Characterization of the Dielectric Properties of 3D Printing Filaments Using Cavity Perturbation Technique for 5G Applications

Abstract

Cavity perturbation method is applied in this paper to assess the electric permittivity (ɛ_r) and loss tangent (tanδ) of dielectric materials at the 3.5 GHz microwave frequency of the 5G test band of the Global System for Mobile communications Association (GSMA) spectrum. These characteristics are important in the design of radomes, antenna fixture parts and spacers for airfilled multilayer structures for antennas and microwave circuits. A cylindrical cavity with two ports was designed and fabricated to operate in the TM₀₁₀ mode. The characterization process includes the preparation of cylindrical samples with thickness of 12.5 mm with concentrations of 25%, 50%, 75% and 100% of the following materials: acrylonitrile butadiene styrene (ABS), Tritan, polyethylene ethylene glycol terephthalate (PETG), acrylonitrile styrene acrylate (ASA), polyamide (Nylon), Polylactic acid (PLA) and CRcarbon. The measured S-parameters allowed calculating the quality factor, the electrical permittivity and the loss tangent of the analyzed samples by comparison to numerical results obtained by the Finite Element Method (FEM) using Ansys HFSS. The results obtained demonstrate that the filling percentage of the samples is an efficient technique to control the effective dielectric constant of 3D printed parts, provided that the filling mesh dimensions are much smaller than the operating wavelength. Such a condition is easily achieved at 3.5 GHz with modern 3D printers. Finally, a dielectric resonator antenna has been designed and measured, whereby excellent agreement between the simulation predictions and measured results has been achieved, hence demonstrating the accuracy of the proposed dielectric measurement technique.

Index Terms
Cavity perturbation technique; 3D printing; dielectric properties; dielectric resonator antennas.

I. INTRODUCTION

Materials characterization aims to explore the intrinsic properties of matter, with the purpose of providing valuable insights for both science and industry in general. Knowledge of the dielectric properties of materials is of fundamental importance in several areas of Engineering, such as in food conservation, energy transmission, electronics and, in particular, telecommunications sector. Several characteristics should be considered during the design of devices, such as the dielectric constant (ε_r′), the dissipation factor (tanδ), the ability to absorb moisture, the thermal expansion parameters, among others [¹]. In this way, a detailed view of the materials will be offered in order to guide in technological processes of preparing raw materials for the development and production of new materials and devices for future technological applications.

Advances in the study of dielectric materials have gained considerable proportions due to 3D printing technology, which is a process for manufacturing three-dimensional solid objects that is based on the addition of material in layers. It provides great flexibility in the design and construction of structural components with complex geometries quickly, with high precision, reduced costs and less material waste when compared to traditional manufacturing methods [²], [³]. This technology can provide an affordable method for prototyping radio frequency (RF) devices [⁴] and antenna designs [⁵], in particular in the development of low-cost microwave electronic circuits [⁶], metallic antennas [⁷], dielectric resonator antennas (DRAs) [⁸] and hybrid antennas, composed of metal, dielectric and conducting polymers [⁹].

First, it is necessary to characterize the dielectric properties, usually in terms of their permittivity and dissipation factor of the materials used in 3D printing. This helps to determine the ideal material from the desired dielectric properties. Different metallization techniques were proposed in [⁷] for manufacturing metal antennas using 3D printing technology, such as i) covering the printed device with a copper tape, ii) application of conductive spray paint, or iii) using conductive filament.

The methods for material characterization generally fall into nonresonant methods and resonant methods. The former are often used to provide a general knowledge of the electromagnetic properties over a frequency range, whilst the latter are used to assess accurate knowledge of dielectric properties at a single or at several discrete frequencies [¹⁰]. Besides the resonant cavity method, the literature extensively investigates other methods for characterizing dielectric properties [¹¹], which are generally divided into coaxial probe method, transmission line method (waveguide), capacitive methods, free space method, parallel plate method and planar transmission line method [¹²]. Each one has advantages based on the available equipment, sample geometry and material properties. The choice of method depends on the frequency range, the type of material (solid, liquid, powder), the sample geometry, and the desired precision. The resonant-cavity method was chosen for this work, since it is very simple and yields accurate results.

This paper consists of characterizing the dielectric properties (ε_r′ and tanδ) of samples with cylindrical geometry, with thickness h_s = 12.5 mm, produced with the following 3D printing filaments: ABS, Tritan, PETG, ASA, Nylon, PLA and CR-carbon. Different concentrations (C_s) have been considered: 25%, 50%, 75% and 100% for using the cavity perturbation technique. The samples were characterized in the test band (3.5 GHz) of fifth-generation (5G) technology.

