Technical report, IDE1057, November 2010
Microwave Components Based on Magnetic Wires
Master’s Thesis in Microelectronics and Photonics Sizhen Lan & Lian Shen
School of Information Science, Computer and Electrical Engineering Halmstad University
2 Copyright
by
Sizhen Lan and Lian Shen 2010
3
Microwave Components Based on Magnetic Wires
By
Sizhen Lan and Lian Shen
M.Sc. Electrical Engineering, Halmstad University, 2010
Abstract
With the continuous advances in microwave technology, microwave components and related magnetic materials become more important in industrial environment. In order to further develop the microwave components, it is of interest to find new kinds of technologies and materials. Here, we introduce a new kind of material -- amorphous metallic wires which could be used in microwave components, and use these wires to design new kinds of attenuators. Based on the fundamental magnetic properties of amorphous wires and transmission line theory, we design a series of experiments focusing on these wires, and analyze all the experimental results.
Experimental results show that incident and reflected signals produce interference and generate standing waves along the wire. At given frequency, the insertion attenuation S21[dB] of an amorphous wire increases monotonically with dc bias current, the empirical formula of attenuation with dc current is: . The glass cover will influence the magnetic domain structure in amorphous metallic wires. Therefore, it will affect the circumference permeability and change the signal attenuation. It is necessary to achieve the impedance matching by coupling to an inductor and a capacitor in the circuit. The impedance matching makes the load impedance close to the characteristic impedance of transmission line.
The magnetic wire-based attenuator designed in this thesis work are characterized and compared to conventional pin-diode attenuator.
0
0 1
( ) (8.686 C) ( I I )[ ]
A I C d Z R R e dB
4
Key Words
Microwave component, Amorphous magnetic wire, GMI effect, Domain structure, Permeability, Impedance matching, Attenuator.
5
Acknowledgement
With the help and support of many people, we could complete this thesis successfully. At first, we are honored to express our gratitude to our dedicated supervisor, Emil Nilsson. Through his guidance, we have gradually realized what we need to do for our paper. His erudition and preciseness has inspired us to write this essay with an open and positive mind. His interesting discussion with us was also informative and useful. We appreciate all his efforts. We also want appreciate our major teachers Håkan Pettersson, Jörgen Carlsson and Lars Landin. Their earnest, profession and enthusiasm inspired us deeply.
We also would like to thank our parents for their hard work and support of our graduated studies from the very beginning of our postgraduate study. In the future study, we will maintain this enthusiasm and efforts.
Lan sizhen Shen Lian
Halmstad University Nov. 2010
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Contents
Abstract 3
Acknowledgement 5
Chapter 1 Introduction 8
1.1 Microwave Components 8
1.2 Amorphous Wires 8
Chapter 2 Magnetic Properties of Amorphous Metallic Wires 10
2.1 Magnetic Properties 10
2.1.1 The Magnetic Domain Structure 10
2.1.2 Zero-Magnetostrictive Effect 11
2.1.3 Co-Fe-based Amorphous Metal Wire’s Magneto-Impedance Effect 11
2.2 Giant Magneto Impedance (GMI) Effect and Skin Effect 12
Chapter 3 Transmission Line 1 6 3.1 Descriptions 1 6 3.2 Transmission Line Equation 1 7 3.3 Characteristic Impedance 1 9 3.4 Reflectance 1 9 3.5 Impedance Matching 20
3.6 Standing Wave 20
3.7 Microstrip Transmission Line 2 1 3.8 Attenuation of Amorphous Metallic Wires 23
Chapter 4 Experiment 24
4.1 Wire Preparation 2 4 4.1.1 Amorphous Glass-Covered Wires 24
4.1.2 Glass Cover Removal 2 5 4.2 Experiment Procedure 25
Chapter 5 Analysis and Design 2 7 5.1 Analysis 2 7 5.1.1 The Characteristic Analysis of Signal Attenuation 27
5.1.2 Direct Current Effects on the Signal Attenuation 32
5.1.3 Amorphous Metallic Wire without Glass Cover 35
5.1.4 Impedance Matching Analysis 36
7
5.2 Design 39 5.2.1 Electronically Controlled Attenuators 39
Chapter 6 6.1 Conclusion 4 4 6.2 Future Work 4 5
Reference 4 6
8
Chapter 1 Introduction
With the continuous advances in microwave technology, microwave components and related magnetic materials become more important in industrial environment. They are widely used in microwave communication, telemetry system, radar, navigation, biological medicine, artificial satellite, spacecraft etc. As the operating frequency of microwave devices further increases, the power capacity increases, the noise reduces, as well as the efficiency and reli ability improve, especially in the integration realization, which leads to new changes in microwave electronic systems. Amorphous materials especially for amorphous wires have a lot of significant benefits in their properties, such as high strength, high toughness, high magnetic permeability, and excellent chemical properties. It is of interest to know the prospects of amorphous wires for implementation as microwave components.
