A Development of a Common-Mode
Filter Using an EBG Structure in High
Speed Serial Links
YING-CHUN LAI
Master Thesis
Stockholm, Sweden 2012
XR-EE-ETK 2012:012
Master Degree Project in Electromagnetic Theory
A Development of a Common-Mode Filter
Using an EBG Structure in High Speed Serial
Links
September, 2012
Ying-Chun Lai
Supervisor: Ingvar Karlsson (Ericsson AB)
Examiner: Martin Norgren (KTH)
School of Electrical Engineering
Royal Institute of Technology (KTH)
Stockholm, Sweden 2012
Abstract
As signal speed increases and electronic products become progressively smaller,
the risks of electromagnetic radiation and interference are also heightened.
Ericsson’s SCXB, an Ethernet switch card, experiences exactly this problem,
with excessive emission levels probably caused by common-mode noise.
In this project, a common-mode filter using the electromagnetic bandgap
(EBG) structure has been designed and implemented in the SCXB. Unlike
conventional common-mode filters, the common-mode filter is embedded in
the printed circuit board (PCB) beneath the differential lines. The effect of
the common-mode filter is assessed by measuring the insertion loss and the
power radiation of a shielded cable connected to the common-mode filter.
A compact common-mode filter using an EBG structure has been proposed
in this project and this works effectively at 937.5 MHz. One of the results
from the parametric analysis shows that the common-mode filter is suitable
to work in a high frequency range due to the smaller structure and the wider
bandwidth range. The common-mode filter is constructed with the PCB
fabrication process. No additional components are necessary, although more
layers of the PCB’s stack up are required in which to embed the commonmode filter.
Contents
Abstract
Contents
I
List of Figures
III
List of Tables
VI
Abbreviation
VII
1 Introduction
1
1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Causes of Common-Mode Noise . . . . . . . . . . . . . . . . . 2
1.2.1 Asymmetric Routing . . . . . . . . . . . . . . . . . . . 5
1.2.2 Differing Rising/Falling Time . . . . . . . . . . . . . . 5
1.2.3 External EM-field . . . . . . . . . . . . . . . . . . . . . 6
1.3 Common-Mode Filter Techniques . . . . . . . . . . . . . . . . 7
1.3.1 Common-Mode Choke . . . . . . . . . . . . . . . . . . 7
1.3.2 Defected Ground Structure (DGS) . . . . . . . . . . . 8
1.3.3 The High-impedance Surface Electromagnetic Bandgap
(HIS-EBG) Structure . . . . . . . . . . . . . . . . . . . 9
1.4 Objective of the Thesis Project . . . . . . . . . . . . . . . . . 10
2 Principle of Coupled Lines
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Characteristic of Coupled Lines . . . . . . . . . . . . . . . . .
2.2.1 The Lumped Model of Coupled Lines in Per Unit Length
2.2.2 Even Mode . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Odd Mode . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Characteristic Impedance . . . . . . . . . . . . . . . .
2.2.5 The Differential Signal and the Common-Mode Signal
On the PCB . . . . . . . . . . . . . . . . . . . . . . . .
I
11
11
11
12
16
16
17
18
2.3
Network Analysis of Coupled Transmission Lines . . . . . . . 19
2.3.1 Two Port Network . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Mixed-mode Network . . . . . . . . . . . . . . . . . . . 22
3 Electromagnetic Bandgap Structure
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The Mushroom Type EBG Structure . . . . . . . . . . . . . .
3.2.1 The Equivalent Model of the Mushroom Type EBG
Structure . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 The Improvement of the Mushroom Type EBG Structure . . .
3.3.1 Inductance Increment . . . . . . . . . . . . . . . . . . .
3.3.2 Capacitance Increment . . . . . . . . . . . . . . . . . .
3.3.3 The Cascaded and the Double Stack-UP EBG structure
3.4 The Coplanar Type EBG Structure . . . . . . . . . . . . . . .
26
26
26
4 The Common-Mode Filter using the EBG Structure
4.1 The Structure of the Common-Mode Filter . . . . . . . . . . .
4.1.1 General Description . . . . . . . . . . . . . . . . . . . .
4.1.2 The EBG Structure with the Double Spirals . . . . . .
4.1.3 The PCB Stack-UP . . . . . . . . . . . . . . . . . . . .
4.1.4 The Specification of EBG Structure with Double Spiral
4.2 Analysis Methods for the Common-Mode Filter . . . . . . . .
4.2.1 S-parameter Measurement . . . . . . . . . . . . . . . .
4.2.2 Pseudo Common-Mode Signal Environment . . . . . .
4.3 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Resonant Frequency Error Correction . . . . . . . . . .
4.3.2 The Common-Mode Signal of the 10GBASE Ethernet .
4.3.3 The Power Radiation of a Shielded Cable Connected
the CM-Filter . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 The Differential Signal of the 10GBASE Ethernet . . .
4.3.5 The Mode-conversion of the 10GBASE Ethernet . . . .
4.4 Parametric Analysis . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 The Effect of the Patch’s Size and the Spiral Turns . .
4.4.2 The Effect of the Width of the Rectangular Patch . . .
4.4.3 The Effect of the Gap Distance Between Unit-Cells . .
4.4.4 The Effect of the Height of the EBG Structure . . . . .
33
33
34
34
35
35
36
36
37
40
40
42
5 Conclusion
61
II
28
29
29
29
30
31
45
47
51
52
52
54
56
57
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
GBN coupling between the power plane and the ground plane
The schematic of the ideal differential lines in ADS simulation
tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Input signals on ideal differential lines running with 2 Gbps
bit sequence (b) output signals (c) differential-mode signal (d)
common-mode signal . . . . . . . . . . . . . . . . . . . . . . .
(a) Input signals on the asymmetrical differential lines with
skew effect (b) output signals (c) differential-mode signal (d)
common-mode signal . . . . . . . . . . . . . . . . . . . . . . .