II. CAVITY PERTURBATION TECHNIQUE FOR ACCURATE MEASUREMENT OF THE COMPLEX PERMITTIVITY

The perturbation technique is widely used in characterizing dielectric properties in cavities. The main parameter to be measured, the complex electrical permittivity, is defined as [¹³]

(1) $${\epsilon }^{\ast }={\epsilon }^{\prime }-j{\epsilon }^{\prime \prime },$$

where ɛ' and ɛ'' are the real and imaginary parts of the permittivity, respectively. Both parts can be determined from the variations of the resonance frequency ∆f and the inverse of the cavity quality factor ∆(1/Q), respectively, due to the change in the geometric configuration of the electromagnetic fields caused by the insertion of a sample inside the resonant cavity.

In an empty cavity, resonances occur when the excited electromagnetic field is in phase with the reflected components, composing a standing wave through constructive and destructive interference. For cylindrical resonant cavities, the frequencies of angular resonances for the TM_nmp modes can be calculated using [¹⁴]

(2) $${\omega }_{nmp}=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\sqrt{{\left(\frac{P_{nm}}{r}\right)}^2+{\left(\frac{p\pi }{h}\right)}^2},$$

where µ₀ = 4π.10^-7 H/m and ɛ₀ = 8.854.10^-12 F/m are the magnetic permeability and the electrical permittivity of vacuum, r and h are the internal radius and height of the cavity, respectively. P_nm stands for the m-th zero of the n-th order Bessel function of the first kind J_n(ζ) and the parameters n, m and p are the indices corresponding to the resonance modes, indicating the number of variations of the electromagnetic field along the ϕ, ρ and z cylindrical coordinates, respectively.

According to the perturbation theory, the shift of complex angular frequency of the cavity (∆ω = ω_s - ω_c) can be expressed in terms of the electromagnetic fields before (${\overrightarrow{E}}_c,{\overrightarrow{H}}_c$) and after (${\overrightarrow{E}}_s,{\overrightarrow{H}}_s$) introducing the sample into the cavity. The shift in resonance frequency can be given as [¹⁵], [¹⁶]

(3) $$\frac{\mathrm{\Delta }\omega }{{\omega }_s}=\frac{{\iiint }_{V_c}[({\mu }_s-{\mu }_c){\overrightarrow{H}}_c\cdot {\overrightarrow{H}}_s-({\epsilon }_s-{\epsilon }_c){\overrightarrow{E}}_c\cdot \overrightarrow{E_s}]dV}{{\iiint }_{V_c}({\epsilon }_c\overrightarrow{E_c}\cdot \overrightarrow{E_s}+{\mu }_c\overrightarrow{H_c}\cdot \overrightarrow{H_s})dV},$$

where V_c is the volume of the cavity, ω_s and ω_c are the complex resonant angular frequencies of the cavity with and without the sample, respectively. The parameters (ɛ_c) and (µ_c) are the permittivity and permeability of the medium in the unpertubed cavity. Whereas, (ɛ_s) and (µ_s) are the electrical permittivity and complex magnetic permeability of the sample.

Although equation (3) is an exact equation, calculating the variation in the resonance frequency is not recommended, since the electric (${\overrightarrow{E}}_s$) and magnetic (${\overrightarrow{H}}_s$) fields distribution after insertion of the sample are unknown. However, approximate measurements can be carried out considering a homogeneous sample with a much smaller volume when compared to the volume of the cavity. This means that the electromagnetic fields undergo small changes and the losses in the cavity wall are the same for the disturbed and undisturbed cavity. In other words, the electromagnetic fields in the empty part of the cavity are negligibly altered by the insertion of the sample. In this way, we can assume that $\overrightarrow{E_c}\approx \overrightarrow{E_s}$ and $\overrightarrow{H_c}\approx \overrightarrow{H_s}$ in the denominator components of equation (3) [¹⁷]. Thus, the components become ${\left|{\overrightarrow{E}}_c\right|}^2$ and ${\left|{\overrightarrow{H}}_c\right|}^2$, respectively. Admitting equality in (4),

(4) $${\epsilon }_0{\iiint }_{V_c}{\left|{\overrightarrow{E}}_c\right|}^{2}dV\approx {\mu }_0{\iiint }_{V_c}{\left|{\overrightarrow{H}}_c\right|}^{2}dV.$$

Assuming that the medium inside the cavity is vacuum and that the samples described in this article are non-magnetic, then ɛ_c = ɛ₀ and µ_c = µ_s = µ₀. In this case, equation (3) can be rewritten as

(5) $$\frac{{\omega }_s-{\omega }_c}{{\omega }_s}=-\left(\frac{{\epsilon }_r-1}{2}\right)\frac{{\iiint }_{V_s}{\overrightarrow{E}}_c\cdot {\overrightarrow{E}}_{s}dV}{{\iiint }_{V_c}{\left|{\overrightarrow{E}}_c\right|}^{2}dV}$$

where (ɛ_r = ɛ^∗/ɛ₀) is the relative complex permittivity of the sample and V_s is the volume of the sample.