1.1 Microwave Components
In the microwave systems, microwave components are the devices which achieve the directional microwave signal transmission, attenuation, isolation, filtering, phase control, transformation of waveform and polarization, impedance transformation [1]. Microwave components are the electromagnetic components which work in the microwave bands. In low-frequency electronic circuits, the most commonly used passive components are resistors, capacitors, inductors, transformers and so on. Similarly, in microwave circuits, passive components such as resistors, capacitors, inductors are also widely used. However, due to the increased frequency, the performance of these passive components will change a bit and some kinds of components used in low-frequency circuits can’t be used in microwave frequency bands. Owing to the research and development of microwave technology, such as asymmetric transmission lines, we could realize the functions of inductors and capacitors in microwave frequency bands. In order to constitute a microwave circuit with certain functions, it’s necessary to connect several passive microwave components, such as directional couplers, power dividers, impedance matching devices, microwave filters, attenuators, terminal loads, etc. In order to develop microwave components, it is of interest to find new kinds of techniques and materials. In this report, we introduce the properties of amorphous magnetic wires and analyze the experimental results, after these we design a new attenuator based on the amorphous wires.
1.2 Amorphous Wires
Amorphous materials refer to the status of non-crystalline materials. If cooling the molten alloy rapidly, the structure after solidification presents the state of glass. Amorphous materials have many excellent properties such as high strength, high toughness, excellent magnetic properties and corrosion resistance. It seems that the magnetic properties of amorphous material are widely used and these materials can be made in a variety of shapes, such as films, ribbons, wires, powders [3].
In particular, amorphous wires have attracted a lot of interest from industry due to their potential applications in electronic systems.
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Fig 1.1 Schematic representation of an amorphous glass-covered metallic wire
Fig 1.1 illustrates the schematic representation of an amorphous glass-covered wire (AGCW).
Here d is the diameter of the metallic (magnetic) core, and D is the diameter of wire with glass cover. These wires are obtained from the melt by the glass-coated melt spinning method. This method will be introduced in chapter 4. Amorphous magnetic wires with glass cover were prepared for the first time in 1974 by Wiesner and Schneider [4], but the wires didn’t show excellent reproducible performance, wherefore the interest in these wires decreased [5]. Due to the developing of theory and technology and many application potentials in the last several years, amorphous magnetic wires have been reconsidered.
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Chapter 2
Magnetic properties of Amorphous Metallic Wires 2.1 Magnetic Properties
Amorphous metallic wires are relative new materials which have attracted a lot of interest for basic research and potential applications in microwave components. These wires have a specific magnetic behavior which originates from their special magnetic domain structure due to the stress difference between the surface and center during preparation [6]. During the process of magnetization in longitudinal direction, the length of amorphous wires will change and the magnitude can be expressed as magnetostriction coefficientλ. If the length increases, the wires are called positive magnetostrictive materials such as Fe-based amorphous wires. If the length decreases, the wires are called negative magnetostrictive materials such as Co-based amorphous wires. Fe- and Co-based amorphous wires are very important amorphous metallic materials, because they have their own electromagnetic properties (e.g. high resistivity for Fe-based amorphous wires and high permeability for Co-based amorphous wires).
2.1.1 The Magnetic Domain Structure
Some kinds of amorphous materials with low magnetic domain wall energy are isotropic. If shape and stress anisotropy exist, there will be higher domain wall energy. Different domain structures are observed in different types of materials. In the rapid cooling preparation process for amorphous wires, the cooling rates of surface and center of the wires are different. There will be a stress difference between the surface and center. When the direction of an external magnetic field is consistent with the stress direction, tensile stress will make the distance between atoms increase, and increase material magnetostriction coefficientλ. When direction of magnetic field is opposite to the stress direction, the compressive stress will make the distance between atoms decrease, and increase the absolute value of negative magnetostriction coefficientλ[8]. Because the amorphous materials do not have grain-boundaries, there is no grain-boundary resistance. In low magnetic field, Barkhausen jumps may occur due to irreversible displacements of domain walls in the process of magnetization. With the magnetic field increasing, all atoms in the domain wall reverse, only one or two Barkhausen jumps will complete the annexation displacement of domain wall [9][10], and this kind of amorphous metallic wire is a large magnetostrictive soft magnetism material.
Fig2.1 (a) shows the domain structure of positive magnetostrictive amorphous wires (e.g.
Fe-based wires). The outer shell domain is a radial domain with closure domains and the inner core domain with longitudinal magnetisation. Fig2.1 (b) shows the domain structure of negative magnetostrictive amorphous wires (e.g. Co-based wires). Because the surface anisotropy is circular and inner anisotropy is perpendicular to the axis of wire, the outer shell domain is circular and inner core domain is axial.
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Fig 2.1 Domain structures of Fe-base (a) and Co-base (b) amorphous metal wire
Different domain structures have different magnetic properties. By applying alternating current in the amorphous wire, there will be a circular magnetic field in the circumferential direction of the wire and wire will be magnetized in this direction. For positive magnetostrictive amorphous wires, stress distribution may result in radial easy axes in the outer shell, but for negative magnetostrictive amorphous wires, stress distribution will result in circumferential easy axes in the outer shell, so the circumferential magnetization is different, larger magnetization shows higher permeability and larger permeability gives higher magnetization [11]. For amorphous glass covered wires, because the glass and metallic core have different expansion coefficients, there will exist stress differences between glass and metallic core during the preparation, and the domain structure will be influenced by the glass cover.
