CHAPTER 1 INTRODUCTION
1.4 Organization
This thesis comprises several chapters. The electromagnetic shielding theory described in chapter 2 includes the introduction of the shielding effectiveness under far field and near field. Chapter 3 mentioned about the shielding material fabrication, including the introduction of nanotube properties, properties of engineering plastic matrices - liquid crystal polymer and polyimide, the fabrication methods of carbon nanotubes, and the fabrication methods of carbon nanotube plastic composites. Chapter 4 demonstrated the EM shielding performance of the MWCNT-LCP composite and its application in packaging. Chapter 5 focused on the MWCNT dispersion, including the dispersion mechanism investigation. Chapter 6 demonstrated the shielding performance of the dispersed MWCNT-PI composite and its application in packaging. The summary of this study is finally concluded in chapter 7.
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CHAPTER 2
ELECTROMAGNETIC SHIELDING THEORY
Electronic circuits need packaging to get an adequate mechanical protection to avoid the possible damage during manipulation and assembly, such as the soldering and mounting upon the system module boards. Packaging is necessary especially when delivering the final commercial products, such as televisions, radios, and computers, to the end users. Usually, the electronic products need adequate metal packaging to enclose the whole electronic circuits. The first reason is due to the metal can offer an excellent mechanic protection to avoid the risky damage from external forces such as collision and pressure. The second reason is to protect the enclosed electronic circuits from being damaged by a direct electrical static discharge (ESD), where the metallic package can offer a discharge path outside the enclosed electronic circuits. The third reason is to protect the end users from being hurt by the electrical shocks. And the last and most important reason is to offer an excellent electromagnetic shielding capability for the EMC concern.
For EMC concern, the packaging of the electronic devices is requested to maintain an adequate electromagnetic shielding capability to avoid the unintended electromagnetic radiation from the enclosed electronic circuits leaking to the ambient environment.
Because these unintended radiations could influence the ambient electrical facilities, such as wireless communication and radio broadcasting, even possibly injury human health. It is the so-called EMI concern. In fact, there are a few governmental organizations responsible to define the rules and constraints for EMI such as the famous FFC regulations in USA and the FTZ/VDE in Germany. The packages are also used to protect the enclosed electronic circuits from the external interference emission, that means to reduce the influence from the neighboring external radiation sources such as the strong radiations from the radio stations, mobile base stations, and TV stations. It is the so-called electromagnetic susceptibility (EMS) concern. For this, the packaged electronic devices are tested to understand their EMS performance.
In general, the interference emission sources are from two major parts, one is the radiated emission (30 MHz~12 GHz) and another is the conducted emission (several
KHz~30 MHz) [1]. The radiated emission is in the form of electromagnetic wave, which transmits the electric and magnetic fields in the air, such as the intended radiation electromagnetic wave from the radio broadcasting antenna and the unintended radiation electromagnetic wave from the high-speed transceivers. As for the conducted emission, it is the noise from the poor EMC designed inter-connections such as electrical cables and power wires. And the noise is possible to influence the electronic circuits seriously.
While mentioning about the electromagnetic shielding, it is usually relevant to the radiated emission only. The conducted emission is another subject especially for the noise prevention in system level. Figure 2.1 shows the frequency spectrum, which covers from the AM radio band (~106 Hz) to the Gamma ray band (~1018 Hz) [2]. The so-called radio frequency (RF) focuses on the range from 3 Hz to 300 GHz [3]. And as for the microwave frequency, it is part of the RF range, and it focuses in the frequency range from 30 MHz to 300 GHz [4].
2.1 Mathematical Model of Shielding Effectiveness
The electromagnetic shielding capability of a material is called shielding effectiveness (SE). Fundamentally it is the insertion loss of the shielding material, and it is defined as the ratio of incident power to the transmitted power. Usually the ratio is expressed in decibel unit as
Figure 2.1 Frequency spectrum from AM radio to Gamma rays [2].
Pt log Pi
SE =10 10 (2-1)
where Pi is the incident power to the material, and Pt is the transmitted power which penetrates through the material.
Figure 2.2 illustrates the EM wave reflection and transmission upon a material. A normal uniform planar wave is incident to the material from the left side. The material is with the thickness of t, and with the electrical conductivity of σ, the permittivity of ε, and the permeability of µ.
The uniform electromagnetic planar wave with the electric field Ei and the magnetic field Hi is incident into the material from the left side. Part of the incident electromagnetic wave is reflected in the opposite direction with field Er and field Hr.
However, still part of the incident wave is transmitted through the material to the right side with fields Et and Ht. The electric field shielding effectiveness of the material can be expressed as
σ,µ,ε t Ei
Hi
Er Hr
Et
Ht
Figure 2.2 A uniform plane wave is normal incident to a material.