Generally the empty cavity and dielectric materials have losses. Therefore the angular frequency (ω) associated with a dissipative system is a complex quantity and can be written as [¹⁰], [¹⁵]

(6) $$\omega ={\omega }_r+j{\omega }_i,$$

It is related to the real resonance frequency and the cavity quality factor Q, defined as

(7) $${\omega }_r=2\pi f,$$

(8) $$Q=\frac{{\omega }_r}{2{\omega }_i}.$$

If we consider only the first order perturbation caused by the sample and assume that ω_rc = ω_rs, ω_i << ω_r, we have

(9) $$\begin{array}{rl}\frac{{\omega }_s-{\omega }_c}{{\omega }_s}=\frac{({\omega }_{rs}-{\omega }_{rc})+j({\omega }_{is}-{\omega }_{ic})}{{\omega }_{rs}(1+j\left(\frac{{\omega }_{is}}{{\omega }_{rs}}\right))}\approx [\left(\frac{f_s-f_c}{f_s}\right)& +j(\frac{1}{2Q_s}-\frac{1}{2Q_c})](1-j\frac{1}{2Q_s})\\ & \approx \left(\frac{f_s-f_c}{f_s}\right)+j(\frac{1}{2Q_s}-\frac{1}{2Q_c}).\end{array}$$

The last assumption made in (9) is that Q_s >> 1 and applying (9) to (5), we can observe that the variations in the resonance frequency ∆f = f_s - f_c and the inverse of the cavity quality factor 1/Q, will be related to the real and imaginary parts of the complex permittivity, respectively. Thus, Equation (5) will be given by [¹⁵], [¹⁸]

(10) $$\left(\frac{f_s-f_c}{f_s}\right)+j(\frac{1}{2Q_s}-\frac{1}{2Q_c})=-\left(\frac{{\epsilon }_r-1}{2}\right)\frac{{\iiint }_{V_s}{\overrightarrow{E}}_c\cdot {\overrightarrow{E}}_{s}dV}{{\iiint }_{V_c}{\left|{\overrightarrow{E}}_c\right|}^{2}dV}.$$

Equation (10) can be broken down into the following two equations

(11) $$2\left(\frac{f_s-f_c}{f_s}\right)=-({\epsilon }_r^{\prime }-1)A,$$

(12) $$\frac{1}{Q_s}-\frac{1}{Q_c}={\epsilon }_r^{\prime \prime }A,$$

where, we can write the complex relative permittivity of the sample as ${\epsilon }_r={\epsilon }_r^{\prime }+j{\epsilon }_r^{\prime \prime }$, and f_s and f_c are the resonance frequencies of the cavity with and without the sample, respectively, Q_s and Q_c are the respective quality factors of the cavity with and without the sample and the coefficient A is given by [¹⁷], [¹⁹]

(13) $$A=\frac{{\iiint }_{V_s}{\overrightarrow{E}}_c\cdot {\overrightarrow{E}}_{s}dV}{{\iiint }_{V_c}{\left|{\overrightarrow{E}}_c\right|}^{2}dV}.$$

Generally, the parameter A is independent of the sample properties and can be assumed as a constant value. However, one can observe in equations (11), (12) and (13), that the disturbed field ($\overrightarrow{E_s}$) is related not only to the real and imaginary part of the permittivity, but also to the shape and size of the sample, which can change from case to case. Therefore, to obtain more accurate results, two parameters ^K′ and K′′, similar to the coefficient A, will be introduced into the cavity perturbation equations (11) and (12), given by [¹⁸], [²⁰]

(14) $${\epsilon }_r^{\prime }=K^{\prime }\frac{V_c}{V_s}\left(\frac{f_c-f_s}{f_s}\right)+1,$$

(15) $${\epsilon }_r^{\prime \prime }=K^{\prime \prime }\frac{V_c}{V_s}(\frac{1}{Q_s}-\frac{1}{Q_c}),$$

where K′ and K′′ are coefficients related to the depolarization factor, which depend on the geometric parameters of the sample, its location inside the resonant cavity and the resonant mode of the cavity. These coefficients are generally obtained through a calibration method using a standard sample of known complex permittivity and similar geometry to the sample to be measured [¹⁸], [²¹].