2.1.2 Zero-Magnetostrictive Effect
One of the main properties of amorphous magnetic wire applications is the zero-magnetostrictive effect. Zero magnetostrictive effect means that the material magnetostriction coefficient tends to zero. It makes the material have low magnetic domain’s wall energy, easy inversion of domain wall and high permeability. Co-Fe-based amorphous wire has zero magnetostriction coefficient [12]. It has high magnetic induction at low magnetic field. During the magnetization process, the length of Co-Fe-based amorphous wires with zero magnetostriction is constant and these wires are excellent soft magnetic materials. Under the condition of small magnetic field，these wires all have the characteristics of fast response and high stability [7].
2.1.3 Co-Fe-based Amorphous Metalic Wire’s Magneto-Impedance Effect
When high frequency current passes through the Co-Fe-based amorphous metallic wires, the impedance of the wires will change due to the so called skin effect. Under the external applied magnetic field, the skin depth and the impedance of the wires will change. This is called the magneto-impedance (MI) effect [13]. The amorphous wire with zero magnetostrictive effect will generate MI effect when coupled to alternating current. The induced electromotive force is directly proportional to the differential magnetic permeability along circumferential direction of wire. The sensitivity of MI effect is inversely proportional with the dynamic coercivity along circumferential direction of wire [14].
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2.2 Giant Magneto-Impedance (GMI) Effect and Skin Effect
The giant magneto-impedance effect was observed by Machado et al. [15]. Here the impedance of soft magnetic amorphous metals undergo a large change under the condition of external magnetic fields. This effect is called “giant magneto-impedance” (GMI). Many researchers have recently been attracted by it because of its prospective applications in microwave components [16]. Some previous researchers found that when the magnetostictive coefficient of the amorphous wire is close to zero, and the frequency is larger than 10KHz, the GMI effect can be observed [17][18].
The common used circuit for GMI measurement is shown in Fig 2.2.
Fig 2.2 Simplified circuit for GMI measurement
When iac flows through the wire, it will induce a circular magnetic field Hac and the amorphous wire will be magnetized in the circumferential direction. The external field Hac will weaken the circumferential magnetization. When Hac increases, circumferential permeability decreases rapidly.
Hence one can see that the circumferential permeability varies sensitively with external field is the major cause of GMI effect. When the signal frequency increases, the magnetic field will enhance, leading to high magnetization. The permeability could be considered as the function of frequency and field. When a dc bias current Idc is applied on the amorphous wires, it will induce a circumferential dc magnetic field Hdc. In this case, the asymmetry in GMI appears, due to the direction and magnitude of Idc. We know that, the main cause of skin effect is due to the eddy current generated within the amorphous wire. The dc bias current will weaken the eddy current and thus the skin effect will be reduced.
Now it is very common to use the traditional framewore of electromagnetic theory to explain the GMI effect of amorphous wire. In the early reports on GMI phenomenon [19][20], people considered the origin of GMI effect as related to classical electromagnetic skin effect. When high frequency current flow through the conductor, the current distribution is not uniform in the conductor cross section owing to the skin effect and the current density is mainly concentrated in the surface of conductor.
13
In a magnetic field, the impedance of the magnetic materials can be written as follows:
(2.1) Where is the angular frequency of the input, is the effective permeability of materials, Hex
is the external magnetic field [21].
Using Fourier analysis method to analyze the impedance of amorphous wire, we can get the mathematical model of the GMI effect. The impedance Z can be presented as follow [22].
(2.2)
Here is the direct current resistance per unit length, and are respectively the zero order and one order of Bessel functions, is the skin depth, r is the radius of wire. In the strong skin effect, we can get the impedance
(2.3)
In the long straight section of a wire, the constant current is uniformly distributed. The electrons flow through the wire in a manner similar to the way water flows through a pipe. This means that the path of any one electron essentially can be anywhere within the volume of the wire.
Fig 2.3 A wire that is connected to a dc source
When alternating current passes through the wire, due to the induction effect, the distribution of current density is not uniform in the conductor cross section. The more close to the conductor surface, the greater the current density. This phenomenon is called as "skin effect" [23]. When high frequency current flow through the wire, it can be considered that current flow through only in a thin surface layer of wire. This is equivalent to the wire cross-section decreases, resistance increases.
(
2)
1
= σπr Rdc
eff
( )
δ k 1- j
=
( )
krJ0 J1
( )
kr( )
kr J( )
krJ kr R
Z dc 0 1
2
= 1
eff( ,
ex)
eff( ,
ex)
Z R
H jX
H1 1
(1 ) 2 2
Z j
r
14
Fig 2.4 A wire that is connected to an ac source [24]
For the alternating current, the self-induced electromotive force (EMF) will appear to resist the adoption of current in the wire. This EMF is in proportion to the size of the conductor cutting magnetic flux per unit time. With circular section conductor in Fig 2.4, the closer to the center of conductor, the greater self-induced EMF is generated by the external magnetic field. The closer to the surface of the conductor, the smaller influence can be affected by the internal magnetic field, and thus less self-induced EMF. As the self-inducted EMF increases with the frequency, skin effect will be more prominent and small skin depth will be obtained. These make the effective cross-sectional area smaller when the current passes through the conductor, thereby, causing the effective resistance larger [25].
There is another explanation of the skin effect which is related to the process of electromagnetic wave infiltrate into the conductor. When the electromagnetic wave infiltrate into the conductor, it will be attenuated due to the energy loss. The depth where the amplitude attenuation is times of the surface amplitude is called skin depth of electromagnetic field in the conductor. A simple example is the penetration of plane electromagnetic wave to semi-infinite conductor, the equation of skin depth is [26]:
(2.4)
Where f is the frequency, is conductor conductivity, is the permeability. The skin depth is inversely proportional to the square root of the three parameters.
