As various applications in the area of communication, medicine, and defense, among others, are being developed and deployed rapidly, the demand for microwave absorbers is also increasing. Microwave absorbers are used for anechoic chambers [1], mobile phones, EMI/EMC problems, stealth air planes [2], and other applications. Particularly, they are required to minimize the hazards of EMP attacks.

The current commercial absorbers are usually made of ferrite materials, which are expensive and bulky. To replace these materials, many other types of absorbers have been introduced and developed. Recent advancements in metamaterial research have opened the possibility for metamaterial absorbers (MA) [3–5]. The literature shows that MAs can be realized very thinly, but their bandwidth is still narrow. Thus, a double layer may have to be used [5].

A conventional absorber is the Salisbury screen [6]. The Salisbury screen is made of a 377-Ω resistive film placed at a distance of quarter wavelength above a conducting plane. The thickness of the absorber is relatively thick at low frequencies because of the required spacing of λ/4, but its bandwidth is still not satisfactory. To achieve a wide-bandwidth absorption property, a multi-layer structure was also studied [7]. Although the bandwidth is excellently enhanced with a multilayer, the complexity and the considerable absorber size are always troublesome. A single layer is always preferable because of its simple and compact geometry, and its performance is comparable with that of the multi-layer. Single-layer reactive screens usually modeled by a lumped series RLC resonator have also been examined with results of much wider bandwidth than those of Salisbury screens [8,9]. Especially in [10], simple closed-form solutions for the RLC absorbers with a layer thickness of λ/4 were derived from the impedance match and zero susceptance (or reactance) slope conditions for broadband design. With this method, complete absorption at and near a design center frequency can be achieved, and the 99% absorption bandwidth is about 54% (enough to cover the whole X-band) when an air or Styrofoam layer is used. The same design methodology was extended to absorbers with a layer thickness less than a quarter of a wavelength, but it was found to be not as effective as in the case of the quarter wavelength layer.

In this paper, the absorbers with a layer thickness less than a quarter of a wavelength are designed using a resistive and capacitive (RC) screen. The reason why the capacitive RC screen is employed is that the impedance of the layer, which has a thickness less than a quarter of a wavelength, is inductive. Convenient design equations are derived using a proper equivalent circuit. The provided design equations are useful for synthesizing any particular absorber at a specific frequency, and they also give us physical insight into the bandwidth trade-offs between the thick and thin absorbers. Particularly, the bandwidths of the RC absorbers are compared with those of the metamaterial-type absorbers. Finally, for the validity of the formulation, an RC absorber made of a silver nanowire (AgNW) resistive film is designed at 3 GHz, fabricated, and measured. Comparisons and discussions are then conducted.

The proposed absorber is composed of an RC screen and a conducting plane separated by a distance of less than a quarter of a wavelength. Fig. 1 shows the equivalent circuit of the RC absorber, where η₀ is the intrinsic impedance of air (377 Ω) and η₁ is the intrinsic impedance of the layer between the conducting plane and the RC screen. h is the layer thickness, and θ₀ is the electrical length of the layer given by βh, where β is the propagation constant in the layer. The RC screen can be modeled by a series connection of a resistor with R₀ and a capacitor with C₀. Y_in is the input admittance. The admittance Y₀ of the RC screen at an angular design center frequency ω₀ is given by

and the admittance Y₁ of the layer when its electrical length is θ₀ is given by

For the input admittance match of the absorber to free space, we require

By separately equating the real and imaginary parts of (3), we obtain the unique solutions of R₀ and C₀ expressed as

and

Fig. 2 illustrates the required circuit values of R₀ and C₀ as a function of the electrical thickness θ₀ of the layer when η₁ = η₀ = 377 Ω and the design center frequency f₀ is assumed to be 3 GHz. As θ₀ increases from 0° to 90°, R₀ monotonically increases from 0 Ω to 377 Ω. However, C₀ is symmetric about θ₀ = 45° and goes to infinity as θ₀ goes to 0° or 90°. These observations indicate that when θ₀ goes to 90°, the screen is practically reduced to the conventional Salisbury screen. More discussions will follow later.

Fig. 3(a) shows the absorptions (= 1–|S₁₁|²) as a function of normalized frequency f/f₀ for different θ₀ of 11.25°, 22.5°, 45°, 57°, and 90°. Each absorber has a perfect absorption at the design center frequency as expected. Note that although C₀ depends on f₀ as shown in (5), Fig. 3(a) holds true for any f₀. In Fig. 3(b), the 90% absorption bandwidths are plotted as a function of θ₀. As the absorption characteristics are not symmetric, especially near θ₀ = 45°, the fractional bandwidths are been calculated on the basis of the center frequencies. One notable observation is that as θ₀ increases from 0°, the bandwidth increases only up to about 57° but decreases beyond that. The 90% absorption bandwidth is shown to have a maximum of about 93% when θ₀ is about 57°. Thus, the RC absorbers are not recommended with a layer thickness larger than 57°.