(a) Input signals with 0.05 ns difference in rising time on the
differential lines (b) output signals (c) differential-mode signal
(d) common-mode signal . . . . . . . . . . . . . . . . . . . . .
The power distribution network and the equivalent circuit in
package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Common-mdoe choke . . . . . . . . . . . . . . . . . . . . . . .
The typical defected ground structure and its equivalent model
The lumped model of three conductor transmission lines in
per unit length . . . . . . . . . . . . . . . . . . . . . . . . .
The trend of odd-mode and even-mode impedance varied with
line-to-line spacing [2] . . . . . . . . . . . . . . . . . . . . .
Fields in odd mode and even mode (a) electric field in odd
mode (b) electric field in even mode (c) magnetic field in odd
mode (d) magnetic field in even mode [2] . . . . . . . . . . .
The two port network of scattering parameter . . . . . . . .
The four port network of scattering parameter . . . . . . . .
The mixed-mode network of scattering parameter . . . . . .
2
3
4
5
6
8
8
9
. 12
. 19
.
.
.
.
20
21
23
23
The mushroom type of the EBG structure . . . . . . . . . . . 27
The demonstration of the capacitance and inductance of the
high-impedance surface structure . . . . . . . . . . . . . . . . 27
III
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
The lumped circuit model for the HIS-EBG embedded in the
power plane . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The HIS-EBG structure with (a) the shorting via meander (b)
the spiral pattern on the metal patch . . . . . . . . . . . . . .
The HIS-EBG structure with the high dielectric constant material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The cascaded HIS-EBG structure . . . . . . . . . . . . . . . .
The Double-Stacked EBG Structure . . . . . . . . . . . . . . .
The Coplanar EBG structures (a) the uni-planar compact
EBG structure[25] (b) the L-bridge EBG structure[26] (c) the
alternating impedance EBG structure[27] . . . . . . . . . . . .
The equivalent model of the unit-cell of the UC-EBG structure
The proposed common-mode implanted on the test board . .
The top view of the common-mode filter . . . . . . . . . . .
The stack up of the common-mode filter on the test board .
The specification of the EBG patch . . . . . . . . . . . . . .
The set up of the VNA measurement . . . . . . . . . . . . .
The schematic of the common-mode noise environment . . .
The illustration of the resonant frequency tuning strategy . .
The test board with the modified common-mode filter . . . .
The simulation of Scc21 for modified case comparison with
pre-modified board . . . . . . . . . . . . . . . . . . . . . . .
The measured Scc21 in comparison with HFSS simulation for
the common-mode filter . . . . . . . . . . . . . . . . . . . .
The measured Scc21 in the wide frequency range 10 MHz to
20 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The effects of common-mode filter for one and four differential
pair(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The two-port network with series element . . . . . . . . . . .
The electric field of the common-mode filter in common-mode
at first resonant 921.7 MHz . . . . . . . . . . . . . . . . . .
The demonstration of the power radiation measurement in the
reverberation chamber . . . . . . . . . . . . . . . . . . . . .
The power radiation of the shielded cable driven by commonmode signal with/without the common-mode filter . . . . . .
The measured Sdd21 for each differential pairs in wide frequency range . . . . . . . . . . . . . . . . . . . . . . . . . .
The eye diagram of a differential pair in 100 mm without the
common-mode filter . . . . . . . . . . . . . . . . . . . . . . .
IV
.
.
.
.
.
.
.
.
28
30
30
31
31
32
32
35
36
36
37
38
39
40
41
. 41
. 43
. 43
. 44
. 45
. 45
. 46
. 47
. 48
. 49
4.19 The eye diagram of a differential pair with the common-mode
filter (a) without FFE (b) with FFE . . . . . . . . . . . . . .
4.20 The eye diagram of a differential pair applied with the commonmode filter connected to the 500 mm TSR-491-602 cable (a)
without FFE (b) with FFE . . . . . . . . . . . . . . . . . . .
4.21 The electric field of the common-mode filter in differentialmode at the first resonant 921.7 MHz . . . . . . . . . . . . .
4.22 The measured Scd21 and Scd12 in wide frequency range . . .
4.23 The simulated model of the common-mode filter . . . . . . . .
4.24 The resonant frequency for common-mode signal versus the
dimension of the unit-cell . . . . . . . . . . . . . . . . . . . . .
4.25 The simulated model with w2 is variable . . . . . . . . . . . .
4.26 The trend of sweeping w2 for the cases with w1 = 1.3 mm,
4.3 mm, g is 0.2 mm and N = 1 . . . . . . . . . . . . . . . . .
4.27 The simulated model with g as variable . . . . . . . . . . . .
4.28 The trend of sweeping g for the cases with w1 is 1.3 mm, w2
is 0.7 mm and N = 1 . . . . . . . . . . . . . . . . . . . . . .
4.29 The Scc21 of sweeping g for the cases with w1 is 1.3 mm, w2
is 0.7 mm and N = 1 . . . . . . . . . . . . . . . . . . . . . .
4.30 The simulated model with h1, h2 as variable . . . . . . . . .
4.31 The trend of sweeping h1 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1 . . . . . . . . . . . . . . .
4.32 The Scc21 of sweeping h1 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1 . . . . . . . . . . . . . . . .
4.33 The trend of sweeping h2 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1 . . . . . . . . . . . . . . .
4.34 The Scc21 of sweeping h2 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1 . . . . . . . . . . . . . . . .
V
49
50
51
52
53
54
55
55
56
56
57
57
58
59
60
60
List of Tables
1.1
The description of the net name in the schematic . . . . . . .
2.1
2.2
The definition of the differential signal and the common-mode
signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