The values of the cavity quality factors measured without and with sample (Q_c and Q_s) are calculated in terms of the resonance frequency and bandwidth, where the amplitude of the resonance curve is 3 dB lower than the maximum central frequency, according to (16) [¹³]

(16) $$Q_{\nu }=\frac{f_{\nu }}{\mathrm{\Delta }{f}_{(3dB)}}$$

where (ν = s or c). The loss tangent (tanδ) of dielectric materials can be determined by [²²]

(17) $$\tan \delta =\frac{{\epsilon }_r^{\prime \prime }}{{\epsilon }_r^{\prime }}.$$

III. MATERIALS AND METHODS

A. Sample preparation

Cylindrical samples with diameter D_s = 28 mm and height h_s = 12.5 mm were printed with volume fillings 25%, 50%, 75% and 100% for seven different materials (Fig. 1a): ABS, Tritan, PETG, ASA, Nylon, PLA and CR-carbon. This allows the characterization of the electrical permittivity ε_r' and the loss tangent tanδ of the samples with the resonant-cavity method. The schematic representation of the electromagnetic model of the cylindrical cavity, designed in the HFSS software, is shown in Fig. 1b. In addition to the cavity, two SMA connectors, along with two exciters, were added to the structure.

Fig. 1
Three-dimensional representation: (a) Sample geometry; (b) Model of the cylindrical cavity.

B. Experimental setup and measurement technique

The experimental setup consists of a model Creality K1 Max 3D printer (Fig. 2a), a resonant cavity cylindrical geometry, calibration kit and a network analyzer (Agilent E5080B with an operating range between 300 kHz and 40 GHz). The experimental schematic diagram is shown in Fig. 2b. In the present setup, the cavity radius was chosen so that the resonance frequency under unloaded conditions is equal to f_c = 3.5 GHz, which is the test frequency for the development of new technologies for 5G systems [²³].

Fig. 2
Experimental setup: (a) Creality K1 Max 3D Printer; (b) Network analyzer wtih coaxial cable cinnected to cylindrical resonant cavity at 3.5 GHz.

The cavity excitation is achieved through probe coupling, whereby it is possible to observe the connectors and excitation pins (monopoles) attached to the top cavity wall. In this configuration, the TM₀₁₀ mode was excited, although it is a mode with a low quality factor. If an appropriate ratio between the height and radius of the cavity is chosen, this mode resonates in a frequency far away from other modes, hence avoiding interference. This issue is extremely important for measuring the dielectric properties of the analyzed samples.

According to [¹⁴], [²⁴], if the radius-height ratio (2r/h)² is chosen to be greater than 1, the TM₀₁₀ will be the dominant mode. Its electromagnetic field configuration is shown in Fig. 3a (profile view) and Fig. 3b (top view). Therefore, a ratio of 2.5 was chosen, resulting in h = 1.27r. This gives us a height of approximately 41.65 mm, providing good isolation to the closest mode TE₁₁₁.

Fig. 3
Electric field distribution in a cylindrical resonant cavity for TM₀₁₀ mode. (a) Profile view; (b) Top view.

From Equation (2), the radius of the cylindrical cavity referring to the dominant mode TM₀₁₀ does not depend on the height of the cavity, as the field varies only in the direction r, and can be calculated by

(18) $$r=\frac{P_{01}}{2\pi f_c\sqrt{{\mu }_0{\epsilon }_0}}.$$

By taking P₀₁ = 2.4048 [²⁴], which corresponds to the first zero of the Bessel function J₀ (x), and fixing p = 0, it comes out that r = 32.8 mm. Considering these internal dimensions, the commercial electromagnetic software ANSYS HFSS was used, which is based on the finite element method (FEM), to optimize the cavity parameters. The optimized dimensions are presented in Table I.

TABLE I
Physical and numerical parameters of the cylindrical cavity

Parameters	Calculated value (mm)	Simulated value (mm)
r	32.8	32.25
l	20.0	7.56

A very good agreement can be observed between the cavity radius calculated analytically using equation (18) and the radius simulated in the HFSS software. A systematic error can be observed between the measured and simulated results for the parameter l, with a deviation of 62.2%. This occurs due to the excitation technique used to feed the resonant cavity, which is not taken into account in the analytical formulation presented above.