Fig. 4 illustrates a unit structure of the RC absorber with dimensions determined at a design frequency of 3 GHz using EM simulations for the case of η₁ = η₀ = 377 Ω and θ₀ = 45° (h = 12.5 mm =λ₀/8). The unit of the RC screen consisting of a square resistive sheet and four gaps is placed above a conducting plane. Based on (4) and (5), R₀ and C₀ of the RC screen are 188.5 Ω and 0.28 pF, respectively. These required circuit values can be realized by surface resistance per square (R_s) and the gap. The determined values (a, l, R_s) using HFSS simulations are a = 35 mm (0.35 λ₀), l = 28 mm, and R_s = 110 Ω/□. Table 1 summarizes the theoretically required values of R₀ and C₀ using (4) and (5), the obtained dimensions of the absorbers using EM simulations, the used surface resistance (Ω/□), and the 90% absorption bandwidths for different electrical lengths (θ₀) at 3 GHz. The terminal impedance Z₀ of the RC screen in Fig. 4 is evaluated after proper de-embedding using EM (HFSS) simulations. It denotes the impedance of the RC screen alone.

Fig. 5 demonstrates the real and imaginary parts of Z₀ as a function of frequency based on circuit (Fig. 1) and EM simulations for the case of θ₀ = 45° at 3 GHz. The excellent agreement implies that the required circuit values of R₀ and C₀ are well realized by the RC screen dimensions as summarized in Table 1.

In Fig. 6, the EM-simulated input impedance Z_in (1/Y_in) is compared with the circuit-simulated (or theoretical) impedance shown in Fig. 1, and the two impedances are shown to be in good agreement. The impedance behaviors for frequencies higher than 3 GHz are shown to be better for wideband characteristics than those for lower frequencies.

Fig. 7 shows a photograph of the fabricated RC absorber made of AgNW resistive film. The AgNW film with 110 ±4 Ω/□, produced by Cosmo AM&T (www.cosmoamt.com), was cut by a laser-cutting machine. The whole patterned film was then attached to a Styrofoam layer. The unnecessary part was detached later. One unit is composed of a square-shaped AgNW film, a Styrofoam layer of 12.5 mm (λ₀/8 at 3 GHz), and a conducting plane. The size of the unit is 35 mm × 35 mm (0.35 λ₀ × 0.35 λ₀ at 3 GHz ).

Fig. 8 presents the measurement setup to estimate the absorptions of the fabricated absorber with one horn antenna. The size of the fabricated absorber is 35 cm (10 units) × 25 cm (7 units). The measurements were conducted to change the distance between the standard horn antenna and the absorber from 3.5 cm to 23 cm. Although the absorber is placed somewhat in the near field, the following extraction procedures have been found to give closer results than the EM-simulation results [11].

Fig. 9 illustrates the measured reflection coefficients of the horn antenna in free space (S₁₁ without the absorber), with the conducting plane (S₁₁ with the conducting plane), and with the absorber (S₁₁ with the absorber) as a function of frequency. The calibration method in [11] was used. The magnitude of the reflection coefficient referenced on the absorber surface under the condition of a normal plane wave incidence can be estimated using |S_{11, plane wave}| = |S₁₁ with absorber| / |S₁₁ with conducting plane|.

This estimation removes the effects of the used horn antenna and minimizes the effects of the used near-field measurements. The measured absorption is calculated using (1–|S_{11, plane wave}|²).

In Fig. 10, the measured absorption is shown to agree well with the theoretical (or circuit-simulated) and EM-simulated absorptions. The measured 90% absorption bandwidth is approximately 76% (2.3–5.1 GHz) with a complete absorption at the design center frequency of 3 GHz.

In Table 2, the absorption characteristics of the thin absorbers in [12–15] are compared with those theoretically expected by the proposed design method. Except for the case of [15] in which the measured bandwidth of 7% is wider than 5.7%, the bandwidth characteristics of the rest are shown to be at best comparable with or even far worse than those of the presented simple RC absorbers although diversified structures have been employed.

An RC absorber with a layer thickness of less than a quarter of a wavelength has been examined from a simple equivalent circuit. Closed-form design equations have been derived and presented. The validity of the presented formulation has been demonstrated by a design example for the RC absorber at 3 GHz. The RC absorber has been designed, fabricated with AgNW resistive film, and measured. The absorber is shown to offer a 90% absorption from 2.3 GHz to 5.1 GHz (76%) with a layer thickness of 1/8 wavelength. The proposed design methodology is scalable to other frequencies.