Microwave Components Based on Magnetic Wires Technical report, IDE1057, November 2010

Microwave Components Based on Magnetic Wires  Technical report, IDE1057, November 2010
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
Sizhen Lan and Lian Shen
Microwave Components Based on
Magnetic Wires
Sizhen Lan and Lian Shen
M.Sc. Electrical Engineering, Halmstad University, 2010
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 S 21[dB] of an
amorphous wire increases monotonically with dc bias current, the empirical formula of attenuation
I I
with dc current is: A( I )  (8.686C d Z C ) ( R0  R1e 0 )[dB ]. 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.
Key Words
Microwave component, Amorphous magnetic wire, GMI effect, Domain structure, Permeability,
Impedance matching, Attenuator.
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
Chapter 1
1.1 Microwave Components
1.2 Amorphous Wires
Chapter 2
Magnetic Properties of Amorphous Metallic Wires
2.1 Magnetic Properties
2.1.1 The Magnetic Domain Structure
2.1.2 Zero-Magnetostrictive Effect
2.1.3 Co-Fe-based Amorphous Metal Wire’s Magneto-Impedance Effect
2.2 Giant Magneto Impedance (GMI) Effect and Skin Effect
Chapter 3
Transmission Line
3.1 Descriptions
3.2 Transmission Line Equation
3.3 Characteristic Impedance
3.4 Reflectance
3.5 Impedance Matching
3.6 Standing Wave
3.7 Microstrip Transmission Line
3.8 Attenuation of Amorphous Metallic Wires
Chapter 4
4.1 Wire Preparation
4.1.1 Amorphous Glass-Covered Wires
4.1.2 Glass Cover Removal
4.2 Experiment Procedure
Chapter 5
Analysis and Design
5.1 Analysis
5.1.1 The Characteristic Analysis of Signal Attenuation
5.1.2 Direct Current Effects on the Signal Attenuation
5.1.3 Amorphous Metallic Wire without Glass Cover
5.1.4 Impedance Matching Analysis
5.2 Design
5.2.1 Electronically Controlled Attenuators
Chapter 6
6.1 Conclusion
6.2 Future Work
Chapter 1
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.
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.
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 coefficient λ . 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 coefficient λ . 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 coefficient λ [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
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.
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].
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.
In a magnetic field, the impedance of the magnetic materials can be written as follows:
Z  R eff ( , H ex )   jX eff ( , H ex ) 
Where  is the angular frequency of the input,
is the external magnetic field [21].
is the effective permeability of materials, H ex
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].
R kr J 0 (kr ) J 1 (kr )
2 dc
(1 - j )
Here Rdc = 1 σ (πr 2 ) is the direct current resistance per unit length, J 0 (kr ) and J 1 (kr ) 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
1  1
(1  j )
 2 2r
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
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 e -1 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]:
 f 
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
Aeffective   r 2    r       2r   
The impedance of the wire is Z  R  j L , only consider R, we can get the resistance of wire
with length l:
 Aeffective
  2r   
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
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].
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
 dU ( z )  R  jL I ( z )dz
 dI ( z )  G  jC U ( z )  dU ( z )dz
Omit small higher-order, then:
 dU ( z )
 dz  RI ( z )  jLI ( z )
 dI ( z )  GU ( z )  jCU ( z )
 dz
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.
Differentiate z on the both sides of equation (3.2), we could obtain
 d 2U ( z )
dI ( z )
 dz 2    R  j L  dz
 2
 d I ( z )    G  jC  dU ( z )
 dz 2
Combine with equation (3.2), equation (3.3) could be rewritten as
 d 2U ( z )
 dz 2   R  j L  G  jC U ( z )   U ( z )
 2
 d I ( z )   R  j L  G  jC  I ( z )   2 I ( z )
 dz 2
 R  j L  G  jC 
The general section of equation (3.4) is:
U ( z )  A1e  z  A2e z
 z
 I ( z )  A3e  A4e
According to the first formula of equation (3.6) and equation (3.2), we could get
I ( z) 
R  j L
( A1e  z  A2e z ) 
( A1e  z  A2e z )
ZC 
R  j L
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
    j
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 ( R  G  0), we get
 0
   LC    
It explains that in the process of wave traveling there is no attenuation, and the wave moves with a
wavelength of 2 radians of phase delay. Here
 is the permeability and  is the permittivity.
