, using self-complementary metasurface, we have designed a miniature power limiter operating in the S-band frequency. A Fano-type resonance peak occurs at the operating frequency of the miniature power limiter, improving the maximum isolation of the device. The isolation bandwidth, however, is compromised. The effect of miniaturization has been shown in numerical simulation and verified in experiment. Experimental results also show that the power limiter proposed has achieved the power limiting effect with a maximum isolation of 8.4 GHz and isolation bandwidth of approximately 200 MHz.
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