The variable description for the two-port network . . . . . . . 21
4.1
4.2
The summary of the design concept for the common-mode filter 34
The three groups in the measurement . . . . . . . . . . . . . . 38
VI
4
Abbreviation
EMI
EMC
EBG
PCB
HIS
GBN
SSN
PDN
DGS
UHF
LVDS
CM
VNA
RC
FFE
Electromagnetic Interference
Electromagnetic Compatibility
Electromagnetic Bandgap
Printed Circuit Board
High Impedance Surface
Ground Bounce Noise
Simultaneous Switch Noise
Power Distribution Network
Defected Ground Structure
Ultra High Frequency
Low Voltage Differential Signaling
Common Mode
Vector Network Analyzer
Reverberation Chamber
Feed Forward Equalizer
VII
Chapter 1
Introduction
1.1
Research Motivation
As the frequency of transmitted signal is increasing, the electromagnetic
emission of products becomes important to be examined before released. A
switching board called SCXB in Ericsson had existing electromagnetic compatibility (EMC) problem that the emission of SCXB is over the regulation.
The amount of the emission at 937.5 MHz is over the margin of regulation in
the Electromagnetic-field emission testing. After investigating, the emission
is suspected of common-mode noise on the 10GBASE Ethernet signal. The
10GBASE Ethernet is a serial link that transmitted by four parallel differential pairs.
The differential pair is commonly used for the high-speed signal transmission.
It gives the better signal performance but it will easily create the commonmode noise on the PCB. The differential pair fabricated on the PCB is hard
to be a symmetrical routing. The imperfect differential lines can cause the
common-mode noise and serious electromagnetic interference (EMI) problem
in the system.
The common-mode noise/current flowing in transmission lines generates emissions in the electrical system and leads to EMI problem as well as modeconversion. The mode-conversion is that more common-mode noise converts
into the differential-mode and vice versa. Therefore, it is essential to put
great emphasis on the common-mode noise issue in the high speed system
design.
The cause of the common-mode noise on the SCXB is probably the ground
bounce noise (GBN). Ground bounce noise is the high-frequency noise from
the power distribution network (PDN) that can degrade not only the power
integrity but also the signal integrity [1][2]. Figure 1.1 shows the illustration
1
CHAPTER 1. INTRODUCTION
of the GBN coupling to signal/ground by vias.
Overall, the SCXB suffers the EMC problem which origins from the commonmode noise. The goal of the thesis project is to investigate the common-mode
noise issue and to propose a solution to suppress the noise.
Figure 1.1: GBN coupling between the power plane and the ground plane
1.2
Causes of Common-Mode Noise
The greatest benefit of the differential lines is to give a better signal performance and to reject the noise. Ideally, the common-mode noise will be
cancelled out at the output side. However, the common-mode noise still be
a problem on PCB. The three major factors are the asymmetric routing of
the differential lines, the differing rising/falling time from the signal driver
and the external electromagnetic field, e.g. ground bounce noise (GBN) and
crosstalk [3][4].
Example: Ideal Case
Assuming that the data rate of input signal is 2 Gbps with rising/falling time
0.05 ns and the voltage amplitude is 1 V, the bit sequence transmits on the
ideal coupled lines. The impedance of the coupled lines in differential mode
is 100 Ω and the one in common-mode is 25 Ω. Also, both transmission lines
2
CHAPTER 1. INTRODUCTION
are terminated by 25 Ω.
Figure 1.2 shows the schematic of an ideal differential pair in simulation
software - ADS. The description of net name is shown in table 1.1.
The differential signal is the subtraction of the output signals on each coupled
lines, which can be written in
Sdd = 1p − 1n
On the other hand, the common-mode signal is the sum of the output signals
on each coupled lines, which is
Scc =
1
(1p + 1n)
2
As shown in Figure 1.3, the common-mode signal is zero level and the magnitude of the differential signal is two times the input one.
Figure 1.2: The schematic of the ideal differential lines in ADS simulation
tool
3
CHAPTER 1. INTRODUCTION
Table 1.1: The description of the net name in the schematic
Variables
In p
In n
1p
1n
Sdd
Scc
Description
Input signal on the positive transmission line
Input signal on the negative transmission line
Output signal on the positive transmission line
Output signal on the negative transmission line
Output differential-mode signal
Output common-mode signal
Figure 1.3: (a) Input signals on ideal differential lines running with 2 Gbps
bit sequence (b) output signals (c) differential-mode signal (d) common-mode
signal
4
CHAPTER 1. INTRODUCTION
1.2.1
Asymmetric Routing
The timing skew is caused by the the asymmetrical routing of the differential
pair. The asymmetrical routing is the difference in length between coupled
lines. It can result from the bend routing, the serpentine traces and the
incomplete ground plane.
Example: Timing Skew
The timing skew is simulated by adding 5 degree electrical length at 1 GHz
to one of the differential lines. The simulation result in Figure 1.4 shows
that the significant common-mode noise is generated due to the timing skew
signals.
Figure 1.4: (a) Input signals on the asymmetrical differential lines with skew
effect (b) output signals (c) differential-mode signal (d) common-mode signal
1.2.2
Differing Rising/Falling Time
The input signals with the different rising/falling time can cause commonmode noise. The input signal is generated from the IC driver which is difficult
to avoid by modifying routing of differential lines.
5
CHAPTER 1. INTRODUCTION
Example: Differing Rising/Falling time
This case can be simulated by setting the rising time of the input signals
is 0.05 ns and 0.1 ns on each differential lines. The difference of the rising