The cylindrical cavity was manufactured entirely from aluminum to prevent radiofrequency waves from escaping from the cavity. In addition, two female-type SMA connectors and two copper filaments were added to the structure for excitation, the latter being estimated to have a length of around λ₀/4 as a first design approach, which corresponds to, approximately, 20 mm, and adjusted to yield excellent power coupling between the ports (Table I). To better fit the sample into the base, an indentation of approximately 30 mm in diameter and 1 mm in depth was milled in the cavity bottom wall [²⁵].

IV. EXPERIMENTAL AND NUMERICAL RESULTS

Experimental and numerical results of the S-parameters for the empty resonant cavity and with samples of various materials for different volume fillings were carried out. The frequency responses for the unloaded (empty) cavity are plotted in Fig. 4. Note that the shapes of the curves in Fig. 4(a) and 4(c) are very similar. However, there is a deviation of approximately -0.56 dB in the magnitude and a frequency shift of 3 MHz verified between experimental and simulated results, which is due to tolerances inherent of the resonant cavity fabrication. These deviations can be compensated by including an additional term as a calibration factor in the simulated curves, as demonstrated in Fig. 4(b) and Fig. 4(d), whereby both experimental and numerical curves fit one on the other.

Fig. 4
Frequency response of the empty cavity: (a) Transmission; (b) Calibrated transmission; (c) Reflection; (d) Calibrated reflection.

Figure 5(a) shows the transmission curves under different conditions, i.e., empty cavity and loaded with samples of different materials with 100% filling. The samples were located along their symmetrical axis, in the position of maximum electric field intensity, as shown in Fig. 3. Thus, one can assume that the samples are placed in an originally uniform field. It is worth mentioning that the ABS and CR-carbon samples present the smallest and largest disturbance inside the cavity, corresponding to the smallest and largest values of permittivity and insertion losses, respectively.

Fig. 5
Cavity transmission at 3.5 GHz. (a) Cavity loaded with samples of different materials with 100% filling; (b) ABS sample; (c) Tritan sample; (d) PETG sample; (e) ASA sample; (f) Nylon sample; (g) PLA sample; (h) CR-carbon sample.

The influence of samples filling on the transmission parameter S₂₁ and the operating frequency f_s was investigated. The Fig. 5 shows the frequency responses of the ABS (Fig. 5(b)), Tritan (Fig. 5(c)), PETG (Fig. 5(d)) ASA (Fig. 5(e)), Nylon (Fig. 5(f)), PLA (Fig. 5(g)) and CR-carbon (Fig. 5(h)) samples with 25%, 50%, 75% and 100% fillings, along with the empty cavity response. It is clear that, increasing the samples filling percentage causes a shift in the resonance frequency to lower values and an increase in insertion losses. These changes in the resonance curves are due to the fact that both the effective permittivity inside the cavity and the microwave energy losses in the samples increase with increasing concentration in each sample [²⁶].

Due to the disturbance of the electromagnetic fields inside the resonant cavity due to the samples and consequent shift of the resonance curves, it is possible to extract information about the electrical permittivity and loss tangent of the materials using the measured S₁₁ and S₂₁ curves.

Several authors present mathematical formulations for calculating the electrical permittivity and loss tangent [¹⁹], [²⁷]. In particular, in this work, the electrical permittivity and loss tangent of the samples were calculated from the curves of the S-parameter measured with the network analyzer, fitted through a parametric study in the ANSYS HFSS software and validated analytically (equations (14) and (17)) . The objective is to evaluate the values of the resulting resonance frequency and estimate the most appropriate values of ε_r′ and tanδ for each sample at each concentration. These parameters can be evaluated by varying ε_r′ and tanδ in the simulation model, so that the simulated curves S₁₁ and S₂₁ fit the measured curves.

Relations (14) and (15) were obtained under some simplifying assumptions. To test their validity, measurements were made on samples of different materials and fillings at 3.5 GHz. The quality factors for the empty cavity (Q_c = 60) and loaded Q_s were calculated from (16), and tabulated in Table II, along with the resonance frequency and insertion losses for all samples at each concentration.

TABLE II
Parameters obtained for different samples at various concentrations

Sample	Filling (%)	fs (GHz)	S21 (dB)	Qs
	25	3.37	-0.95	58.6
ABS	50	3.33	-1.15	57.0
	75	3.30	-1.26	56.4
	100	3.24	-1.54	54.4
	25	3.38	-0.95	58.4
TRITAN	50	3.33	-1.14	57.0
	75	3.28	-1.35	55.8
	100	3.22	-1.55	54.2
	25	3.36	-LOO	58.0
PETG	50	3.32	-1.34	55.6
	75	3.28	-1.45	55.2
	100	3.22	-1.60	54.0
	25	3.36	-1.30	56.0
ASA	50	3.33	-1.55	54.0
	75	3.29	-1.84	52.2
	100	3.23	-2.22	50.0
	25	3.36	-1.93	52.0
NYLON	50	3.31	-2.30	49.4
	75	3.26	-2.75	47.6
	100	3.20	-3.00	44.8
	25	3.38	-1.13	57.5
PLA	50	3.32	-1.48	54.8
	75	3.26	-1.69	53.2
	100	3.20	-2.06	50.4
	25	3.34	-1.55	54.0
CR-CARBON	50	3.26	-2.15	50.6
	75	3.17	-2.70	46.6
	100	3.12	-3.40	42.0