When the transverse dimension of conductors in a wire is smaller than the skin depth, the distribution of current density over the cross-section will become uniform and the resistance there will be similar to dc value. Determining the ac resistance of a wire from Maxwell’s equations is difficult for even the simplest cross-sectional shapes, such as circular wires [27][28]. However, if the skin depth is small compared to the dimensions of the cross section of the wire, then we could obtain very good results by assuming that the current is flowing in the skin depth of the outer surface of the wire.
The approximate effective area of a circular wire shows in Fig 2.5 was previously determined as
(2.5) The impedance of the wire is , only consider R, we can get the resistance of wire with length l:
(2.6)
e-1
2
2
2
effective
A r r r
Z R j L
1
f
2
effective
l l
R A r
15
In extremely strong skin effect, the radius of the wire is much bigger than the skin depth (r >>δ), so in the formula (2.6), δ can be neglected.
Fig 2.5 Effective area of current pass through the wire
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Chapter 3
Transmission Line 3.1 Descriptions
A transmission line is a kind of waveguide structure which can transmit electrical energy from one point to another. Although the input port can be connected directly to the output port, the input port is usually located some distance away from the output port. We then use a transmission line to connect the input and output port.
The purpose of the transmission line is to transfer the energy with the lowest possible power loss.
In order to achieve this, it is necessary to obtain special physical and electrical characteristics of the transmission line. In many electric circuits, the length of wires connecting the components can be ignored. There are several exceptions, one is that, if the interval of voltage is similar to the wavelength of signal in the wire, the length of wires should not be ignored and the wire should be treated as transmission line. A common empirical method is that, if the length of wire is greater than 1/10 of wavelength, it can be treated as a transmission line [29]. At this length, the phase delay, reflection and interference in the line need to be considered. Without using the transmission line theory, the microwave systems will have some unpredictable behaviors.
There are several structures of transmission line in Fig 3.1. Various kinds of waveguides, which can transfer TE mode, TM mode, or mixed-mode, could be considered as generalized transmission line. We could use the viewpoint of the equivalent transmission line to analyze the distribution of the electromagnetic field along the propagation direction in waveguide.
Fig 3.1 Example structures of transmission line[30].
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3.2 Transmission Line Equation
Consider an uniform transmission line, the input port is connected to a sinusoidal signal source with angular frequency , and the output port is connected to a load impedance ZL. Suppose that the original point of coordinates is on the initial, we could get the complex voltage and current at z point is U(z) and I(z). After dz section, the voltage and current equal U(z)+dU(z) and I(z)+dI(z), respectively. As shown in Fig 3.2.
Fig 3.2 Equivalent circuit of an element of a transmission line with a length of dz [31].
A short transmission line could be described by four lumped parameters: R, L, G, C, which represent the resistance in both conductors per unit length in Ω/m, the inductance in both conductors per unit length in H/m, the conductance of the dielectric media per unit length in S/m and the capacitance between the conductors per unit length in F/m, respectively.
The incremental voltage dU(z) is generated by the distributed inductance Ldz and the distributed resistance Rdz, and the incremental current dI(z) is generated by distributed capacitance Cdz and distributed conductance Gdz. According to Kirchhoff's law, it is easy to write the equations
dz z dU z U C j G z dI
dz z I L j R z dU
) ( ) ( )
(
) ( )
(
(3.1) Omit small higher-order, then:
) ( )
) ( (
) ( )
) ( (
z CU j z dz GU
z dI
z LI j z dz RI
z dU
(3.2) Equation (3.2) is a first-order ordinary differential equation, and is also known as transmission line equation. It describes the variation of voltage and current on uniform transmission line of each infinitesimal section. According to the solution of this equation, we could obtain the expressions of voltage and current at any point on the transmission line, as well as the relationship between them. Therefore, equation (3.2) is the basic equation for uniform transmission lines.
18
Differentiate z on the both sides of equation (3.2), we could obtain
(3.3) Combine with equation (3.2), equation (3.3) could be rewritten as
(3.4)
Therefore：
(3.5) The general section of equation (3.4) is:
(3.6) According to the first formula of equation (3.6) and equation (3.2), we could get
(3.7) Where
C
R j L
Z
(3.8)
Here, ZC is the characteristic impedance of transmission lines. Commonly refers to the transmission line wave propagation constant, a dimensionless complex number. The propagation constant could be used to describe the attenuation and phase shift of voltage and current traveling along the transmission line. Usually it is expressed as
(3.9) Here, the real part represents attenuation constant whose unit is dB/m and the imaginary
represents phase shift constant whose unit is rad/m. For the non-loss line ( ), we get
(3.10)
It explains that in the process of wave traveling there is no attenuation, and the wave moves with a wavelength of radians of phase delay. Here is the permeability and is the permittivity.