time is 0.05 ns. The simulated result in Figure 1.5 shows the common-mode
noise.
Figure 1.5: (a) Input signals with 0.05 ns difference in rising time on the
differential lines (b) output signals (c) differential-mode signal (d) commonmode signal
1.2.3
External EM-field
In a compact circuitry board, the signal traces and the power trances can
easily interfere with each others. The common external field on a PCB are
the crosstalk and the ground bounce noise. Moreover, the external EM-field
can simple cause the common-mode noise on the PCB.
Crosstalk
The crosstalk is that the EM-field of signal traces interact to each others.
The crosstalk can cause malfunctions on the electric circuit or electronic
products. For instance, a signal trace suffered the external EM-field can lead
6
CHAPTER 1. INTRODUCTION
to the signal distortion. Also, it causes common-mode noise when the differential pairs suffer the EM-field.
Ground Bounce Noise
Ground bounce noise is a phenomenon of the power/ground level fluctuation. It is resulted from the capability of the pull-up and pull-down transistors [1][5]. A typical power distribution network (PDN) contains IC chips,
decoupling capacitors and ferrite beads. The demonstration of the ground
bounce noise is shown in Figure 1.6. Once the transient current (dI/dt) flows
through the power bus containing the parasitic inductance (Lpwr ), it causes
the ground level variation which can be interpreted in
V = Lpwr
dI
dt
The parasitic inductances is from the bonding wires, the vias and the solder
balls. Once the wavelength of the high-frequency noise is comparable with
the dimension of power/ground planes, the noise will radiate outwards to
everywhere of the circuit board. Besides, the quality of the power distribution
network is also correlated to signal integrity; further, it will influence the
electrical system.
1.3
Common-Mode Filter Techniques
Researches on the common-mode noise suppression have been widely studied. The common-mode noise is known to cause the serious emissions. A
brief introduction to the current techniques of common-mode filters will be
given in this section.
1.3.1
Common-Mode Choke
The ordinary fashion to suppress CM-noise is to apply the common-mode
chokes, which is shown in Figure 1.7. The common-mode choke is a welldeveloped technique and already utilized on common-mode noise problem for
a long time[6]. It works well for the common-mode noise in Mega-hertz range.
Nevertheless, it is not suitable for the common-mode noise in Giga-hertz
range owning to the characteristic of the ferro-magnet. The permeability of
the ferro-magnet decreases rapidly as frequency becomes higher.
7
CHAPTER 1. INTRODUCTION
Figure 1.6: The power distribution network and the equivalent circuit in
package
Figure 1.7: Common-mdoe choke
1.3.2
Defected Ground Structure (DGS)
The defected ground structure (DGS) has been proposed to eliminate the
common-mode noise [7]. The design concept is based on the different return path between differential signal and common-mode signal. Accordingly,
DGS structure is an equivalent parallel LC resonator. The etched pattern is
8
CHAPTER 1. INTRODUCTION
designed on the return path of common-mode signal to degrade the commonmode signal. However, the dimensionof the DGS becomes larger when it is
operated below ultrahigh frequency (UHF) range. Also, the performance
of DGS degrades significantly when it is implanted in the multi-layer PCB;
hence, it is not practicable to be applied in the today’s product. Besides,
the etched pattern on the ground plane also affects power integrity on the
PCB. Figure 1.8 shows a typical defected ground structure and its equivalent
circuit model.
Figure 1.8: The typical defected ground structure and its equivalent model
1.3.3
The High-impedance Surface Electromagnetic Bandgap
(HIS-EBG) Structure
The HIS-EBG (High-impedance surface electromagnetic bandgap) is used
to apply in the antenna, power integrity and microwave application. Also,
the application on common-mode noise suppression is studied in recent [8][9].
The HIS-EBG is a periodic structure of which unit cell is composed of a patch
and a via connected to the ground plane. The structure can be regarded as an
LC resonator which behaves high impedance around the resonant frequency.
In other word, the HIS-EBG structure creates a bandgap that can prevent
electromagnetic wave to transmit. More details of the HIS-EBG structure
will be introduced in Chapter 3.
9
CHAPTER 1. INTRODUCTION
1.4
Objective of the Thesis Project
In this thesis project, the design of a common-mode filter is based on the
concept of the EBG structure which can prevent the common-mode noise
from transmitting on the differential pairs.
The major tasks can be summarized as follows:
1. The differential pairs and high-impedance surface structures should be
studied. Also, the effects of the common-mode filter using the HISEBG structure needs to be understood. Afterwards, pros and cons of
the method should be evaluated.
2. A compact common-mode filter for high-speed serial links, of which
resonant frequency is at 937.5 MHz, will be proposed. The bandwidth
is defined by Scc21 < −10dB in the project.
• First of all, a common-mode filter based on the EBG structure
that fulfils the requirement will be designed by using simulation
tool HFSS 1 .
• Secondly, the common-mode filter for the SCXB which is created
in Cadence Allegro PCB Editor Design needs to be implemented.
The unnecessary components will be removed from the SCXB to
give space for the common-mode filter as well as the connectors.
• Thirdly, the simulated 3D model will be created directly from
layout file by using Ansoftlinks and also the simulation results
will be verified with measurement ones.
3. The s-parameter of the common-mode filter will be measured by vector
network analyzer (VNA); also, the measured results will be analyzed
