# Impact of Dielectric Constant on Embedded Antenna Efficiency

Authors: Van Thuan Nguyen; Chang Won Jung
Journal: International Journal of Antennas and Propagation
 (2014)

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## Abstract

The impact of dielectric constant on radiation efficiency of embedded antenna located inside human body or another liquid environment is investigated both analytically and numerically. Our research is analysed and simulated at 403 MHz in the MedRadio band (401–406 MHz) and within a block of 2/3 human muscle phantom. Good agreement is achieved between analysis and simulation results. This work provides a guidance in selecting insulator for embedded antennas.


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## Body

## 1. Introduction

An antenna working in a dissipative medium such as human body or other liquid environments needs to be insulated to avoid short circuit, oxidation, and corrosion caused by surrounding medium, which lead to the use of a dielectric medium that encloses the antenna. However, the question is what the rules to choose dielectric constant value for this insulator are. Previous studies have utilized different relative permittivity values for implanted antennas, for instance,εr=10.2 [1, 2], εr=10 [3], and εr=30 [4]. A high dielectric constant has an advantage of reducing the size of embedded antenna, but does it impact on antenna radiation efficiency? Briefly, we are motivated to answer these questions.Antennas employed in implantable devices should be compact, lightweight, small in size, and high in radiation efficiency. While a small size permits these devices to be inserted inside the human body, high radiation efficiency lengthens their operating time. Therefore, both size and radiation efficiency are important factors for implanted antenna. Nevertheless, in other embedded devices such as underwater applications, space limitation for antenna may not be a crucial factor; then antenna sizes can be large to have a high efficiency.The goal of this study is to specify a dielectric constant value of insulating materials in order to maximize the radiation efficiency of embedded antennas. Our approach makes use of a foundation presented in [5] of Tai and Collin. In their inspiring work, the authors analyzed theoretically power transmission coefficient of a Hertzian dipole immersed in a dielectric medium surrounded by a dissipative medium. In this paper, the foundation is developed in the following ways:(i)
applying the theory of a Hertzian dipole in a general dissipative medium for a block of 2/3 muscle model phantom having similar characteristics to human body (this content is shown in Section2);(ii)
using a real loop antenna in HFSS simulation to confirm the theory above since the Hertzian dipole is an unrealistic antenna (this part is presented in Section3).Throughout this work, the main contributions are as follows:(i)
this work proves that, for implantable devices, a vacuum insulator can maximize the antenna radiation efficiency;(ii)
for other applications (e.g., underwater applications), the antenna radiation efficiency becomes very high at some certain dielectric constant values (so-called resonant points in antenna radiation efficiency). Surprisingly, these have not been done before.This work is performed at 403 MHz in the band of Medical Device Radio Communications Service (MedRadio, 401–406 MHz) as required by the Federal Communication Commission (FCC). This is the operating frequency band of pacemaker. Also, the proposed method presented in this paper can be applied for other frequency bands. Limitation and some related works are going to be discussed at the end of this paper.


## 2. Theory of a Hertzian Dipole in a Dissipative Medium

Here,t Hertzian dipole with a dipole moment “p” is inserted in a dissipative medium of infinite extent and is insulated by a dielectric sphere, radius of R1 as shown in Figure 1.Figure 1
An insulated dipole in a lossy medium.In Figure1, a block of 2/3 human muscle phantom is selected to model the biological media of the human body. Therefore, the parameters of this medium (medium 2) are absolute permittivity ε2=εr2ε0=42.807ε0, absolute permeability μ2=μ0, and conductivity σ2=0.6463 S/m [2]. The parameters of the insulating media (medium 1) are ε1=εr1ε0, μ1=μ0, and  tanδ1=0.0023. The goal here is to specify the value εr1 that produces the highest radiation efficiency of the dipole. According to [5], the authors used method of the Hertzian potential function П to calculate E and H field. The radiated power obtained at the surface of insulating sphere can be computed through Poynting vector S by
(1)P=real{∫02π∫0πSds}=12real{∫02π∫0πE×H*ds}.This integration is taken over the sphere surface on which the power radiates outwardly. Finally, the authors found out a general formula for radiated power generated by the Hertzian dipole as shown in following equation (2), where
(2)P=[+2(r1cos⁡2k1R1+r2sin2k1R1))9)1(k13D3p2b)h×(3πε1[(1+b)2+a2]hh×[1+r12+r22+2(r1cos⁡2k1R1+r2sin2k1R1)]3πε1[(1+b)2+a2]1)-1+2(r1cos⁡2k1R1+r2sin2k1R1))-1)9]×([(a2+b2)22a+4a2D+2a(a2+b2)D2hh+(a2+b2)2D2+(a2+b2)2D3])×([A0+A1D+A2D2+A3D3hhh+A4D4+A5D5+A6D6])-1,
where(i)
p is dipole moment,(ii)
k1=ω(ε1μ1)1/2 is propagation constant in medium 1,(iii)
D=k1R1,(iv)
r1,r2,a,b,  and  Ai(i=1→6) are constants derived from medium 1’s and medium 2’s parameters.Once parameters of media 1 and 2 are determined, it is straightforward to calculate the radiated power as a function of dipole moment “p.” The normalized radiated power (reference power P1 with εr1=1) is displayed in Figures 2 and 3 for small and large radii R1 of dielectric sphere, respectively. The dielectric constant εr1 runs from 1 to 500.Figure 2
Normalized radiated power versus dielectric constant with smallR1 at 403 MHz.Figure 3
Normalized radiated power versus dielectric constant with largeR1 at 403 MHz.When radiusR1 is small, for example, R1=3,5,7,9 mm, Figure 2 shows that Pi/P1 ratio achieves the highest value of unity with εr1=1 and decreases when the dielectric constant increases. It demonstrates that vacuum insulator is able to result in the highest radiation efficiency. This case is equivalent to implanted devices since the size of device must be small to embed in human body.Oppositely, when radiusR1 of the insulating sphere becomes greater, Pi/P1 ratio can be very high at some certain values of dielectric constant, so-called resonance points in radiated power which change when R1 changes as shown in Figure 3. The resonance occurs when radius R1 of insulating sphere is approximately an integer of half-wavelength in medium 1 [5].So far, the theory of the Hertzian dipole immersed in a lossy medium has been analyzed and discussed. In the next section, HFSS simulation is adopted to confirm the results above.