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.
ZC 
R  j L
G  jC
At high frequency,that is ωL >> R , ωC >> G , then
ZC  L C
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 Z C = 1 νC , here v 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
3.4 Reflectance
When Z L ≠ Z C , 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 Γ = Γ e jψ , and the mode Γ remains
unchanged alone the line as the angle changes linearly. In the load (reflection points), the initial
value of ψ and Γ is only related with the ratio of Z C Z L .
The relationship between   z  and input impedance Z ( z ) = U ( z ) I ( z ) on z point in transmission
line is
( z ) 
Z ( z )  ZC
Z ( z )  ZC
When Z ( z ) |z  L  Z C , ΓL = 0 , 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.
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].
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  r . Three important
electrical parameters for microstrip line design should be noticed, they are the characteristic
impedance ZC, the guide wavelength g , 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]
αc =
and α d =
2Z C
And the total attenuation is given by
α = αc + α d
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  0 .
Ca 
2 0
ln 8H
4H 
Ca   0   1.393  0.667 ln   1.444   ,
Where C a is the capacitance of the unscaled air-filled line.
The effective dielectric constant
e 
 e for the microstrip line is given by
The characteristic impedance is given by
ZC 
 
 e 0 0 
There is an easier way to find
 0 0 1
 e Ca
 e . Schneider [38] deduced a quite simple formula for the effective
dielectric constant of a microstrip line which is illustrated at below.
  1   1  12 H 
 e  r  r 1 
2 
W 
 F   r , H   0.217( r  1) T
Where F  r , H   0.02  r  11  W H  for W H  1 and equals zero for W 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].
Rs  1 1 4 W 
 
W  2
T 
 10
The loss ratio (LR) is given by
LR  1
W 
LR  0.94  0.132  0.0062  
 10
0.5 
And the normalized series resistance RD of the ground plane is given by
RD 
W W H  5.8  0.03 H W
Rs is the skin-effect resistance which is equal to 1 (σδ ) ,  is skin depth and  is the conductivity
of wire. The total series resistance is the sum of RC and RD, so we can get
 c   c ,microstrip   c , groundplane   RC  RD  2Z C
In our experiment, because the attenuation caused by dielectric losses is very small, we only
consider the attenuation caused by conductor losses [38].
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
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 W  T  d, according formula (3.21), then we get
the normalized series distributed resistance for the wire is
Rs  1 1
  2 ln 4 
W  
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 constant α c is given by
A[dB]  20 L log e  8.686 L
-2 l
The power in length l is p  l   p  0  e , where p(0) is the input power. The attenuation of the
wire can be obtained as.
c 
Rs  LR  1 1
  2 ln 4  
Z c  W   
 H (W H  5.8  0.03 H W ) 
Chapter 4
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.