by using Mixed Mode Analyzer.
1
HFSS stands for High Frequency Structure Simulator which can be used to calculate parameters such as S-Parameters, Resonant Frequency, and Fields. It employs the
Finite Element Method (FEM), Integral Equation (IE) or Physical Optics (PO) solution
techniques to 3D EM problems.
10
Chapter 2
Principle of Coupled Lines
2.1
Overview
The low voltage differential signaling (LVDS) has become increasingly popular in digital circuit design for transmitting the high-speed signal. It has
been widely used in advanced electronics and high speed transmission cables,
such as 10GBASE Ethernet, SATA3.0 and USB3.0. The benefit of using the
differential lines is the common-mode noise rejection that cancels the external noise and further improves the signal quality.
In this chapter, the theory of the coupled transmission lines will first be
introduced by presented mathematically. The definition of even-mode and
odd-mode will be explained. Next, the behavior of the differential pair routed
on the PCB will be discussed. Subsequently, the scattering parameter will
be explained explicitly and then the mixed-mode analysis will be introduced.
It is of central importance to analyze the common-mode filter in this project.
2.2
Characteristic of Coupled Lines
Once two transmission lines are put closely together, the electromagnetic field
between the transmission lines will alter according to the different incident
modes [10][11]. The two incident modes on the coupled line are odd-mode
and even-mode. The odd mode is that the two coupled lines are driven by
same amplitude voltage with 180 degree out of phase signals. Contrariwise,
the even mode is that the two coupled line are driven by same amplitude
voltage with in phase signal.
11
CHAPTER 2. PRINCIPLE OF COUPLED LINES
2.2.1
The Lumped Model of Coupled Lines in Per Unit
Length
The coupled transmission lines can be modeled by the self-inductance of
conductor 1 (l1 ), the self-inductance of conductor 2 (l2 ) and mutual inductance (lm ). Furthermore, the self-capacitance of conductor 1 (c1 ), the selfcapacitance of conductor 2 (c2 ) and mutual capacitance (cm ). Figure 2.1
demonstrates the model of the coupled lines in per unit length.
Figure 2.1: The lumped model of three conductor transmission lines in per
unit length
The current flows through on a capacitor conforms to
I=C
dV
dt
Hence, the current flow on the per-unit-length transmission line are
dV1 (z + ∆z, t) dV2 (z + ∆z, t)
I3 = cm ∆z
−
dt
dt
dV1 (z + ∆z, t)
dt
dV2 (z + ∆z, t)
I5 = c2 ∆z
dt
I4 = c1 ∆z
12
!
(2.1a)
(2.1b)
(2.1c)
CHAPTER 2. PRINCIPLE OF COUPLED LINES
According to Kirchhoff’s law, Equation (2.1) can be written into
dV1 (z + ∆z, t)
dV2 (z + ∆z, t)
I3 + I4 = ∆z (c1 + cm )
− cm
dt
dt
= I1 (z, t) − I1 (z + ∆z, t)
dV2 (z + ∆z, t)
dV1 (z + ∆z, t)
I5 + I3 = ∆z (c2 + cm )
− cm
dt
dt
= I2 (z, t) − I2 (z + ∆z, t)
(2.2)
Corresponsively, the voltage across a inductor conforms to
V =L
dI
dt
Hence, the voltage across on the per-unit-length transmission line is
dI1 (z, t)
dI2 (z, t)
+ lm ∆z
dt
dt
dI2 (z, t)
dI1 (z, t)
V2 (z, t) − V2 (z + ∆z, t) = l2 ∆z
+ lm ∆z
dt
dt
V1 (z, t) − V1 (z + ∆z, t) = l1 ∆z
(2.3)
To achieve a limitation of the ∆z, Equation (2.2) (2.3) are first divided by
∆z. Next, let ∆z → 0. The formula can be written as
dV1
dz
dV2
dz
dV1
dz
dV2
dz
dI1
dI2
− lm
dt
dt
dI2
dI1
= −l2
− lm
dt
dt
dV1
dV2
= −(c1 + cm )
− cm
dt
dt
dV2
dV1
= −(c2 + cm )
− cm
dt
dt
= −l1
Generalized Equations of the Transmission Lines
Introduce the new parameters,
L11 = l1
L22 = l2
L12 = L21 = lm
C11 = c1 + cm
C22 = c2 + cm
C12 = C21 = −cm
13
(2.4a)
(2.4b)
(2.4c)
(2.4d)
CHAPTER 2. PRINCIPLE OF COUPLED LINES
The equations for the per-unit-length transmission lines can have a generalized format as shown below
d
d
V (z, t) = −L I(z, t)
(2.5)
dz
dt
d
d
I(z, t) = −C V (z, t)
(2.6)
dz
dt
where, V1 (z, t)
V (z, t) =
: voltage vector
V2 (z, t)
I (z, t)
I(z, t) = 1
: current vector
I
2 (z, t)
L11 L12
L=
: inductance matrix in per unit length
L21 L22 C11 C12
C=
: capacitance matrix in per unit length
C21 C22
Quasi-TEM Mode
The wave propagating in two different phase velocity between two mediums
is termed as quasi-TEM. Moreover, the dominant mode of microstrip line is
quasi-TEM mode. The microstrip line is the example to illustrate the mode
because EM wave propagates both in substrate and air. Furthermore, for
the case of coupled microstrip lines, the wave propagates in two quasi-TEM
modes due to two conductors. The quasi-TEM mode should tally with the
properties of LC matrices shown below
1. Symmetric, Lij = Lji and Cij = Cji
2. Positive-definite, L > 0 and C > 0
3. All Lij > 0
4. Diagonal element Cii > 0
5. Off-diagonal elements Cij ≤ 0(i 6= j)
Time Dependence
The voltage and current both vary with time and location which are dependent on ejωt and e∓jβz . Hence, the Equation (2.5) and (2.6) can be formulated in frequency-domain by letting d/dt → ∓, jω d/dz → ∓jβ shown
below
(2.7)
∓ jβV = −ωLI
14
CHAPTER 2. PRINCIPLE OF COUPLED LINES
∓ jβI = −ωCV
(2.8)
Further, Equation (2.8) can be re-formulated into
±I =
ω
CV
β
(2.9)
After substituting Equation (2.9) into Equation (2.7), the new equation turns
into an Eigen value problem
βn2
LC − 2 Vn = 0
(2.10)
ω
And vice versa,
βn2
CL − 2 In = 0
ω
(2.11)
Next, the eigenvector V , I are related to
Vn = ZIn
In = YVn
of which the characteristic impedance/admittance matrix is Z =
Y−1 [12].
√
LCC−1 =
Coupled Microstrip Lines Case
For applying the related equations on the case of two coupled micro-strip
lines, we first assume the inductance and capacitor matrices are
L1 L2
L=
L2 L1
C1 −C2
C=
−C2 C1
Therefore,
LC = CL
L1 C1 − L2 C2 L2 C1 − L1 C2
a b
=
=
L2 C1 − L1 C2 L1 C1 − L2 C2
b a
15
(2.12)
CHAPTER 2. PRINCIPLE OF COUPLED LINES
,where a2 − b2 > 0 determined by positive-definite.
Secondly, the voltage eigenvalue equation can be written in