## 3. Simulation Results

Because of the unrealistic property of the Hertzian dipole a simple loop antenna is adopted in HFSS simulation to validate the results shown in Figures2 and 3. Simulation will be divided into two cases, one for implanted devices and one for other applications.Case 1 (implanted devices).
To illustrate the impact of dielectric constant, a cardiac pacemaker is selected as an example for an implanted device. The typical size of a pacemaker is shown in Figure4 [6]. An embedded loop antenna is designed as depicted in Figure 5.Figure 4
Typical sizes of a cardiac pacemaker.Geometry of embedded loop antenna: (a) top view; (b) side view.
(a)
(b)In this simulation model, the thickness of the insulator fixed at 6 mm (T1=3 mm) is the same as the thickness of the pacemaker in Figure 4. The thickness of muscle layer T2 is fixed at 7 mm as done in [7]. The loop antenna located in the center of the insulator has dimensions of L1×L2×W=69.1mm×50mm×5mm. These dimensions of antenna are designed to resonate at 403 MHz with dielectric constant εr1=42 since a high dielectric constant similar to that of dissipative media can widen antenna bandwidth as proved in [8].To study the effect of dielectric constant on the antenna radiation efficiency, dielectric constant is changed from 1 to 300, keeping loss tangent of insulator unchanged(tanδ1=0.0023) as in Section 2. When changing the dielectric constant, impedance mismatch of the antenna occurs, and radiation efficiency quickly degrades. For the sake of considering only the impact of the dielectric constant (ignoring mismatch loss), the radiation efficiency is given by
(3)Efficiency=PoutPin-PmismatchPout=Pin-Pmismatch-Pdiel-Ptissue,
where Pin is the input power of the antenna, Pmismatch is the power loss due to antenna-source mismatch, Pdiel is the dielectric loss, Ptissue is the loss absorbed by the tissue material, which is dominant, and Pout is the total power received at the outside of the tissue block. In the simulation, copper loss is neglected; a perfect electric conductor for antenna is assumed [8].From Figure6, it is obvious that εr1=1 (vacuum) leads to the highest radiation efficiency for implantable devices and the radiation efficiency decreases when the dielectric constant value increases. This result is consistent with those of Figure 2.Figure 6
Antenna efficiency versus dielectric constant (εr1) at 403 MHz.When taking into account the mismatch loss in radiation efficiency that occurs in real situations, changing the sizes of the loop antenna is necessary to achieve acceptable impedance matching whenεr1 changes. Some examples are taken for εr1= 1, 10, 20, and 42(tanδ1=0.0023). Reflection coefficient, radiated power, dimensions, and radiation efficiency of the loop antennas for these four cases are shown in Figures 7 and 8 and Table 1. Evidently, even though the volume of muscle in the first case (εr1=1) is the largest due to the largest dimensions of antenna (fixing T1 and T2), these results still show a trend that the dielectric constant εr1=1 brings the highest radiation efficiency to antenna.Table 1
Design parameters (in mm) of embedded loop antennas.
ε
r
1
L
1
L
2
W
Radiation efficiency (%)
1
173.8
70
10
0.86
10
87
51
5
0.74
20
78
45.8
5
0.5
42
69
48.9
5
0.51Figure 7
Return loss of antenna with different dielectric constants (1, 10, 20, and 42) at 403 MHz.Figure 8
Radiated power (in dBm) with different dielectric constants (1, 10, 20, and 42) at 403 MHz; input power = 1 mW.Briefly, in the case of implanted devices when thickness of device is thin (several millimeters), the radiation efficiency of the antenna achieves the highest value with insulator having relative permittivity of 1 (vacuum insulator).Case 2 (other applications).
In other applications such as underwater ones, the thickness of insulator can be much greater than that in Case1, which results in the occurrence of resonant points. To this end, T1 is set up at 40 mm and the simulation is performed for two cases: T2=7 mm and 60 mm. Sizes of antenna are L1×L2×W=69.1mm×50mm×5mm as in Case 1. By changing the dielectric constant of the insulator from 1 to 50, step = 2, and using the efficiency definition in (3) (or ignoring impedance mismatch), the radiation efficiency of the antenna is computed and plotted in Figures 9 and 10.Figure 9
Antenna radiation efficiency withT1=40 mm, T2=7 mm at 403 MHz.Figure 10
Antenna radiation efficiency withT1=40 mm, T2=60 mm at 403 MHz.As can be seen, the radiation efficiency in Figure10 is far less than that in Figure 9 because of the thicker muscle layer (T2=60 mm versus 7 mm). However, in both cases, the radiation efficiency with dielectric constant εr=1 is not the highest one as in Case 1. Instead, the highest radiation efficiencies occur at εr=18 and 10 with T2=7 mm and 60 mm, respectively. These results coincide well with the trend shown in Figure 3.Next, in order to have acceptable impedance matching atεr1=18and 10 in Figures 9 and 10 when taking into account mismatch loss in real situations, the sizes of the antenna are varied to have the designed resonant frequency. The reflection coefficient, sizes of antennas, and radiation efficiency are shown in Figure 11 and Table 2. As shown in Table 2, at εr1=18, although the thickness of the muscle layer is the same as in Case 1 (T2=7 mm), the efficiency is far greater (32.12% versus 0.86%; maximal efficiency withεr=1). Similarly, at εr1=10, even though the muscle layer is much thicker (T2=60 mm versus T2=7 mm at Case 1), efficiency is still greater (1.58% versus 0.86%). Radiated power received at the outside of muscle block is −4.93 dBm and −18 dBm with T2=7 mm and 60 mm, respectively (input power = 1 mW). Again, both cases demonstrate the existence of resonant points when the size of the insulator is large enough.Table 2
Design parameters (in mm) of embedded loop antennas with dielectric constants 18 and 10 at 403 MHz.
ε
r
1
L
1
L
2
W
T
2
Radiation efficiency (%)
18
15
66.5
5
7
32.12
10
40
74.5
5
60
1.58Figure 11
Reflection coefficient for two resonant points with dielectric constants 10 and 18 at 403 MHz.