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
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,
Fig 4.4 Two-port network equivalent circuit of wire sample
At port t 1, the input voltage and reflected voltage could express as V1+and V1 , and at port t 2, the
input voltage is V2+ and V2 , then the relationship between the input voltage and reflected voltage
could be expressed as
V1  S11V1  S12V2 and V2  S21V1  S22V2
S11 
S12 
V2  0
S21 
V1  0
S22 
V2  0
V1  0
The return attenuation (S11[dB]) which represent the magnitude of reflected signals and insertion
attenuation (S21[dB]) which represent the magnitude of transmitted signals :
S11[dB] = 20log(S11 )
S21[dB] = 20log(S 21 )
For the reciprocal network, |S12|=|S21|, for the symmetric network, |S11|=|S22|, for the non-loss
network, |S 11|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 η is
0  1
The loss attenuation Loss[dB] could be expressed as
Loss[dB] = 10log(η) = 10log(1 - ( S11 + S12 ))
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, d  29 m, D  69 m, l  8.2cm glass covered wire (d is the metallic
diameter and D is the diameter of wire with glass covered, l is the length of the wire
Fig 5.1 (b) The attenuation of loss signals (Loss[dB]) with frequency at different dc bias
currents, d  29 m, D  69 m, l  8.2cm glass covered wire
Fig5.1 (a) illustrates the changes of reflected signal which expressed by S 11[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.
Fig 5.2 The attenuation of transmitted signals (S21[dB]) with frequency at different dc bias
currents, d  29 m, D  69 m, l  8.2cm glass 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 S 21[dB]
for different dc bias currents. The periodic variation of S 21[dB] curves will be more obvious as the
dc bias current increases.
In the absence of dc bias current, the trends of S 21[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.
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 | V1 |. 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
V  V1 e z  V1 e z
Where     j , Γ is the voltage reflection coefficient, by its definition, we can write   V  V 
So the magnitude of V is given by
| V || V1 ||1  e2 z || V1 ||1  e2 l |
Where l = -z is the position distance from port 2 to port 1 in Fig 5.4
Let  equal  |  | e j , then
| V || V1 | e 2 l |1 |  | e j (  2  l ) |
 | V  | e 2 l [(1 |  |) 2  4 |  | sin 2 (  l  )]
2 l
This equation illustrates the value of | V | fluctuating between maximum value | V1 | e (1 |  |),
when  l  2  n and minimum value | V1 | e 2 l (1 |  |), when  l  2  n   2, here
n is 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 l      2   2,
where  is the wavelength.
Fig 5.4 the schematic diagram for the transmitted and reflected signals in the wire
In Fig 5.2, wire length is l  n  l  8.2cm , using the formula (3.20), we can get the effective
dielectric constant  e  5.5 , Hence,
f 
 3 10
2l  e
2  8.2 102  5.5
 0.78 109 [ Hz ]
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 S 21.
Fig 5.5 Transmitted signal attenuation (S21[dB]) with wire length at different frequencies for
d  15.6 m, D  47 m, I  10.5mA wire
Consider the curve at frequency f  2.5GHz , we can get the wavelength
2.5GHz 
f e
3 108
 5.1[cm]
2.5 109 5.5
l  n 2  n  2.55cm , when n=2, and l=5.10cm, then the attenuation of S21 is maximum.
Because of λ2.5GHz = 2 λ5GHz = 3 λ7.5GHz = 4 λ10GHz , 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.
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
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.
A I 1
A 1
I p
Where ΔA(I ) ΔI is the ratio of attenuation change to current change, and it describes the sensitive
of attenuation to the current, ΔI Δp is the ratio of current vibration to power consumption
vibration, AMax 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
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.
p  UI  I 2 R
Where U is the voltage, I is the current applied on the sample, R is the series resistance.
We choose the wire with d  30 m, D  65 m, l  8.2cm 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.
Table 5.1 the Q-values for the amorphous wire with d  30 m, D  65 m, l  8.2cm.
From the above table, we could know sample have better performance at frequency 1GHz. We
choose this position as the analysis point. Fig 5.7 shows the transmitted signal attenuation change
with control current for different wires at frequency 1GHz.
Fig 5.7 Control current and transmitted signal attenuation (S21[dB]) for different
samples at 1GHz, d is the metallic diameter and D is the diameter of wire with glass
It is easy to see that S 21[dB] curves for four kinds of wires have similar trends. For a specific wire,
in the absence of current, the attenuation values of S 21 are minimums. When increasing current,
S21[dB] increases and the increment of S21[dB] decreases gradually. The reason for such change is
that as the controlled current increases, the magnetic field around the amorphous wire will change,
thereby weakening the magnetic permeability. The increase of skin depth leads to reduced
amorphous wire resistance, in turn causing the increase of S21[dB].