0 LC 2
0 R G
j
2
2
2
2
2
( ) ( )
( ) ( )
d U z dI z
R j L
dz dz
d I z dU z
G j C
dz dz
2
2 2
2
2 2
( ) ( ) ( )
( ) ( ) ( )
d U z
R j L G j C U z U z dz
d I z
R j L G j C I z I z dz
R j L G j C
1 2
3 4
( ) ( )
z z
z z
U z A e A e I z A e A e
1 2 1 2
( ) (
z z) 1 (
z z)
C
I z A e A e A e A e
R j L Z
19
3.3 Characteristic Impedance
The ratio of voltage and current could be expressed as impedance or resistance. For a lossless transmission line, the current is in phase with the voltage and the impedance is re al. It is called the
"Characteristic Impedance". It has no relationship with frequency, only depends on the line itself, such as the physical parameters and geometric dimensions. Usually, it is a complex constant. From formulas (3.5) and (3.8), the characteristic impedance can be expressed as follow.
(3.11)
At high frequency，that is ωL >>R,ωC >>G, then
(3.12) A transmission line can be treated as a circuit composed of many inductance and capacitance.
Here, the characteristic impedance can be considered as a real resistance. The energy generated from the generator will be stored temporarily in this effective resistor, and at some time later, the energy will be extracted and return to the generator, or convert to heat in a real resistance [32].
Because the transient distribution of electromagnetic field in cross section of transmission line is similar to the distribution of two-dimensional electrostatic field and static magnetic field, we can use static magnetic field and constant-current method to calculate the distribution of parameters C and L, and calculating the characteristic impedance ZC. Usually only calculate C, we can get the characteristic impedance by formula , here is the velocity of signal transmission.
Therefore, we could further understand the characteristic impedance as a pure resistance, only related with the parameters of form, size of transmission line and the medium, but independent on frequency.
3.4 Reflectance
When , here ZL is the load impedance coupled with the terminal, the incident wave which is transmitted to the load will generate reflected wave from the load to the source. On one point at the transmission line, the ratio of reflected wave voltage and incident wave voltage is the voltage reflection coefficient for this point, referred to as the reflection coefficient, usually it is a complex constant. For non-loss line, the reflection coefficient is , and the mode remains unchanged alone the line as the angle changes linearly. In the load (reflection points), the initial value ofψand is only related with the ratio of .
The relationship between and input impedance on z point in transmission line is
(3.13)
When , , there is only an incident wave transmitted to the load, no reflected wave from the load. Without any reflected wave, the transmission line is said to be impedance matched.
νC ZC =1
Γ ψ
Γ= ej Γ
Γ
L
C Z
Z
( )
z U( ) ( )
z I z Z =( ) |z L C
Z z Z ΓL =0
( ) ( )
( )
C
C
Z z Z z Z z Z
C
R j L
Z G j C
Z
C L C
v
L C
Z ≠Z
z
20
3.5 Impedance Matching
Since a transmission line has impedance built in, one question is how does the impedance affect signals which transmit through a transmission line? The answer to this question mainly depends on the impedances of devices to which the transmission line is attached. If the impedance of the transmission line doesn’t equal the impedance of the load, the signals propagating through the line will only be partially absorbed by the load. The rest of the signal will be reflected back. Reflected signals are generally bad things in electronics. They represent an inefficient power transfer between two electrical devices [33]. The purpose of impedance matching is to transfer maximum power from transmission line to load.
3.6 Standing wave
When the signal transmits through the transmission line, there will be signal reflect because of the impedance mismatching. The interaction of input signal and reflected signal will create a standing wave. Fig 3.3 shows a typical resulting standing wave pattern for a mismatching transmission line.
The schematic is shown the amplitude of signal versus position along the transmission line [34].
Fig 3.3 Schematic of a typical resulting standing wave pattern for a mismatching transmission line
A term used to describe the standing wave is the voltage standing wave ratio (VSWR), which is the radio of the maximum to minimum voltage. An ideal VSWR is 1:1, that is, the load impedance is equal to the characteristic impedance of transmission line, but it is almost impossible to achieve.
Larger VSWR gives higher reflected power. For example, if VSWR equals to 1.25:1, the reflection power is 1.14% and the VSWR equals to 1.5:1, the reflection power is 4.06% [35].
21
3.7 Microstrip Transmission Line
The microstrip line is one of the most common types used in microwave circuit. It consists of a strip conductor and a ground metal plane separated by a dielectric medium [36]. The geometry of microstrip transmission lines is illustrated in Fig 3.4. A strip conductor of width W, and thickness T is printed on a grounded dielectric of thickness H and relative permittivity . Three important electrical parameters for microstrip line design should be noticed, they are the characteristic impedance ZC, the guide wavelength , and the attenuation constant .
Fig 3.4 Schematic of single microstrip Fig 3.5 The EM fields are not contained entirely within a microstrip line but propagate outside of the line as well
In a microstrip transmission line, as shown in Fig 3.5, the dielectric substrate half surround the conducting strip, the electromagnetic (EM) field lines are propagated in both the substrate and outside of the microstrip [37].
Both dielectric losses and conductor losses will introduce attenuation. The attenuation caused by the finite conductivity of the conductors is accounted for by the series resistance R, while attenuation caused by dielectric loss is modeled by the shunt conductance G in the distributed circuit model of the microstrip line. The separate attenuation constants are given by [38]
C
c Z
α R
= 2
andC
d Y
α G
= 2
(3.14) And the total attenuation is given byd
c
α
α
α = +
(3.15) The following formulas give excellent results for the capacitance per meter of strip of width W at a height H above a ground plane, the air dielectric constant is .