Et log Ei
SE=20 10 (2-2)
And the magnetic field shielding effectiveness of the material can be expressed as
Ht log Hi
SE=20 10 (2-3)
If the media in the left of the material is identical with the right, then the equations (2-2) and (2-3) are exactly equal. Because the intrinsic impedance of the media is the ratio of the electric field to the magnetic field. If the media is the air then the impedance of E/H is a constant of 377 Ω.
Theoretically the shielding effectiveness of a material is contributed from three main portions. They are the reflection loss, the absorption loss, and the multi-reflection loss.
As shown in Figure 2.3, the incident wave from left of the material is reflected partially, and the other portion continuously penetrates into the material. Then the penetrated wave will be transmitted inside the material and attenuated due to the absorption of the material.
Once the remaining transmitted wave arrived at the right interface, the second reflection
Figure 2.3 Reflection and transmission of an incident wave to a material.
is occurred and the second reflected wave will transmit in the opposite direction, toward left. And the rest wave continuously penetrates the right interface, then exit to the right media. The second reflected wave transmitted toward left is attenuated until arriving the left interface. Then the penetration and reflection will occur again, this kind of phenomenon will repeatedly happen again and again. So the incident wave is declined by the reflection and the absorption. In case the material thickness is much greater than the skin depth then the multi reflection can be ignored. Because the attenuation increases as the transmission distance increases, the wave is attenuated to 1/e at skin depth, if the material thickness is longer than skin depth then there is just few succeeding reflection can be sustained. So the total shielding effectiveness can be expressed as
SEdB =RdB +AdB +MdB (2-4)
where RdB is the reflection loss, AdB is the absorption loss, and MdB is the multi-reflection loss.
The electromagnetic shielding effectiveness of the material depends on the distance between radiation source and the shielding material. While the radiation source is quite far from the shielding material, the shielding effectiveness is called as far field SE, it will be described in section 2.2. As for the short distance case, it is called as near field SE and will be described in section 2.3.
2.2 Shielding Effectiveness in Far Field
When the incident radiation source of the material is very far from the shielding material (greater than λ π
2 ), then the incident field of the material can be considered as a uniform planar wave. That radiation source is called as far field source. Here we consider
the approximate solution that assumes the thickness of material is much greater than the skin depth under the operation frequency.
As shown in Figure 2.4, the incident uniform planar wave with electric field Ei is incident into the material from the air in left side. Partial wave transmits into the material with the electric field Eb, so the coefficient of transmission in the left interface is Eb/Ei. Then the wave with field Eb will continuously goes through the right material interface and transmits to the air as field Et, so the coefficient of transmission in the right interface is denoted as Et/Eb.
Here the shielding effectiveness of the material from reflection can be expressed as Et/Ei, which can be further calculated as [5]
0 0
(
0 0)
2Figure 2.4 The electric field Ei from air is incident into a material with the characteristic impedance η, Eb is the electric field that transmits inside the material, and Et is the electric field that transmits through the material.
where η0 is the wave impedance of air, and η is the characteristic impedance of the shield material.
In case the material is a good conductor, then η << η0.
Substitute formula (2-5) into formula (2-2), then [5]
( )
permittivity of air, σ is the electrical conductivity, then RdB can be further expressed as [5-6] the electrical conductivity of the copper , the electrical conductivity of copper isSm
So far the attenuation of the electromagnetic wave in the material during wave propagation is not taken into account, the Eb amplitude is assumed not attenuated inside the material.
However, the attenuation is really happened inside the shielding material due to the absorption loss, the amplitude of the EM wave is declined during wave traveling, and it can be mathematically expressed as [5-6]
AdB =131.4t fµrσr (2-9)
As for multi-reflection loss, it can be mathematically expressed as [5-6]
t
where t is the thickness of the shielding material, and δ is the skip depth under the operation frequency, β is the propagation constant.
It can be ignored if the thickness of the shielding material is greater than the skin depth under the operation frequency and a good conductor. The transmitted EM fields will be dramatically attenuated during a long-distance propagation inside the shielding material. But when the shielding material is not thick enough, and thinner than then skin depth, then the multi-reflection loss will be negative.