By some calculations, we try to deduce empirical formula in line with S 21[dB] curve. Using
formula (2.6) and skin-effect resistance, it’s easy to obtain the resistance R(I) which changes with
R( I ) 
Rs ( I )l
 (d   )
Rs is the skin-effect resistance which is equal to 1 (σδ ) ,  is the skin depth,  is the conductivity of
the wire, l is the wire length, d is the metallic diameter.
In the experiment, the frequency range is from 10MHz~12GHz, the skin depth  is very small
and produce a strong skin effect, d   , formula (5.8) can be approximated as:
R( I ) 
Rs ( I )l
Using formulas (3.27), (3.28) and (5.9)
R( I )  
Z c A( I )
8.686C d
Where A(I) is a function between attenuation and control current. For a certain wire ,at a given
frequency, ZC is the characteristics impedance, and
 LR  1 1
 1
 [m ]
  2 ln 4  
 H (W H  5.8  0.03 H W ) 
 W   
Choose sample with d  29 m, D  69 m, l  8.2cm. For the sample, which the height of the
substrate H  1.5 10 m and relative permittivity  r  4, through the formulas (3.16), (3.19),
(3.20), (3.22) and (3.27), we could obtain Z C  153 and C  1.93 104 m-1, then
R( I )  9.7 A( I )[]
The relationship between resistance and current is shown in Fig 5.8. Using Matlab, we could find
an appropriate but simple function as follows.
R( I )  [ R0  R1e
Where R0 , R1 , I 0 can be obtained from a certain curve, the unit of R0 , R1 are Ω, and I 0 is ampere.
Combine with the formula (5.10), we could find the relationship between attenuation and current.
A( I )  
8.686C d
( R0  R1e I0 )[dB]
For the sample, we could obtain:
R( I )  80  122e
[] and A( I )  [8.25  12.58e
Fig 5.8 Impedance and Current for d = 30μm, D = 65μm,l = 8.2cm wire
For the other wires, get the empirical formula and the parameters are demonstrated as follows
d, D (μm)
C (m-1)
ZC (Ω)
I0 (10-3 A)
2.88 x10
1.99 x10
1.93 x10
Table 5.2 The parameters of the empirical formula of each wire
5.1.3 Amorphous Metallic Wire without Glass Cover
As known, magnetic domain structure of amorphous metal wire is not only relevant to material
stress, but also relevant to the surface state of wire. Because glass and metallic core have different
expansion coefficients, there will be stress difference between them. The domain structures of
amorphous glass covered wire and the wire after glass removal should be different. The wires
without glass cover should have lower domain wall energy. At the same magnetic field, the wire
after glass removal will be more easily to be magnetized. This means that the permeability of wire
after glass removal is larger, so that the skin effect will be stronger and we could obtain larger
impedance and signal attenuation. Therefore, it affects the circumference permeability of
amorphous wire and further leads to changes in transmitted signal.
Fig 5.9 The attenuation of transmitted signals (S21[dB]) with frequency at different
currents for glass removal wire and glass covered wire
The comparison of S 21 for glass removal and for glass covered wire is demonstrated in Fig 5.9.
Generally, the curves have same trend of variation. In the absence of current and at a low signal
frequency, the magnitude of attenuation S 21 for glass removal is smaller than for glass covered. As
the current or frequency increases, S21 of glass removal and glass covered will approach. In order
to compare the performance of the two curves, we use the formula (5.6).
Choose the variation value of power consumption p from 0 to 70mV. Table 5.3 shows Q-value
for glass covered and glass removal wire at different frequencies.