2 0
ln 8
4 Ca
H W
W H
, (3.16)
0 1.393 0.667 ln 1.444
a
W W
C H H ,
W 1
H
(3.17)
rg
0W 1 H
22 Where is the capacitance of the unscaled air-filled line.
The effective dielectric constant for the microstrip line is given by e
a
C
C (3.18) The characteristic impedance is given by(3.19)
There is an easier way to find . Schneider [38] deduced a quite simple formula for the effective dielectric constant of a microstrip line which is illustrated at below.
(3.20)
WhereF
r,H
0.02
r1 1
W H
2for W H1 and equals zero forW H 1.We evaluate the conductor loss is caused by finite conductivity of the microstrip and the ground plane. For the same microstrip line, the normalized series distributed resistance for the microstrip is RC [38].
(3.21) The loss ratio (LR) is given by
W 0 . 5
H (3.22) 0.5 W 10
H (3.23) And the normalized series resistance RD of the ground plane is given by
(3.24)
Rs is the skin-effect resistance which is equal to , is skin depth and is the conductivity of wire. The total series resistance is the sum of RC and RD, so we can get
(3.25) In our experiment, because the attenuation caused by dielectric losses is very small, we only consider the attenuation caused by conductor losses [38].
Ca
2
1 1 4
s ln
C
R W
R LR
W T
e
e2
0.94 0.132W 0.0062 W
LR H H
5.8 0.03
s D
R W H
R W W H H W
1
LR
( )
σδ 1W 10 H
0 0 0 0
1
e C
e a
Z L
C C C
, ,
2
c c microstrip c groundplane
R
CR
DZ
C
1 1 12
1/21 , 0.217( 1)
2 2
r r
e r r
H F H T
W WH
23
3.8 Attenuation of Amorphous Metallic Wires
In our experiments, we will analyze the signal transmission and loss for the amorphous metallic wires. Therefore, we need to deduce a formula of signal attenuation for the amorphous metallic wires.
Fig 3.6 The electromagnetic (EM) field lines of amorphous wire sample.
Fig 3.6 shows the electromagnetic field lines of our sample. Comparing Fig 3.5 and Fig 3.6, we could find that the electromagnetic field lines distributed in the dielectric substrate is similar and the density of the electromagnetic field distributed in the middle of the substrate is larger than both sides. Therefore, based on the neglect of certain factors, by changing some of variables, we can directly apply the formulas of microstrips into our samples.
Because the wire is circular, it can approximate , according formula (3.21), then we get the normalized series distributed resistance for the wire is
(3.26)
The loss ratio is given by formula (3.22), (3.33). The normalized series resistance RD of the ground plane is the same with formula (3.24)
The attenuation constantα is given by c
(3.27)
The power in length l is , where p(0) is the input power. The attenuation of the wire can be obtained as.
(3.28) 2
1 1 1
W ln 4 ( 5.8 0.03 )
s c
c
R LR
Z H W H H W
[ ] 20 log 8.686
A dB L e L
W T d
2
1 1
W ln 4
s C
R LRR
0 -2 l p l p e 24
Chapter 4 Experiment
4.1 Wire Preparation
4.1.1 Amorphous Glass-Covered Wires
The preparation of amorphous metallic wires with glass cover is based on high frequency induction heating melt spinning method. After a suitable temperature annealing, amorphous samples can be turned into amorphous metallic glass-covered wires. This method was initially used by Taylor in 1924 [39]and improved by Ulitovskiy [40].
The schematic diagram is illustrated in Fig 4.1. It mainly includes three parts: high-frequency induction heater, vacuum system, drawing system. Insert small pieces or powder of the metallic alloy into the pyrex tube after the tube is evacuated and the tube is subsequently filled with an inert gas. A high-frequency inductive coil is used to heat and melt the alloy. The glass wall becomes soft by the molten alloy. Due to the molten metal drop and the mechanical tension, the molten alloy and softening glass will be formed to the shape of glass-covered alloy wire. It immediately passes through the cooling liquid jet, and then the amorphous glass-covered alloy wire can be obtained.
Fig 4.1 Schematic diagram of the glass-coated melt spinning process [41].
This is a modification of the Taylor method. It can easily produce the alloy systems with low wire forming capacity. The metallic melt stream will break into droplets before solidification. Since the presence of the glass cover, the molten metal and cooling liquid will not contact directly, this will drastically reduce the ability of melt stream break into droplets before solidification. It is not easy to break into droplets with the melt stream in glass cover which ensures a smooth cylindrical shape. So that we could obtain higher cooling rates, and produce amorphous wires more easy. Fig 4.2 shows two examples of amorphous metallic wires.
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Fig 4.2 The SEM images of Pyrex-covered amorphous wire [42].
4.1.2 Glass Cover Removal
The amorphous glass covered wires have many potential applications in electronics industry. It offers a lot of advantages due to the insulating glass cover. However, for some special applications, it is necessary to remove the glass cover of the wires. As said before, the glass cover will affect the domain structure of amorphous wires. The magnetization of amorphous wires after glass removal will be different, and lead to different value of permeability. We could obtain a higher sensitivity of measured magnetic quantity [43]. The glass removal process can provide a strong effect on the magnetic and mechanical properties. In this thesis, we also study the magnetic properties of glass removal wires. There are two methods of removing the cover. The first is a chemistry method, which uses aqueous HF solution to dissolve the glass cover, a method utilized for the first time by Taylor [40]. It is necessary to control the reaction time accurately, otherwise the amorphous wires will be destroyed due to the strong HF solution. The other method is to use a tool to rub off the glass cover from the wire under a microscope. Using aqueous HF solution will be more complex and difficult. In our experiment, we use the second method to remove glass cover.