β2
2
b  V1 β
a − ω 2
LC − 2 V = 
=0
β 2  V2
ω
b
a− 2
ω


β2
b  I1 β2
a − ω 2
CL − 2 I = 
=0
β 2  I2
ω
b
a− 2
ω
The non-trivial solution can be derived as
2
β2
β2
a − 2 − b2 = 0 =⇒ 2 = a ± b > 0
ω
ω
2.2.2
(2.13)
(2.14)
(2.15)
Even Mode
After substituting one of the solution from Equation (2.15) into equation
(2.13), the eigenvalue equation can be written as
−1 1
V1
b
=0
1 −1 V2
The determinant should answer to V1 = V2 for conforming the eigenvalue
equation; similarly, the Equation (2.14) may be applied by the same manner
that give a solution I1 = I2 .
The solution from β 2 /ω 2 = a + b is so called Even-Mode. The wave number
is
√
βe = ω a + b
Eigenvector:
1
Ve = Ve
1
1
Ie = Ie
1
2.2.3
(2.16)
(2.17)
Odd Mode
By the same token, after substituting the another solution from Equation
(2.15) which is β 2 /ω 2 = a − b results in the eigenvalue equation
1 1 V1
b
=0
1 1 V2
16
CHAPTER 2. PRINCIPLE OF COUPLED LINES
The determinant should tally with V1 = −V2 for conforming the eigenvalue
equation; similarly, the Equation (2.14) may be applied by the same manner
that give a solution I1 = −I2 .
The solution from β 2 /ω 2 = a − b is called Odd-Mode. The wave number is
√
βo = ω a − b
Eigenvector:
1
Vo = Vo
−1
1
Io = Io
−1
2.2.4
(2.18)
(2.19)
Characteristic Impedance
The characteristic impedance is different between even-modes and odd-mode
because the mutual inductance and mutual capacitance
is changed with difZ1 Z2
ferential driven mode. Assuming that Z =
, the impedance maZ2 Z1
trix Z should follow the same properties as LC matrices that Z1 > 0 and
Z1 > |Z2 |.
• Even-Mode:
Z1 Z2
1
I
ZIe =
Z2 Z1 e 1
1
= Ie (Z1 + Z2 ) = Ve
1
Characteristic Impedance :
Zeven = Z1 + Z2
(2.20)
• Odd-Mode:
Z1 Z2
1
I
ZIo =
Z2 Z1 o −1
= Ie (Z1 − Z2 ) = Vo
1
−1
Characteristic Impedance :
Zodd = Z1 − Z2
17
(2.21)
CHAPTER 2. PRINCIPLE OF COUPLED LINES
2.2.5
The Differential Signal and the Common-Mode
Signal On the PCB
A differential pair is composed of two coupled transmission lines. Compared
to odd-mode and even-mode, the term of differential signal and commonmode signal are often seen. The driven mode of the differential signal is the
odd-mode. Differential signal is defined as the subtraction of output signal
on each coupled lines. However, the definition of impedance is different. The
impedance of differential signal is the twice of the characteristic impedance
in odd mode.
On the other hand, the driven mode of the common-mode signal is the evenmode. Also, the common-mode signal is the half of the summation of output signal on each coupled lines. However, the definition of impedance of
common-mode signal is defined as half of the impedance in even mode. The
definition of the differential and common-mode signal is summarized in Table
2.1.
Table 2.1: The definition of the differential signal and the common-mode
signal
Differential signal
Common-mode signal
Voltage (signal)
Impedance
+
−
Vdif f = Voutput
− Voutput
Zdif f = 2Zodd
Vcomm =
1
+
−
Voutput
+ Voutput
2
Zcomm =
Zeven
2
On the PCB, the odd-mode and even-mode impedance is varied with the
line-to-line spacing. The impedance in both modes approach to single-line
impedance Z0 as the spacing is larger. The coupling in line-to-line is lesser
and transmission lines will strongly couple to the ground plane. Besides, the
odd-mode impedance is always lower than the impedance of the single-end
line; on the other hand, the even-mode impedance is always higher than the
impedance of the single-end line. Figure 2.2 shows the trend of impedance
in odd-mode and even-mode varied with line-to-line spacing.
Due to the different driven signals, the electromagnetic field of differential
signal is distinct from common-mode signal. Figure 2.3 shows the electromagnetic field on odd mode (differential signal) and even mode (common-mode
18
CHAPTER 2. PRINCIPLE OF COUPLED LINES
Figure 2.2: The trend of odd-mode and even-mode impedance varied with
line-to-line spacing [2]
signal) for microstrip differential lines on printed circuit board.
2.3
Network Analysis of Coupled Transmission Lines
Scattering parameters are used to describe how voltages and current are
reflected and transmitted in an electrical network [13]. It is able to describe
the normalized power wave when the input and output ports are terminated
and also used to express other electrical properties such as insertion loss,
return loss as well as voltage standing ratio.
The definition of the n-port network is
 − 
  +
V1
S11 S12 · · · S1n
V1
V −   S21 S22 · · · S2n  V + 
 2  
 2 
 ..  =  ..
..
..   .. 
.
.
 .   .
.
.
.  . 
−
Vn
Sn1 Sn2 · · · §nn
Vn+
S-parameter is defined by the ratio of voltages; however, the ratio defined by
power is more practical in measurement technique. The s-parameter can be
simply taken square to achieve the s-parameter power because the power is
2
Pn+ = |Vn+ | /2Zn for giving voltage Vn+ . The reference impedance is defined
19
CHAPTER 2. PRINCIPLE OF COUPLED LINES
Figure 2.3: Fields in odd mode and even mode (a) electric field in odd mode
(b) electric field in even mode (c) magnetic field in odd mode (d) magnetic
field in even mode [2]
as Zn = Vn+ /In+ .
2.3.1
Two Port Network
Two-port network is the simplest case to give introduction. Figure 2.4 shows
the two-port network [13][14]. Also, V1− V2− is the reflected wave each at port
1 and port 2. The input impedance at port 1 and port 2 are each defined
as Zin1 , Zin2 . V1+ V2+ is the incident wave each at port 1 and port 2. The
description of the variables is shown in table 2.2. As mentioned in above
section, the s-parameter is determined by the ratio of voltages. Equation
(2.22) is the definition of the two-port network.
− V1
S11 S12 V1+
=
(2.22)
V2−
S21 S22 V2+
Interpretation:
V1− : the reflection factor in port 1 when port 2 is matched that
V1+ V2+ =0
V2+ = 0
S11 =
20
CHAPTER 2. PRINCIPLE OF COUPLED LINES
Table 2.2: The variable description for the two-port network
Variables
V1+
V1−
V2+
V2−
Z1
Z2
Zin1
Zin2
Description
Incident wave at port 1
Reflected wave at port 1
Incident wave at port 2
Reflected wave at port 2
Characteristic impedance of the system at port 1
Characteristic impedance of the system at port 2
Input impedance at port 1
Input impedance at port 2
Figure 2.4: The two port network of scattering parameter
S22
V2− = +
: the reflection factor in port 2 when port 1 is matched
V2 V1+ =0
that V1+ = 0
V2− : the transmission factor from port 1 to port 2 when port
V1+ V2+ =0
2 is matched that V2+ = 0
S21 =
V1− : the transmission factor from port 2 to port 1 when port
V2+ V1+ =0
1 is matched that V1+ = 0
S12 =
Normalization
It is more convenient to normalize the s-parameter by using the characteristic impedance for practical applications. The definition of the normalized
21
CHAPTER 2. PRINCIPLE OF COUPLED LINES
s-parameter is listed below:
Interpretation:
√
V1− / Z1
s11 = + √
V1 / Z1
√
V2− / Z2
s22 = + √
V2 / Z2
√
V2− / Z2
s21 = + √
V1 / Z1
√
V1− / Z1
s12 = + √
V2 / Z2
v − V2+ =0 = 1+ +
v1 v2 =0
v2− V1+ =0 = + +
v2 v1 =0
v2− +
=
V2 =0
v1+ v2+ =0
v − V1+ =0 = 1+ +
v1 v1 =0
For the case Z1 = Z2 = Z0 , the s-parameter is independent of Z0 and also
conforms to the following rules.
• Reciprocal if s12 = s21
• Matched if s11 = s22 = 0
• Lossless if [sT ][s∗ ] = [U ] ,that [U ] is identity matrix
2.3.2
Mixed-mode Network
One differential pair is a four-port network which is shown in Figure 2.5;
however, it is hard for us to analyze the behavior of the differential pair
system directly from the four-port network. Hence, the mixed-mode network
is proposed that is shown in Figure 2.6 [15][16][17]. It gives the connection
from unitary driven network (the four-port network) to the odd/even -mode
driven network (the mixed-mode network). Thereby, it provides a straightforward manner to analyze the modes propagating on differential pair. It
describes all properties of coupled lines that are
- Differential signal Sdd
- Common-mode signal Scc
- Mode-conversion from common-mode signal to differential signal Sdc
22
CHAPTER 2. PRINCIPLE OF COUPLED LINES
- Mode-conversion from the differential signal to common-mode signal
Scd
The mixed-mode s-parameter can be derived by the numerical computations.
The following states the procedure to achieve the mixed-mode s-parameter.
Figure 2.5: The four port network of scattering parameter
Figure 2.6: The mixed-mode network of scattering parameter
The four-port network is defined as:
  