Glass covered wire
Glass removal wire
Table 5.3 the Q-values for glass covered wire and glass removal wire
From the table, we found that at low frequencies, Q-values of glass removal wires are significantly
larger than that of the glass covered wire. That is to say, for glass removal wire, in this frequency
range, current play a great role on regulation of transmitted signal. With frequency increasing, the
two Q-values are gradually approaching.
5.1.4 Impedance matching analysis
From the preceding analysis we saw that the reflected signal was found to be much greater than
the transmitted signal,which is quite negative to signal transmission. As a result, we need to
consider reducing the reflected signals. The prevailing method is to make wire impedance equal to
transmission line characteristic impedance, so as to achieve impedance matching. Choose the
metallic radius 30μm wire as a sample. When there is no current applied, its impedance is about
200Ω which is much bigger than transmission line characteristic impedance. The impedance
mismatched causes strong reflection, so the main point is to make the load impedance as close to
50Ω as possible.
In order to achieve impedance matching, we need to adjust the value of the load impedance Z 1 by
coupling with inductor or capacitor in the circuit. As shown in Fig 5.10
Fig 5.10 Couple in capacitance and inductance, to achieve impedance matching
For our sample with d  30  m, D  65 m, l  7cm , the substrate dielectric constant is 3, and
thickness is 0.7mm. The condition of impedance matching is:
Z1 
1 L
Z0 C
For the chosen wire, the impedance of the wire Z 0 = 200Ω, and the transmission line characteristic
impedance Z C = 50Ω. We then get the following relationship between inductance and capacitance:
L[ H ]
C[ F ]
 1104 [2 ]
Choose an inductor 744760118C produced by Wurth company, whose inductance is 18nH, the
maximum current 500mA, maximum direct current resistance 200mΩ and self-resonant frequency
3.3GHz. According to formula (5.15), we use the capacitor with capacitance 1.8pF.
Through approximate impedance matching, we obtained results shown in Fig5.11
Fig 5.11 The attenuation of three signals with frequency, I=26mA
S21[dB] increases with signal frequency, reaches its maximum value at 640 MHz, then sharply
declines with increasing frequency. It reaches its minimum value at 2.5GHz, after which it will
increase slowly. A frequency of 640MHz thus makes the impedance matching better. In the
frequency range from 640MHz to 2.5GHz, a series of inductance in the circuit will obstruct high
frequency, and most of the signal is reflected. When the frequency is larger than the inductance
self-resonant frequency, the inductance parasitic capacitance leaks the signal through it.
Fig 5.12 (a) Measurement of S11[dB], S21[dB] and Loss[dB] with controlled current at f=640MHz.
Fig 5.12 (b) The load impedance in Fig 5.10 changes with controlled current at f=640MHz.
Figure 5.12 (a) illustrates that signals change with the controlled current. S21[dB] increases with
increasing dc bias current. When the current is larger than 10mA, it is larger than S11[dB], and the
minimum value of S21[dB] is close to -4dB. Using the formula (5.10), we can get the experimental
impedance of the combination with wire, inductors and capacitors as shown in Fig 5.12 (b). When
current is larger than 26mA, the load impedance Z 1 is approaching to 50Ω which is equal to the
transmission line characteristic impedance ZC and could be considered as impedance matching.
The expression of theoretical load impedance in Fig 5.12 (b) can be written as
R( I )  50  76.7e
Fig 5.13 the attenuation of S21 with the power consumption
Fig 5.13 demonstrates S21[dB] changes with the power consumption in the wire. In the range
0-70mW (when the current ranges from 0-26mA), S 21[dB] obviously changes, but when power
consumption is larger than 70mW, it doesn’t change significantly. Therefore, in the application, we
can set the controlled current below 26mA. Using the formula (5.6), the Q-value is 17.8.
