=Paper=
{{Paper
|id=Vol-3058/paper66
|storemode=property
|title=Characterization And Comparison Of 3D Printed Substrate With Varying Infill Density For Antenna Design Applications
|pdfUrl=https://ceur-ws.org/Vol-3058/Paper-097.pdf
|volume=Vol-3058
|authors=Kush Singla,Balwinder Singh Dhaliwal,Garima Saini
}}
==Characterization And Comparison Of 3D Printed Substrate With Varying Infill Density For Antenna Design Applications==
https://ceur-ws.org/Vol-3058/Paper-097.pdf
Characterization and Comparison of 3D Printed Substrate with
Varying Infill Density for Antenna Design Applications
Kush Singla1, Balwinder S. Dhaliwal2and Garima Saini3
1,2,3
National Institute of Technical Teachers Training & Research, Chandigarh,160109, India
Abstract:
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.
Keywords 1
3D-printed antenna, acrylonitrile butadiene styrene (ABS), dielectric properties, infill density,
infill pattern, loss tangent, additive manufacturing.
1. Introduction
To get smart engineering solutions 3D printing is used for rapid prototyping for major industrial
applications. The low cost and high throughput sector with a less resource requirement for massive
production and customization are evolving due to 3D printing. Fast prototyping, less wastage of material,
design flexibility and low-cost development are some of the advantages offered by 3D printing in the field
of RF applications. Fused deposition modeling (FDM) is the most used approach among all the different
3D printing techniques. It has also been used for printing polymeric materials for RF and microwave
applications. FDM is an extrusion-based method in which the object is formed layer by layer, a plastic
filament is melted and placed on the 3D printer platform. During extrusion, a 2D layer of material is
placed accurately by the extruder[1][2]. Hence, a 3D structure is formed by overlapping 2D layers of
material. Commercial printers deposit layers with height ranging from 50 µm to 300 µm and the
technology is easy to use and cost-effective.
FDM fabrication process using commercial thermoplastic called Acrylonitrile Butadiene Styrene (ABS) is
presented in this paper. Infill density is one of the important parameters in 3D printing [3]. In this paper,
two infill densities have been considered i.e. 40% and 100%. For this paper, the lowest and the highest
possible infill density is considered, and their results are compared. The idea behind choosing only these
two infill densities was that infill density below 40% leads to a lot of air pockets in the design which is
not good for RF characteristics. Rectilinear infill pattern is chosen for this paper [4] tells it’s the best
pattern for RF characterization. Samples with varying infill densities are printed for evaluating the
dielectric properties of the printed substrates. High-frequency structure simulator (HFSS) software has
been used for designing the ring resonator structure and to obtain the dielectric properties of the material.
Moreover, a comparison of the antenna substrate with different infill densities is also presented.
International Conference on Emerging Technologies: AI, IoT, and CPS for Science & Technology Applications, September 06–07, 2021,
NITTTR Chandigarh, India
EMAIL: ksingla02@gmail.com; bsdhaliwal@ymail.com; garima@nitttrchd.ac.in
ORCID: 0000-0001-6558-9192; 0000-0001-5092-017x; 0000-0001-6525-5192
©2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
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:
Figure 1: Dimensions of the microstrip ring resonator.
Figure 1 displays structure of the ring resonator, dimensions of microstrip feeding lines, the ring gap, and
the average radius, rm.
Figure 2 shows the fabricated ring resonator structures having SMA connectors soldered at the edges of
the feed lines. Figure 2(a) shows the 40 % infill density & rectilinear infill pattern substrate and Figure
2(b) shows the 100 % infill density & rectilinear infill pattern substrate.
(a) (b)
Figure 2: Ring resonator structures on substrates with (a) 40% Infill density (b) 100% Infill density.
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).
(b) The measured S21 for 100% infill density and rectilinear infill pattern on vector network analyzer
(VNA).
Figure 3: Shows the measured values of S21 of (a) substrate with 40% infill density& (b) substrate with
100% infill density.