b1
S11 S12
b2  S21 S22
 =
b3  S31 S32
b4
S41 S42
S13
S23
S33
S43
 
S14
a1


S24  a2 

S34  a3 
S44
a4
In addition, the mixed-mode network of a differential pair is
 
  
bd1
Sdd11 Sdd12 Sdc11 Sdc12
ad1
bd2  Sdd21 Sdd22 Sdc21 Sdc22  ad2 
 =
 
bc1  Scd11 Scd12 Scc11 Scc12  ac1 
bc2
Scd21 Scd22 Scc21 Scc22
ac2
23
(2.23)
(2.24)
CHAPTER 2. PRINCIPLE OF COUPLED LINES
(ad1 , ad2 ) are the incident wave in odd mode and (ac1 , ac2 ) are the incident
wave in even mode. Moreover, (bd1 , bd2 ) are the reflected wave in odd mode
and (bc1 , bc2 ) are the reflected wave in even mode. Hence, the relations between the four-port network (2.23) and the mixed-mode network (2.24) are
  
 
bd1
1 −1 0 0
b1
bd2  0 0 1 −1 b2 
 =
 
bc1  1 1 0 0  b3 
bc2
0 0 1 1
b4
  
 
ad1
1 −1 0 0
a1
ad2  0 0 1 −1 a2 
 =
 
ac1  1 1 0 0  a3 
ac2
0 0 1 1
a4
(2.25a)
(2.25b)
Next, assuming the matrix


1 −1 0 0
0 0 1 −1


1 1 0 0  = M
0 0 1 1
Then, after substituting (2.23) into (2.25), the new equation can be expressed
as
  
bd1
S11



b
d2 
S21
M−1 
bc1  = S31
bc2
S41
S12
S22
S32
S42
S13
S23
S33
S43

 
S14
ad1


S24 
a
 M−1  d2 
ac1 
S34 
S44
ac2
(2.26)
The equation (2.26) can be formulated to tally with the equation (2.24).
Furthermore, the mixed-mode s-parameter is derived by the four-port s24
CHAPTER 2. PRINCIPLE OF COUPLED LINES
parameter. The result of numerical computation is shown below:
 


 
bd1
S11 S12 S13 S14
ad1
bd2 
S21 S22 S23 S24  −1 ad2 
  = M

 
bc1 
S31 S32 S33 S34  M ac1 
bc2
S41 S42 S43 S44
ac2

S11 − S12 − S21 − S22 S13 − S14 − S23 + S24
S31 − S32 − S41 + S42 S33 − S34 − S43 + S44
= 0.5 
S11 − S12 + S21 − S22 S13 − S14 + S23 − S24
S31 − S32 + S41 − S42 S33 − S34 + S43 − S44
 
S11 + S12 − S21 − S22 S13 + S14 − S23 − S24
ad1


S31 + S32 − S41 − S42 S33 + S34 − S43 − S44  ad2 

S11 + S12 + S21 + S22 S13 + S14 + S23 + S24  ac1 
S31 + S32 + S41 + S42 S33 + S34 + S43 + S44
ac2
 