5.2 Device
5.2.1 Electronically controlled attenuators
In a microwave system, it is necessary to couple in an attenuator in the system in order to control
the transmitted power, thus leading to better performance. There are two kinds of attenuators:
fixed attenuator and variable attenuator. For the fixed attenuator, the attenuation is constant and
for the variable attenuator, it could be adjusted within a certain range. The attenuator is a two-port
network, and the attenuation can be achieved in two ways. One is due to the internal dissipation in
the network, part of power will radiate as heat, then attenuation be achieved. This kind of
attenuation is called absorptive attenuation. At the network input port, the electromagnetic waves
will reflect, causing the power attenuation. This is the other way to achieve the attenuation and we
call it reflection attenuation.
At present, the microwave attenuator has been developed in a variety of structures. In addition to
attenuation resistor networks, electrically controlled attenuators based on PIN diodes also exist. In
the following we will discuss the advantages and disadvantages of using the amorphous wire as
electrically controlled attenuator component. The basic structure of the attenuator is shown in the
following Fig 5.14
Fig 5.14 Schematic of amorphous wires electronically controlled attenuator.
Where L=18nH, C=1.8pF, R=481Ω, I<26mA, the wire has the dimensions d  30 m, D  65 m
and l  7cm.
According to the analysis of Chapter 5.1.4,we concluded that a wire which is impedance matched
by capacitors and inductors has better performance.
From Fig 5.11 we know, that better transmission performance can be obtained at 640MHz. When
the control current is 26mA, we could obtain impedance matching. From this we determine the
attenuator work frequency range 500-700MHz.
Fig 5.15(a) Insertion loss (S21 [dB]) vs control current
Fig 5.15(b) Return loss (S11[dB]) VS. Control current
Both reflected attenuation and absorbed attenuation exist in the wire attenuator. When the current
is 26mA, the circuit is closed to impedance matching. Then from Fig 5.15(a) we know, the
insertion loss is -4.0dB to -5.0dB, from Fig 5.15(b), the return loss is -5.7dB to-7.7dB, the voltage
standing wave coefficient (VSWR) is less than 3.
Fig 5.16 The range of attenuation (the range between maximum value and minimum value of
attenuation) when the control current I<26mA at different frequencies
Fig 5.16 illustrates the range of attenuation, when the control current I<26mA, the magnitude of it
is between 5dB-7dB.
Fig 5.17(a) Variation of attenuation vs current
Fig 5.17(b) Variation of attenuation vs power consumption
Fig 5.17(a) demonstrates the variation of attenuation with control current. Generally the variation
is in line with A(dB)  4  6.13e  I 7.610 at 640MHz, and the range of control current is from
0-26mA. The power consumption is less than 70mW.
The previous results are in negative numbers, which actually are expressed as gain. For the
attenuator performance parameters, we should use attenuation to express them, then we drop the
minus sign as it is indicated by term loss in "Insertion Loss", "Return Loss" etc. So from the above
information, we can summarize the performance data as follows:
Insertion loss (I=26mA)
Characteristics of the attenuation
Control current
Control Voltage
Power consumption
Return loss (I=26mA)
Table 5.4 The specifications of wire attenuator
According to the range of work frequency, we choose the voltage variable attenuator type
SKY12328-350LF produced by Skyworks company as a comparison. The performance data sheet
of this attenuator is shown in the table below.
Insertion loss
0.5–1.0 GHz
Characteristics of the attenuation ®
0.5–1.0 GHz
Return loss
0.5–1.0 GHz
Control current
Control Voltage
Power Consumption
®. Characteristics of the attenuation include insertion loss.
Table 5.5 the specifications of voltage variable attenuator (Type: SKY12328-350LF),
Z 0 = 50Ω unless otherwise noted
Comparing the two attenuators, we can obtain the advantages and disadvantages of the wire
attenuator. The advantages include a simple structure and a current controlled tunable attenuation.
The disadvantages are small insertion loss, large return loss and VSWR, large control current, large
power consumption, and a relatively small range of attenuation. According to the application, we
choose the different wires or inductors and capacitors to adjust the attenuation value. These could
be applied in narrow-band electronic system.