From the variations in the resonance frequency ∆f and the inverse of the quality factor ∆(1/Q) caused by the insertion of the samples into the cavity, it is possible to calculate the coefficients K′ and K′′ of equations (14) and (15) by a calibration procedure. For this, we will use a Polytetrafluoroethylene (PTFE) standard sample of the same volume, the same geometry as the analyzed samples and known dielectric properties (ε_r′ and tanδ = 0.0003) [²⁸] - [³⁰]. By doing so, K = 1.1 and K = 0.55.

Figure 6(a) shows the transmission characteristics for the empty and disturbed cavity after insertion of the PLA sample with 100% filling. As a consequence, the transmission curve is shifted to the left, increasing the insertion losses. The linear fit of the experimental results between the displacements in the cavity resonance frequency ∆f, and the inverse of the cavity quality factor ∆(1/Q) for the PLA sample at different concentrations are shown in Fig. 6(b). Where they will be needed to calculate ε_r′ and ε_r′′ of the PLA samples through Equations (14) and (15).

Fig. 6
(a) Cavity perturbation due to the insertion of the 100% PLA sample; (b) Linear fit of the experimental results, obtained by the insertion of the PLA sample; (c) Measured and simulated frequency response (100% PLA sample); (d) Dielectric properties of the PLA samples with different filling volumes.

Figure 6(c) (PLA sample), Fig. 7a (ABS sample), Fig. 7b (Tritan sample), Fig. 7c (PETG sample), Fig. 7d (ASA sample), Fig. 7e (Nylon sample) and Fig. 7f (CR-carbon sample), with 100% fill, show the frequency characteristics calculated by the ANSYS HFSS software and fitted to the S-parameters measured by the network analyzer in order to evaluate their respective ε_r′ and tanδ. These parameters were fitted and calculated with Eqs. (14) and (17).

Fig. 7
Measured and simulated frequency response for the 100% samples: (a) ABS; (b) Tritan; (c) PETG; (d) ASA; (e) Nylon; (f) CR-carbon.

The calculated and simulated values of ε_r′ and tanδ for PLA, ABS, Tritan, PETG, ASA, Nylon and CR-carbon samples, at different concentrations, are presented in Table III and plotted in Fig. 6(d), Fig. 8a, Fig. 8b, Fig. 8c, Fig. 8d, Fig. 8e and Fig. 8f, in this order. One can observe a nearly linear behavior, allowing a fast and accurate estimation of the electrical permittivity and loss tangent for structures of different filling percentages at 3.5 GHz, thus representing a very useful and simple means of choosing the parameters (ε_r′ and tanδ) when using a given material for practical purposes. The small variations observed between the estimated and calculated values for the different filling percentages in each type of material (as per Table III) may be related to printing factors of the samples, both in their thickness and in the filling percentage, causing a small error in the dimensions of the samples and in the filling itself. However, the accuracy of the results obtained can be considered very good, if the tolerance limits specified by the 3D printer manufacturer are considered.

TABLE III
Dielectric properties obtained for different samples at various concentrations

Sample	Filling (%)	εr′		tanδ
		Eq. (14)	HFSS	Eq. (17)	HFSS
	25	1.65	1.62	0.0021	0.0023
ABS	5075	1.882.14	1.872.13	0.00410.0049	0.00400.0049
	100	2.55	2.59	0.0067	0.0068
	25	1.60	1.56	0.0025	0.0026
TRITAN	5075	1.892.23	1.882.23	0.00420.0055	0.00420.0055
	100	2.69	2.69	0.0067	0.0067
	25	1.71	1.69	0.0031	0.0030
PETG	5075	1.942.28	1.952.27	0.00620.0065	0.00610.0065
	100	2.69	2.73	0.0070	0.0069
	25	1.71	1.69	0.0064	0.0066
ASA	5075	1.912.22	1.902.21	0.00920.0130	0.00910.0110
	100	2.69	2.73	0.0013	0.0013
	25	1.71	1.70	0.0140	0.0150
NYLON	5075	2.072.41	2.072.40	0.01600.0180	0.01600.0180
	100	2.82	2.90	0.0200	0.0200
	25	1.60	1.58	0.0042	0.0042
PLA	5075	1.922.43	1.932.44	0.00750.0088	0.00750.0088
	100	2.89	2.89	0.0110	0.0110
	25	1.83	1.84	0.0095	0.0095
CR-CARBON	5075	2.433.17	2.462.21	0.01280.0015	0.01250.0015
	100	3.54	3.96	0.0200	0.0210