2.1.1 Dielectric Constant
Calculating the dielectric constant requires a series of equations from (1) to (3), first, the effective
dielectric constant by [7] is calculated from equation (1)
𝑛𝑛𝑛𝑛 2
𝜀𝜀𝑟𝑟,𝑒𝑒𝑒𝑒𝑒𝑒 = � � (1)
2𝜋𝜋𝑟𝑟𝑚𝑚 𝑓𝑓𝑜𝑜
Where fo is the nth resonant frequency of the ring, єr,effis an effective єr,average radius of rm, c speed of
light in vacuum. After equation (1), equation (2) is used to calculate the dielectric constant of ABS:
2𝜀𝜀 𝑟𝑟,𝑒𝑒𝑒𝑒𝑒𝑒 +𝑀𝑀−1
𝜀𝜀𝑟𝑟 = (2)
𝑀𝑀+1
−1
12ℎ 2
where𝑀𝑀 = �1 + � , Weff is the effective strip width for nonzero strip thickness,
𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒
1.25𝑡𝑡 2ℎ
𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 = 𝑊𝑊 + � � �1 + ln � �� (3)
𝜋𝜋 𝑡𝑡
W is width of the copper conductor, t is copper trace thickness, h is the thickness of ABS substrate. Using
(1), (2), and (3), the calculation of values of dielectric constant at resonant peaks is done
2.1.2 Dielectric Loss
To calculate the dielectric loss (tanδ) following equation (4) is used:
𝛼𝛼 𝑑𝑑 𝜆𝜆 𝑜𝑜 (𝜀𝜀 𝑟𝑟 −1)�𝜀𝜀 𝑟𝑟,𝑒𝑒𝑒𝑒𝑒𝑒
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = (4)
8.686𝜋𝜋 𝜀𝜀 𝑟𝑟 �𝜀𝜀 𝑟𝑟,𝑒𝑒𝑒𝑒𝑒𝑒 −1�
where 𝜆𝜆𝑜𝑜 is wavelength of the resonant signal in the free space, 𝛼𝛼𝑑𝑑 = dielectric attenuation factor. To
calculate 𝛼𝛼𝑑𝑑 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)
𝑄𝑄𝐿𝐿
𝑄𝑄𝑜𝑜 = −𝐿𝐿 𝐴𝐴 (5)
1−10 20
where LA is insertion loss of resonant peak in dB. The QL(loaded) is given in equation (6):
𝑓𝑓𝑜𝑜
𝑄𝑄𝐿𝐿 = (6)
𝐵𝐵𝐵𝐵 −3𝑑𝑑𝑑𝑑
where BW-3dB is 3-dB bandwidth of the resonator. The total attenuation constant (𝛼𝛼𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ) is found using
equation (7):
𝜋𝜋 𝑁𝑁𝑝𝑝
𝛼𝛼𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = � � (7)
𝑄𝑄𝑜𝑜 𝜆𝜆 𝑔𝑔 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ℎ
Where 𝜆𝜆𝑔𝑔 is the guided wavelength, sum of conductor factor (𝛼𝛼𝑐𝑐 ),dielectric attenuation factor (𝛼𝛼𝑑𝑑 ) and
radiation attenuation factor (𝛼𝛼𝑟𝑟 ), given in equation (8):
𝛼𝛼𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝛼𝛼𝑐𝑐 + 𝛼𝛼𝑑𝑑 + 𝛼𝛼𝑟𝑟 (8)
1) Conductor Attenuation Factor: Thickness of the strip is taken into account, conduction factor of a
microstripring as in [8], given in equation (9):
𝑊𝑊 1
≤
ℎ 2𝜋𝜋
𝑡𝑡
1 𝑅𝑅𝑠𝑠1 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 2 ℎ ℎ 4𝜋𝜋𝜋𝜋 1 −
ℎ 𝑁𝑁𝑝𝑝
𝛼𝛼𝑐𝑐 (𝑓𝑓𝑜𝑜 ) = �1 − � � � �1 + + �ln � + 1� − 𝑡𝑡 �� � �
2𝜋𝜋 𝑍𝑍𝑜𝑜 ℎ 4ℎ 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝜋𝜋𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝑡𝑡 1 + 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙ℎ
4𝜋𝜋𝜋𝜋
1 𝑊𝑊
< ≤2
2𝜋𝜋 ℎ
𝑡𝑡
1 𝑅𝑅𝑠𝑠1 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 2 ℎ ℎ 2ℎ 1 −
ℎ 𝑁𝑁𝑝𝑝
𝛼𝛼𝑐𝑐 (𝑓𝑓𝑜𝑜 ) = �1 − � � � �1 + + �ln � + 1� − 𝑡𝑡 �� � �
2𝜋𝜋 𝑍𝑍𝑜𝑜 ℎ 4ℎ 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝜋𝜋𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝑡𝑡 1 + 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙ℎ
4ℎ
𝑊𝑊
>2
ℎ
𝑊𝑊 𝑒𝑒𝑒𝑒𝑒𝑒
𝑅𝑅𝑠𝑠1 1 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 ℎ ℎ 2ℎ
𝛼𝛼𝑐𝑐 (𝑓𝑓𝑜𝑜 ) = 2 � + 𝑊𝑊 𝑒𝑒𝑒𝑒𝑒𝑒𝜋𝜋 ℎ � �1 + + �ln � + 1� −
𝑍𝑍𝑜𝑜 ℎ 𝑊𝑊 𝑒𝑒𝑒𝑒𝑒𝑒 2 𝑊𝑊 𝑒𝑒𝑒𝑒𝑒𝑒 ℎ +0.94 𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝜋𝜋𝑊𝑊𝑒𝑒𝑒𝑒𝑒𝑒 𝑡𝑡
� + ln �2𝜋𝜋𝜋𝜋 � +0.94��� 2ℎ
ℎ 𝜋𝜋 2ℎ
𝑡𝑡
1− 𝑁𝑁𝑝𝑝
ℎ
𝑡𝑡 �� � � (9)
1+ 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ℎ
2ℎ
Where,
2 Δ 2
𝑅𝑅𝑠𝑠1 = 𝑅𝑅𝑠𝑠 �1 + tan−1 �1.4 � � ��,
𝜋𝜋 𝛿𝛿 𝑠𝑠
𝜋𝜋𝜋𝜋 𝑓𝑓𝑜𝑜
𝑅𝑅𝑠𝑠 = � ,
𝜎𝜎
1
𝛿𝛿𝑠𝑠 = �
𝜋𝜋𝜋𝜋𝜋𝜋𝑓𝑓𝑜𝑜
R s1 is 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
of the copper trace.
