Characterization and comparison of 3D printed materials based on acrylonitrile butadiene styrene (ABS) filament for antenna design are presented in this paper. The standard ring resonator method has been used to obtain the dielectric properties of the material, where a ring is excited from two ports and its resonance characteristics are used to calculate dielectric characteristics. The effect of different infill densities of the printed substrate on dielectric constant and loss tangent has been thoroughly analyzed. The results obtained are helpful for the antenna design applications for desired frequency of 2.45 GHz, using variation in the dielectric constant and dielectric loss.
2. Characterization of dielectric material
To calculate the dielectric properties of the 3D printed substrate at the desired resonance frequency of
2.45GHz, a standard ring resonator approach has been used[5][6]. Figure 1 displays dimensional details
of the structure:
Periodic frequency resonances are generated by insertion loss (S21) produced by the ring resonator. Using
this approach, with the given radius of 12.6mm ring resonator, dielectric constant (єr) can be obtained
from the location of resonant peaks of the ring resonator. Quality factor (Q) of resonant frequency peaks
is used to obtain the value of dielectric loss (tanδ). Figure 3 shows the plot of S21 as a function of
frequency for both the substrates. Figure 3 values are obtained using a vector network analyzer.
(a) The measured S21 for 40% infill density and rectilinear infill pattern on vector network analyzer
(VNA).
dielectric constant by [7] is calculated from equation (
, Weff is the effective strip width for nonzero strip thickness,
W is width of the copper conductor, t is copper trace thickness, h is the thickness of ABS substrate. Using
(
To calculate the dielectric loss (tanδ) following equation (4) is used: = + 1.25 1 + ln 2ℎ = ( −1) , 8.686 ,
−1 1−10 20
− −3
=
ℎ 2 2
= =
1 − 1 + 4 ℎ 1 − where BW-3dB is 3-dB bandwidth of the resonator. The total attenuation constant ( ) is found using where is wavelength of the resonant signal in the free space, calculate following series of calculations are performed from equations (5) to (12). Initially, in microstrip ring resonator the Qo (unloaded)is obtained by [7], given in equation (5) = dielectric attenuation factor. To radiation attenuation factor ( ), given in equation (8): Where is the guided wavelength, sum of conductor factor ( ),dielectric attenuation factor ( ) and 1) Conductor Attenuation Factor: Thickness of the strip is taken into account, conduction factor of a = + + microstripring as in [8], given in equation (9): ≤ 1 2 − 1 1 2 ℎ 1 − − ℎ
, 1 + ℎ
ℎ +
ℎ − of the copper trace.
Rs1is the surface-roughness resistance of the microstrip. Rs is the surface resistance of the microstrip. Zo is the characteristics impedance of the microstrip. δs is the skin depth of copper. µ = 4 π x 10-7 H/m, σ = bulk conductivity of the metal, fo is the resonant frequency. Δ is the mean surface roughness 2) Radiation Attenuation Factor:In this paper, radiation from the other parts of the structure is neglected while considering only radiation from the ring resonator. From Van der Pauw’s work [9], the radiation quality factor Qr of a ring resonator can be calculated using the given equation (10): Where in this substrate, is permittivity and is permeability. Zo is characteristic impedance. vg is propagation velocity resonant signal. W is operating frequency. After restoring dimensions of dimensionless expression i.e., W, , , Zo and vg, following equation of Qr is derived: The radiation attenuation constant of the ring is given as equation (12) ≈
4 2 2 2 1−34
8 where is the guided wavelength.
Finally, using equation (8) putting values of , , and which is then used to determine loss tangent of ABS substrate using equation (4). , the dielectric attenuation factor is obtained The calculated values of єr&tanδ at 2.58 GHz and 2.59 GHz for substrates with 40% and 100% infill density respectively are shown in table 1, performing all the above calculations.
Calculated values of the dielectric properties using the ring-resonator technique From Table 1, a difference of 0.03 can be observed in the dielectric constant. It was observed that the difference in dielectric constant is low due to more substrate thickness. A small dielectric loss difference of 0.0002 can be seen in Table 1 3. Conclusion This paper talks about the characterization and comparison of results of 3D printed substrates for antenna design applications. The method of ring resonator is being used to calculate the dielectric properties of the substrate. For this analysis, a substrate of thickness 1mm was taken with the rectilinear infill pattern. Hence, it is observed that with the variation in substrate thickness, infill density, and infill pattern the dielectric properties of the substrate can be changed. The resulting values of dielectric constant and dielectric loss can be seen in Table 1. Figure 3 (a) & (b) shows the resonant frequency peaks for 40% infill density and 100% infill density respectively. This method is used on the highest and lowest viable infill densities to measure their dielectric properties and comparing them for the best one so that they can be used for microwave and RF applications. 4. References
O. A. Mohamed, Analytical modeling and experimental investigation of product quality and mechanical properties in FDM additive manufacturing. 2017.