4.2 Experiment Procedure
In experiments, we use a vector network analyzer to analyze signal transmission through amorphous wires. The vector network analyzer (VNA) is an essential tool which can be used to analyze the properties of electrical networks, especially those properties associated with the reflection and transmission of electrical signals known as scattering parameters and it is most commonly used in high frequency range. The range of operating frequencies is 10MHz to 12GHz.
The entire experiment is shown as follows.
Fig 4.3 Schematic structure of our experiments
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The sample in the circuit can be described by a two-port network equivalent circuit, as Fig 4.4.
There are 4 parameters Sij that are defined with the incident waves and reflected waves of input port and output port. S11, S12, S21 and S22 represent the input port voltage reflection coefficient, the reverse voltage gain, the forward voltage gain and the output port voltage reflection coefficient, respectively.
Fig 4.4 Two-port network equivalent circuit of wire sample
At port t1, the input voltage and reflected voltage could express as and , and at port t2, the input voltage is and , then the relationship between the input voltage and reflected voltage could be expressed as
1 11 1 12 2
VS VS V and V2S V21 1S V22 2 (4.1) Where
2
1 11
1 V 0
S V
V
1
1 12
2 V 0
S V
V
2
2 21
1 V 0
S V
V
1
2 22
2 V 0
S V
V
(4.2) The return attenuation (S11[dB]) which represent the magnitude of reflected signals and insertion attenuation (S21[dB]) which represent the magnitude of transmitted signals :
(4.3)
For the reciprocal network, |S12|=|S21|, for the symmetric network, |S11|=|S22|, for the non-loss network, |S11|2+|S12|2=1. In this experiment, it is easy to know that the sample belongs to reciprocal network and symmetric network, but loss exists. Assume loss power is symbol ploss, and the loss coefficient is
0
1
(4.4)The loss attenuation could be expressed as
(4.5) V1+ V1-
V2+ V2-
η
[dB]
Loss
11
[dB] 20log(
11)
S = S
21
[dB] 20log(
21)
S = S
loss in
p
p
2 2
11 12
[dB] 10log( ) 10log(1 ( ))
Loss
=
η= -
S+
S27
Chapter 5 5.1 Analysis
In the process of signal transmission, there will be three kinds of signals. Because of the impedance mismatch, there will be reflected signal generated from the interface. Both wire and ground plane have finite conductivity and will exhibit some series resistance, and therefore lead to heat loss. When there is electric field across the medium, the alternating polarization of medium molecular and lattice collision will generate heat loss. The wire-field structure is semi-open, causing radiation loss. The heat loss and radiation loss constitute loss signal. The remaining part of the signal which transfers through the wire could be called the transmitted signal.
Three aspects will be mainly considered in order to investigate the signal attenuation: The impact of frequency on signal attenuation, how direct current affects the signal attenuation, the comparison between glass removal wire and glass covered wire.
5.1.1 The characteristic analysis of signal attenuation
Fig 5.1 (a) The attenuation of reflected signals (S11[dB]) with frequency at different dc bias currents, d29m D, 69m l, 8.2cmglass covered wire (d is the metallic diameter and D is the diameter of wire with glass covered, l is the length of the wire
28
Fig 5.1 (b) The attenuation of loss signals (Loss[dB]) with frequency at different dc bias currents, d29m D, 69m l, 8.2cmglass covered wire
Fig5.1 (a) illustrates the changes of reflected signal which expressed by S11[dB] with signal frequency at different dc bias currents. Generally, S11[dB] curves show a reduced trend as the frequency increases and have cyclical change. Different curves have the same periodic change with frquency. The explanation for the reason of cyclical change is careful in the next section. The amplitude of curves increases with the increased current and frequency.
Fig5.1 (b) illustrates how the loss signal Loss[dB] changes with signal frequency at different dc currents. Generally for the wire, Loss[dB] curves show an increased tendency as the frequency increases. This is because high frequency will cause strong skin effect. This effect reduces the effective cross-sectional area of the wire, causing conductor loss to increase. Similarly, the curves show cyclical change with signal frequency. Loss[dB] increases with the increased frequency. As the signal frequency increases, the attenuation at different dc bias currents will tend to same constant value.
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Fig 5.2 The attenuation of transmitted signals (S21[dB]) with frequency at different dc bias currents, d29m D, 69m l, 8.2cmglass covered wire.
Fig 5.2 shows the changes of transmitted signal S21[dB] with signal frequency at different dc bias currents. In low signal frequency range, S21[dB] curves appear great changes with increased dc bias current. With the increase in signal frequency, the influence of current to S21[dB] curves gradually weakens. When the signal frequency is higher than 10GHz, there is no change in S21[dB]
for different dc bias currents. The periodic variation of S21[dB]curves will be more obvious as the dc bias current increases.