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):
4𝑍𝑍
𝑄𝑄𝑟𝑟 ≈ 2 2 2 4𝑜𝑜 8 2 2 (10)
𝑤𝑤 𝜇𝜇 𝑣𝑣𝑔𝑔 �1− 𝜀𝜀𝜀𝜀 + 𝜀𝜀 𝜇𝜇 �
3 15
Where in this substrate,𝜀𝜀is permittivity and 𝜇𝜇is permeability. Zo is characteristic impedance. vg is
propagation velocity resonant signal. W is operating frequency. After restoring dimensions of
dimensionless expression i.e., W, 𝜀𝜀, 𝜇𝜇, Zo and vg, following equation of Qr is derived:
𝜀𝜀 𝑟𝑟,𝑒𝑒𝑒𝑒𝑒𝑒 𝑍𝑍𝑜𝑜
𝑄𝑄𝑟𝑟 ≈ ℎ 2 4 8
(11)
120𝜋𝜋 3 � � �1 − 𝜀𝜀 𝑟𝑟 + 𝜀𝜀 2�
𝜆𝜆 𝑜𝑜 3 15 𝑟𝑟
The radiation attenuation constant of the ring is given as equation (12)
𝜋𝜋 𝑁𝑁𝑝𝑝
𝛼𝛼𝑟𝑟 = � � (12)
𝑄𝑄𝑟𝑟 𝜆𝜆 𝑔𝑔 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ℎ
where𝜆𝜆𝑔𝑔 is the guided wavelength.
Finally, using equation (8) putting values of 𝛼𝛼𝑟𝑟 ,𝛼𝛼𝑐𝑐 , and 𝛼𝛼𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 , the dielectric attenuation factor is obtained
which is then used to determine loss tangent of ABS substrate using equation (4).
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.
Table 1
Calculated values of the dielectric properties using the ring-resonator technique
Mode Infill density Resonant Frequency fo Insertion Loss |S21| Ɛr tanδ
n=1 40% 2.58 GHz 33.598 dB 2.62 0.0044
n=1 100% 2.59 GHz 27.567 dB 2.59 0.0042
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
[1] O. A. Mohamed, Analytical modeling and experimental investigation of product quality and
mechanical properties in FDM additive manufacturing. 2017.
[2] A. Pizzagalli, T. Buisson, and R. Beica, “3D technology applications market trends & key
challenges,” in ASMC (Advanced Semiconductor Manufacturing Conference) Proceedings, 2014,
pp. 78–81, doi: 10.1109/ASMC.2014.6846981.
[3] B. T. Malik, V. Doychinov, S. A. R. Zaidi, I. D. Robertson, and N. Somjit, “Antenna Gain
Enhancement by Using Low-Infill 3D-Printed Dielectric Lens Antennas,” IEEE Access, vol. 7, pp.
102467–102476, 2019, doi: 10.1109/ACCESS.2019.2931772.
[4] J. Huang, S. J. Chen, Z. Xue, W. Withayachumnankul, and C. Fumeaux, “Impact of Infill Pattern
on 3D Printed Dielectric Resonator Antennas,” in Proceedings of the 2018 IEEE 7th Asia-Pacific
Conference on Antennas and Propagation, APCAP 2018, Nov. 2018, pp. 233–235, doi:
10.1109/APCAP.2018.8538296.
[5] A. Rida, L. Yang, R. Vyas, and M. M. Tentzeris, Conductive inkjet-printed antennas on flexible
low-cost paper-based substrates for RFID and WSN applications, vol. 51, no. 3. 2009, pp. 13–23.
[6] L. Yang, A. Rida, R. Vyas, and M. M. Tentzeris, RFID tag and RF structures on a paper substrate
using inkjet-printing technology, vol. 55, no. 12. 2007, pp. 2894–2901.
[7] K. Chang, Microwave Ring Circuits and Antenna. New York, Wiley, 1994.
[8] R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Losses is microstrip,” IEEE Trans. Microwave
Theory Tech., vol. MTT-16, pp. 342-350, June1968.
[9] L. J. van der Pauw, “The radiation of electromagnetic power by microstrip configurations,”
IEEE Trans. Microwave Theory Tech., vol. MIT-25, pp. 719-725, June 1977.