The multi-reflection phenomenon is especially easy to happen for the magnetic field, since most incident magnetic fields are penetrated through the entry interface of the shielding material and most penetrated magnetic fields are reflected from the exit interface of the shielding material. But as for the electrical field, the multi-reflection is usually not a serious problem because most of the incident electrical fields are reflected from the entry interface of the shielding material, and just few penetrated electrical fields reflected from the exit interface. There are not many electrical fields left for multi-reflection in the shielding material, especially when the shielding material is a good electrical conductive material. The less multi-reflection phenomenon of the electrical fields can be understood from the formula Eb = 2η Ei / (η0 + η), where the shield is assumed as a good electrical conductive material, so the electrical conductivity of the material η is with a low impedance and less than η0. So basically the electrical field E b that penetrated through the entry interface is small, there is only few electrical field can be retained for multi-reflection.
As for the magnetic field, the behavior is reversed. Because according to the formula Hb = 2η0 Hi / (η0 + η), the penetrated magnetic fields H are remarkable. So the multi-b reflection is a real problem for magnetic field. The influence is more important in the low frequency (such as several KHz) for the magnetic field dominant radiation since the overall shielding effectiveness is low. However, once the frequency gets higher (such as several GHz), the negative contribution from the multi-reflection can be reduced. That’s due to the ratio between material thickness and skin depth became larger as the frequency increases.
In summary, the total far field SE is the summation of the equations (2-8), (2-9), and (2-10). Figure 2.5 plots the numeric calculations for each contribution factor and their sum. This example assumed a material under far field measurement is with thickness of 0.85 mm, electrical conductivity of 6 S/cm, and frequency range within 1 GHz ~ 3 GHz.
In Figure 2.5, the reflection loss decreases as the frequency increases, the absorption loss increases as the frequency increases, and the multi-reflection loss slightly decreases as the frequency increases. However, the multi-reflection term is very small, it is about
0.517 dB ~ 0.016 dB. That is due to the skin depth is smaller than the material thickness of 0.85 mm, the skin depth is about 0.649 mm ~ 0.375 mm within the frequency range of 1 GHz ~ 3 GHz.
2.3 Shielding Effectiveness in Near Field
When the distance between the radiation source and the shielding material is less than λ π
2 , it is the near field. The uniform planar wave assumption used in the far field cannot sustain in the near field. Because the wave front in the near field is not planar but curved, so the wave front is not parallel to the surface of the shielding material. The wave
Figure 2.5 Numeric calculation results for reflection loss, absorption loss, multi-reflection loss, and the total shielding effectiveness under far field condition.
0 10 20 30 40 50 60
1 1.5 2 2.5 3
GHz
SE (dB)
Refle ction Aborption Multi-re flection Total SE
impedance of the near field is not like that of the far field. The wave impedance is a constant in the far field, but the wave impedance of the near field varies with the distance between radiation source and the shielding material. It is not like the constant wave impedance of = =377Ω
E of the near field depends on the distance and the dominant
field. In case it’s an electrical radiation source, that means the electrical field dominates the magnetic field, then it will demonstrate high wave impedance. But the wave impedance decreases as the distance increases in the near field, it can be express as [6]
expression of equation (2-12) [5-6]. It is the near field shielding effectiveness of the reflection loss contribution under the electrical field dominated condition.
⎟⎟
In case it’s a magnetic radiation source, then the wave impedance will be lower than 377 Ω . And the wave impedance increases as the distance increases, it can be expressed as [6].
η0 =2πfµr (2-13)
Substituting equation (2-13) into equation (2-6) to result in expression (2-14) [5-6].
⎟⎟⎠
As for the absorption loss contribution to the total shielding effectiveness in the near field, it is as same as equation (2-9). Both the electrical field and magnetic field, the absorption loss term is same.
2.4 Shielding Effectiveness Model for Mixing Materials
A composite comprises the guest materials and the host material. In this study the guest material is the electrical conductive MWCNT, and the host material is the insulated engineering plastic such as LCP and PI. The electromagnetic shielding effectiveness of the plastic composite can be measured experimentally, and it also can be theoretically calculated according to the ratio of the incident electromagnetic wave to the transmitted electromagnetic wave that passes through the composite. Within the calculation there is an important parameter, the effective relative permittivity ε of the mixture composite, eff has to be known. The effective relative permittivity ε of the mixture composite can be eff approximately calculated from the mixing formula, such as the Maxwell Garnett formula.
A composite comprises the guest materials and the host material. In this study the guest material is the electrical conductive MWCNT, and the host material is the insulated engineering plastic such as LCP and PI. The electromagnetic shielding effectiveness of the plastic composite can be measured experimentally, and it also can be theoretically calculated according to the ratio of the incident electromagnetic wave to the transmitted electromagnetic wave that passes through the composite. Within the calculation there is an important parameter, the effective relative permittivity ε of the mixture composite, eff has to be known. The effective relative permittivity ε of the mixture composite can be eff approximately calculated from the mixing formula, such as the Maxwell Garnett formula.