Fig. 8
Dielectric properties of samples with different filling volumes (ɛ_r and tanδ): (a) ABS; (b) Tritan; (c) PETG; (d) ASA; (e) Nylon; (f) CR-carbon.

A. Comparison of the obtained with those reported in the literature

Table IV presents a comparison between the dielectric properties of the materials proposed in this article and what we find in the literature. The relative permittivity and loss tangent values of materials analyzed around 3.5 GHz can vary depending on material purity, 3D printing parameters (such as infill density/porosity), and manufacturer, making them highly sensitive to variations in thickness, surface flatness, and internal structure. The literature reports a range of ε_r′ and tanδ values for pure materials or filaments, generally around (2.2 to 3.1) and (0.005 to 0.019) for ABS [³¹], [³²]; (2.5 to 3.5) and (0.005 to 0.02) for tritan; (2.7 to 2.8) and (0.001 to 0.043) for PETG; (2.5 to 4.5) and (0.004 to 0.02) for ASA [³³]; (2.8 to 4.2) and (0.005 to 0.03) for Nylon [³⁴], [³⁵]; (2.2 to 3.5) and (0.005 to 0.02) for PLA [³⁴], [³⁶] and values greater than 3 and 0.005 for CR-carbon [³⁷], in that order. Our results show excellent agreement and are consistent with the ranges of values found in the literature.

TABLE IV
Comparison of dielectric properties for samples with 100% filling, around 3.5 GHz.

Material	reference values		ɛr Eq. (14)	HFSS	tan δ
		tan δ			Eq. (17)	HFSS
ABS	2.2 to 3.1	0.005 to 0.019	2.55	2.59	0.0067	0.0068
TRITAN	2.5 to 3.5	0.005 to 0.020	2.69	2.69	0.0067	0.0067
PETG	2.7 to 2.8	0.005 to 0.020	2.69	2.73	0.0070	0.0069
ASA	2.5 to 4.5	0.004 to 0.020	2.69	2.73	0.0013	0.0013
NYLON	2.8 to 4.2	0.005 to 0.030	2.82	2.90	0.0200	0.0200
PLA	2.2 to 3.5	0.005 to 0.020	2.89	2.89	0.0110	0.0110
CR-CARBON	> 3	> 0.005	3.54	3.96	0.0200	0.0210

B. Manufacturing process and discussions

The fabrication of devices and applications in 5G technologies using 3D printing filaments is a process that involves the rapid and low-cost prototyping of complex dielectric components for radio frequency (RF) systems. These components, frequently used as structural elements in antenna supports, parabolic feed horns, dielectric lens antennas, waveguide bodies and enclosures for electronic components, position radiating elements with high precision and are located close to the area where the signal passes during transmission or reception (radiating aperture) [³⁸]. In these cases, the dielectric material ceases to be a passive support and becomes an active part of the electromagnetic system, significantly influencing system performance.

The choice of filament depends on the requirements of the 5G application. An analysis for Radio Frequency applications, including the use of filaments such as PLA, ABS, ASA, and PETG, in the band (1 MHz - 100 MHz) and at higher frequencies up to 40 GHz is described in [³²] - [⁴⁰]. It can be seen that PLA, in general, proved to be more suitable for RF applications. Its ease of printing and the stability of its dielectric properties guarantee good dimensional accuracy, which is fundamental at higher frequencies. However, as PLA is a biodegradable polymer derived from corn starch or sugarcane, it is highly susceptible to ultraviolet (UV) radiation, and is not recommended for permanent outdoor installations without significant protective coating or enclosure.

ASA is often described as “ABS with integrated UV resistance”, representing excellent promise for outdoor RF applications. Both ASA and ABS are difficult to print on standard open-frame 3D printers, requiring an enclosed printer and careful temperature management to avoid warping, which can compromise the dimensional accuracy critical for RF performance [⁴¹]. Although ABS has better thermal resistance than PLA, prolonged exposure to sunlight remains a problem, making it less recommended for outdoor use. In contrast, ASA has exceptional UV resistance, does not degrade significantly when exposed to sunlight, and also possesses good thermal resistance (comparable to ABS) and excellent weather resistance, making it ideal for permanent outdoor antenna installations. ASA is the recommended choice when compared to the low outdoor durability of PLA and the high losses and sensitivity to field disturbance presented by Tritan, PETG, Nylon, and CR-carbon, which are mostly identified as less suitable for RF applications.