Chapter 6
6.1 Conclusion
This thesis work focuses on an investigation of a current controlled microwave attenuator based
on amorphous metallic wires. We discuss the magnetic properties of the amorphous wires, such as
GMI effect and skin effect, as well as their relationship. In a series of experiments we invetigated
the influence of an applied direct current, signal frequency and the amorphous wire length on
reflected signals, loss signals and transmitted signal attenuation.
There are two kinds of amorphous wires used in the experiments. One is amorphous wires covered
with glass prepared by a high frequency induction heating melt spinning method. The other type
is amorphous wires where the glass has been removed by a mechanical rubbing technique.
The sample consists of an amorphous metallic wire, a copper ground plane and two connectors.
Based on the similarity between our samples and conventional microstrip lines, expressions for
the attenuation could readily be deduced.
According to the experiment results, some conclusions can be made:
1) In the process of signal transmission, signals can be divided into reflected signals, loss signals
and transmitted signals. The attenuation of these three signals exhibit the same periodic variation
with frequency, and the period frequency is fT=1.6GHz. Reflected signals will exist due to
impedance mismatch, and the incident and reflected signal will produce interference and generate
standing waves along the wire.
2) A figure of merit Q  A (p  AMax ) is introduced where larger Q indicates better transmission
performance. Best Q-value is achieved at 1GHz in the experiments. The transmitted signal
attenuations have similar trends for all types of wires, and in the absence of current , the signal
attenuation is lowest. With increasing DC control current the attenuation increases and attenuation
increment decreases gradually. The empirical formula in line with this curve is
A( I )  (8.686C d Z C ) ( R0  R1e  I I0 )[dB ] .
3) The glass cover will influence the magnetic domain structure in amorphous metallic wires.
Therefore, it will affect the circumference permeability and change the transmitted signal
attenuation. At low frequencies (f<7.5GHz), the Q-value of wires with removed glass cover is
larger than that of the glass covered wires. With increasing frequency, the two Q-values are
gradually approaching each other. For most frequencies, the DC current for glass removed wires
leads to a better control of the attenuation of the transmitted signal.
4) It is possible to impedance match the wire with a simple LC network also working as a
DC-block. Under impedance matched conditions, the transmitted signal attenuation increases with
signal frequency and reaches its maximum value at 640MHz. The minimum attenuation of S 21 is
close to 4dB. The theoretical impedance of wire is R( I )  50  76.7e 7.610 [].
5) The magnetic wires can be used as microwave attenuators with tunable transmission. The
frequency range spans from 500MHz to 700MHz. The circuit will achieve impedance matching
when the current is 26mA. The insertion loss is from -4.0dB to -5.0dB, the return loss is -5.7dB to
-7.7dB, the voltage standing wave coefficient VSWR is less than 3. The range of current is from
0-26mA. The power consumption is less than 70mW. In comparison between wire attenuators and
the commercial voltage controlled attenuator SKY12146-321, our design offers simplicity and
easily controlled attenuation. The disadvantage is the insertion loss, large return loss, large control
current, power consumption, and the relative small adjustable range of attenuation.
6.2 Future Work
On completion of the previous research, we propose the following further work.
1. Effects of external factors. To date, we have no comprehensive study about external factors
such as stress on the wire, temperature, etc. The external factors will affect magnetic
permeability, causing attenuation change. Because it is complex to control external factor, it
wasn’t researched completely in this paper.
2. Composition of amorphous metallic wires. The amorphous metallic wire with the composition
FeCoSiB is widely used, but it hard to say that it is the best one. The composition is the most
important factor to decide the property of wire, and we can try to find a better composition
which has better properties.
3. Improve the construction of microwave components. This thesis work focuses on the
attenuator. The circuit for the attenuator is not optimized, impedance matching is not complete,
and return losses are large.
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