In the absence of dc bias current, the trends of S21[dB]curves with signal frequency can be expressed as Fig 5.3. We could see that the curve has a minimum value when signal frequency is 500MHz. Magnetization process consists of magnetic domain wall motion and domain rotation. At low frequency, the magnetic domain wall motion plays a major role on the magnetization process, while at higher frequency, the domain wall motion will be damped by the eddy current in amorphous wire and the domain rotation becomes more important. The increased signal frequency will increase the permeability. The increased signal frequency and permeability will enhance the skin effect and GMI effect, causing the impedance and attenuation increased. With further increase of signal frequency, the skin effect will not be enhanced any more, but the eddy current in amorphous wires will still damp the magnetization, causing a decline in permeability. This is not good for GMI effect. At extremely high frequency, the effective permeability will be reduced to a very small value, then the changes of permeability caused by magnetic field can be negligible, that is to say, the magnetic field doesn’t effect on the skin effect, resulting in the disappearance of GMI effect. When the dc bias current passes through, the current will obstruct the eddy current which is generated by high frequency, leading to inhibition of skin effect.
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Fig 5.3 In the absence of dc bias current, the attenuation of transmit signals with frequency
As known, all three kinds of attenuations show cyclical variation with frequency and the periodic frequency is near 1.6GHz. Under the condition that impedance matching, there is no reflected signal, and the magnitude of the voltage along the wire is constant, equal to . When the impedance is mismatched, a reflected signal will be generated. Then the incident and reflected signals could produce interference and generate a standing wave along the wire.
For a low-loss transmission line, the voltage at any point on the wire is given by
1 1
z z
V V e
V e
(5.1) Where , Γis the voltage reflection coefficient, by its definition, we can writeSo the magnitude of V is given by
2 2
1 1
| V | | V
||1 e
z| | V
||1 e
l|
(5.2) Wherel=-zis the position distance from port 2 to port 1 in Fig 5.4Letequal , then
(5.3)
This equation illustrates the value of fluctuating between maximum value , when and minimum value , when , here
nis an integer. These results show that maximum voltage occurs when the incident and reflected waves add in same phase and the minimum voltage occurs when they add in opposite phase, as Fig 5.4. Maximum and minimum voltages appear when the interval is , where is the wavelength.
2
|V1|el(1 | |)
|V|
2
l n
|V1|e2l(1 | |) l 2n 22 2
l
V V
| | e
j
|V1|
j
2 ( 2 )
1
2 2 2 12
| | | | |1 | | |
| | [(1 | |) 4 | | sin ( )]
2
l j l
l
V V e e
V e l
31
Fig 5.4 the schematic diagram for the transmitted and reflected signals in the wire
In Fig 5.2, wire length is , using the formula (3.20), we can get the effective dielectric constant , Hence,
(5.4)
This result is consistent with the curves. From this formula, we could also find that at a certain frequency, as the wire length changes, the signal attenuation will also show periodic variation. Fig 5.5 illustrates the changes of S21 with wire length at different frequencies. We could see that, somewhere between 4.2cm and 6.5cm, there will be a maximum value for S21.
Fig 5.5 Transmitted signal attenuation (S21[dB]) with wire length at different frequencies for
15.6 , 47 , 10.5
d m D m I mAwire
Consider the curve at frequency , we can get the wavelength
(5.5)
, when n=2, and l=5.10cm, then the attenuation of S21 is maximum.
Because of , which mean all the wavelength of them are multiples of 2.5GHz, therefore, using formula (5.5), all curves have the peak value l=5.10cm.
2 2.55
ln
n cmGHz GHz
. GHz GHz
. λ λ λ
λ25 =2 5 =3 75 =4 10 2.5 f GHz
e 5.5
8.2 l n l cm
8 9
0
3 10
20.78 10 [ ]
2
e2 8.2 10 5.5
f c Hz
l
8
2.5 9
3 10 5.1[ ]
2.5 10 5.5
GHz
e
c cm
f
32
5.1.2 Direct current effects on the signal attenuation
The process is shown in Fig 5.6. We control the dc current applied on both ends of the sample and try to find the relationship between current and transmitted signal attenuation. According to our requirements, if the control current has small change, the transmitted signal attenuation should have significant changes. There is some power consumption in wire at the process of current controlled. Obviously, lower dc power loss gives better amorphous wire transmission performances.
The transmission performances of amorphous magnetic wires can be judged by several factors, so we should find a way to compare the performances that contain those factors. We introduce a figure of merit (FOM) as follows in order to compare transmission performances.
1 1
Max Max
A I A
Q I p A p A
(5.6) Where is the ratio of attenuation change to current change, and it describes the sensitive of attenuation to the current, is the ratio of current vibration to power consumption vibration, is the maximum attenuation. Then, we can judge the wires’ performances, higher Q-value gives better transmission performances.
Here we can calculate the power consumption p. Fig 5.6 shows the schematic of current control circuit.
Fig 5.6 Schematic of Current control circuit
In the experiment, a series resistance (481Ω) is connected to the circuit. To calculate power consumption on samples, we should remove the power consumption in R.
pUII R2 (5.7) Where U is the voltage, I is the current applied on the sample, R is the series resistance.
We choose the wire with as an example. Base on the experimental results, use the FOM, we get the Q-value of this wire at different frequency as follow table.
Frequency 10MHz 100MHz 500MHz 1GHz 2.5GHz 5GHz 7.5GHz 10GHz 12GHz
sample 4.23 5.87 6.34 12.78 10.25 6.65 3.88 1.74 1.23
Table 5.1 the Q-values for the amorphous wire with .
( )
I ΔI ΔAΔp ΔI AMax
30 , 65 , 8.2 d m D m l cm
30 , 65 , 8.2 d m D m l cm