V. APPLICATION

In this paper, an ABS filament characterized using the cavity perturbation technique at 3.5 GHz is used to design a square dielectric resonator antenna (DRA) with 100% infill. This type of antenna is widely reported in the literature; therefore, this topology is employed solely to validate the proposed design methodology and the filament characterization process.

The HFSS model of the proposed antenna is shown in Fig. 9a (top view) and Fig. 9b (bottom view), and the dimensions used are listed in Table V. The antenna is fixed using four ABS screws on an FR4 laminate with the following parameters: thickness of 1.524 mm, relative permittivity ɛ_r = 4.4, and loss tangent tanδ = 0.02.

TABLE V
Dimensions used for the DRA design.

			Variables
aDRA	hDRA	aGP	Omsl	amsl	Oslot	Wslot	αslot
(mm)	(mm)	(mm)	(mm)	(mm)	(mm)	(mm)	(deg)
37.17	17.53	128.6	15.14	2.88	26.18	4.76	84

Fig. 9
HFSS model of the squared DRA. (a) Top view; (b) Bottom view.

The antenna was fabricated and the prototype is shown in Fig. 10a and the radiation pattern performance was measured using a spherical near-field scanner (NFS), according to the setup shown in Fig. 10(b). The S-parameter was measured and the obtained result is compared with the electromagnetic simulation performed using Ansys HFSS in Fig. 11. The red and blue solid curves represent the simulated and measured results, respectively. Excellent agreement between the simulated and measured results is observed over the frequency range allocated for 5G technology in Brazil (3.3-3.7 GHz), where the measured reflection coefficient is lower than -15 dB.

Fig. 10
(a) DRA prototyped using ABS material. (b) DRA antenna installed in a spherical near-field scanner.

Fig. 11
Measured and simulated S-parameters of the dielectric resonator antenna.

The measured results are presented in Fig. 12a (E-plane) and Fig. 12b (H-plane), where excellent agreement between the simulated and measured results is observed.

Fig. 12
Simulated and measured radiation pattern: (a) E-plane; (b) H-plane. Solid and dashed lines stand for main and cross-polarizations, respectively.

VI. CONCLUSION

In this paper, the cavity perturbation technique was discussed and used to characterize the dielectric properties of 12.5 mm thick cylindrical samples produced from 3D printing filaments with volume fillings of 25%, 50%, 75% and 100%. The 5G test band at 3.5 GHz was considered. The S-parameters were obtained experimentally using a network analyzer and numerically adjusted in the Ansys HFSS electromagnetic simulator, thus allowing to evaluate and analytically validate the values of the relative electrical permittivity and the loss tangent of the analyzed samples. Through the discussion of the expressions for (ε_r′) and (tanδ) and analysis of the obtained results, it was observed that the dielectric properties of materials can be measured from the existing cavity with good accuracy. The analyses revealed that the cavity resonance frequency is affected by the sample insertion, which not only shifts the central operating frequency to lower values, but also affects the electrical permittivity and loss tangent of the materials. These parameters increase with the sample filling percentage of the materials.

The dielectric properties of the samples analyzed in this work can be dynamically controlled according to the appropriate choice of the filling concentration. This feature provides versatility for the design of different types of devices, such as reusable multifunctional diodes, low-cost electronic devices with little environmental impact, prototyping of radio frequency (RF) devices and antenna design.

ACKNOWLEDGMENT

The authors would like to thank Rural Federal University of Amazonia (UFRA) for granting Prof. Dr. Wagner Castro for post-doctoral internship and to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for the financial support through a post-doctoral research. This work was funded by Research Support Foundation of Rio Grande do Sul - FAPERGS under grant TO 24/25510001280-0. The authors acknowledge the support of the Funding Agency for Studies and Projects (FINEP) under grant 01.25.0083.00, and the National Institute of Science and Technology (INCTSignals), sponsored by Brazilian National Council for Scientific and Technological Development (CNPq) under grant 406517/2022-3.

DATA AVAILABILITY

Research data is available upon request.

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• Editor:
  Carlos E. Capovilla

• Associate Editor:
  Rafael A. Penchel

Publication Dates

• Publication in this collection
  10 July 2026
• Date of issue
  2026

History

• Received
  18 July 2025
• Reviewed
  21 Oct 2025
• Accepted
  20 Feb 2026