## 4. Limitation and Related Works

This paper has been proving that the highest radiation efficiency of implanted antennas can be obtained with dielectric constantεr1=1 (vacuum). Yet, a lower dielectric constant leads to larger dimensions of antennas. Therefore, in antenna design, it is necessary to perform miniaturization techniques and/or have a compromise between the dielectric constant, antenna sizes, radiation efficiency, and bandwidth.In the literature, there are several works solving the impact of insulating material on implanted antennas. For example, authors in [8] used a high dielectric constant (εr1=50) for insulating material in order to widen the bandwidth of designed antenna. However, as shown above, this choice can lower the antenna radiation efficiency.In [9], the authors presented an interesting analysis about “the effect of insulating layers on the performance of implanted antennas.” In [9], the authors computed the impact of insulating materials on radiated power of implanted ideal antennas (infinitesimal dipoles), where the authors made use of 2 insulating layers with the first layer being vacuum. However, they did not explain or demonstrate clearly the reason for using air layer as the first insulation. The current work employed a real loop antenna in HFSS simulation and provided another approach for this issue.In [10], the authors analyzed different aspects of the design of implanted antenna including impact of relative permittivity on antenna radiation efficiency. Our work’s result coincides well with the result presented in [10] (Figure  2(b) [10]).


## 5. Conclusions

The impact of dielectric constant on radiation efficiency of embedded antenna has been investigated both analytically and numerically. The result shows that, for implanted antennas, vacuum insulation is capable of high radiation efficiency. In contrast, for other applications such as underwater ones where size of device can be large, there exist resonant points in radiation efficiency at a certain dielectric constant. This research is analysed and simulated at 403 MHz within a block of 2/3 human muscle phantom. Good agreement is achieved between analysis and simulation results.



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*Source: 758139-2014-10-13.xml*