ad1
Sdd11 Sdd12 Sdc11 Sdc12
Sdd21 Sdd22 Sdc21 Sdc22  ad2 
 
=
Scd11 Scd12 Scc11 Scc12  ac1 
Scd21 Scd22 Scc21 Scc22
ac2
25
(2.27)
Chapter 3
Electromagnetic Bandgap
Structure
3.1
Overview
The Electromagnetic bandgap (EBG) structure is a periodic structure that
can prevent electromagnetic wave to transmit. The EBG structure seizes
attention owning to its ability of blocking electromagnetic mode transmission
and radiation in microwave and millimeter waves. At the first start, it is
mainly applied to improve the antenna design, for instance, to suppress the
crosstalk between antennas, to improve the impedance matching of the lowprofile antenna and to enlarge the gain of the antenna. Afterwards, the
EBG structure is drawn on electromagnetic compatibility (EMC) area. It
is embedded in the power/ground plane for improving the power integrity
as well as electromagnetic interference (EMI). It gives a significant effect
of suppressing ground bounce noise (GBN) and simultaneous switch noise
(SSN). Further, it is also be implemented for solving signal integrity problem
e.g. common-mode noise.
In this chapter, the typical EBG structure will be introduced; further, the
minimization of the EBG structure and the coplanar EBG structure will be
presented.
3.2
The Mushroom Type EBG Structure
Mushroom structure is a typical electromagnetic bandgap (EBG) structure
which is shown in Figure 3.1 [18][19][20]. Its unit cell is composed of a patch
and a via that connects to the ground plane. The unit cell is placed periodically on the ground plane. The mushroom structure is also called high
26
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
impedance surface (HIS) structure because the surface impedance will become very high while applying the mushroom structure to the metal plane.
Figure 3.1: The mushroom type of the EBG structure
The high impedance is resulted from resonance of the EBG structure. As
shown in Figure 3.2, the voltage across the parallel patch is capacitive which
can be modeled by a capacitor. Also, the current flowing through the path
with a via and the ground plane is related to the magnetic field so that it is
modeled by an inductor. Hence, the HIS structure is like an LC resonator
in the specific frequency range. In the specific frequency range, the surface impedance becomes very high and also the electromagnetic wave cannot
transmit.
Figure 3.2: The demonstration of the capacitance and inductance of the
high-impedance surface structure
27
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
3.2.1
The Equivalent Model of the Mushroom Type
EBG Structure
From the circuit of view, the HIS-EBG structure can be analyzed by making
the lump circuit model [21]. As mentioned, it is widely applied to suppressing the undesired noise in power distribution network. The equivalent model
of the HIS-EBG in power plane is shown in Figure 3.3.
Figure 3.3: The lumped circuit model for the HIS-EBG embedded in the
power plane
The height (t1 ) between the mushroom’s patch and the power plane is capacitive because the voltage difference is created between the two metal plates.
It is modeled by the capacitor C1 which is approximately
ε0 εr d 2
C1 =
t1
(3.1)
where
εr : effective dielectric constant in t1 and t2
d : width of the patch
t1 : distance between the power plane and the patch
Further, the current flows through the via modeled by the inductor L1 is
approximately
µ0 t2
1
ln
+α−1
(3.2)
L1 =
4π
α
where
t2 : the distance between the patch and the ground plane
πa2
α = 2 : the ratio of the cross section of via to the one of unit cell
d
28
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
Therefore, the unit cell of the HIS-EBG structure is like a series LC resonator. Also, the lower cut-off frequency can be written as
1
flower = s (3.3)
µ0 h
2π C1 L1 +
4
where h = t1 + h2
Accordingly, the stopband frequency of the HIS-EBG can be determined by
the C1 L1 that is related to the geometry of the unit-cell structure.
3.3
The Improvement of the Mushroom Type
EBG Structure
Several novel HIS-EBG structures have been proposed to broaden the bandwidth and to minimize the HIS-EBG structure. One of the stratagies is to
lower the cut-off frequency of the HIS-EBG structure. The way of the stopband frequency shift is according to the Equation (3.3). It gives hints to
increase C1 L1 . The capacitance of C1 can be increased by enlarging the
dimension of the patch; also, the inductance of L1 can be increased by extending the length of the via. However, the enlarged HIS-EBG structure is
not practical to be implanted in products, neither on antennas nor in PCBs.
In view of the concerns, many methods to improve the HIS-EBG structure
are proposed.
3.3.1
Inductance Increment
The methods of flower shift by increasing L1 are proposed; for instance, the
meander of the shorting vias as well as the etched spiral pattern of the metal
patch which are shown in Figure 3.4 [22]. The methods both increase the
inductance by adding up additional path for the return current. Besides, it
gives a significant amount of the inductance increment.
3.3.2
Capacitance Increment
Furthermore, the method of the capacitance C1 increment is proposed that is
to insert the high-dielectric constant thin film into the substrate of the PCB
29
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
Figure 3.4: The HIS-EBG structure with (a) the shorting via meander (b)
the spiral pattern on the metal patch
which is shown in Figure 3.5 [23]. The capacitance is proportional to the
dielectric constant known from the Equation (3.1). Hence, inserting a high
dielectric constant thin-film into the substrate of the PCB between the power
plane and metal patch can increase C1 without the dimension enlargement
of the HIS-EBG structure.
Figure 3.5: The HIS-EBG structure with the high dielectric constant material
3.3.3
The Cascaded and the Double Stack-UP EBG
structure
To cascade different dimensions of the HIS-EBG is able to broaden the bandwidth. The EBG structure is shown in Figure 3.6 [24]. The method is to
design two different unit-cells of the EBG structure that one covers higher
frequency range and another one covers lower frequency range. It can widen
30
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
the bandwidth by cascading the two unit cells properly. However, the total
dimension of the structure becomes larger by using the method.
Figure 3.6: The cascaded HIS-EBG structure
Afterwards, the doubled-stacked EBG structure is proposed to solve the problem which is shown in Figure 3.7. It integrates two EBG structures with the
different dimensions vertically. The electromagnetic wave transmits through
the EBG structure that gives the wider bandwidth.
Figure 3.7: The Double-Stacked EBG Structure
3.4
The Coplanar Type EBG Structure
The coplanar type EBG structures are periodic etching pattern on the power
or the ground plane [25][26][27]. The coplanar EBG structure is designed on
the 2-dimension plane without a via connection. Several coplanar EBG structures are proposed e.g. the uni-planar compact EBG(UC-EBG) structure,
31
CHAPTER 3. ELECTROMAGNETIC BANDGAP STRUCTURE
the L-bridge EBG structure and the Alternating Impedance EBG(AI-EBG)
structure which are shown in Figure 3.8.
Figure 3.8:
The Coplanar EBG structures (a) the uni-planar compact
EBG structure[25] (b) the L-bridge EBG structure[26] (c) the alternating
impedance EBG structure[27]
On the view of electric circuit, the coplanar EBG structure is like a bandrejection filter. The equivalent model of unit cell for UC-EBG structure is
shown in Figure 3.9. The inductance is resulted from the bridge arm; also
,the capacitance is from the metal patch to the adjacent plane. The lower
cut-off frequency fL is determined by the series inductance and the shunt
capacitance on the etching patch. Furthermore, the higher cut-off frequency
fH is decided by the cavity resonance of the unit cell which is interpreted as
fH =
c
√
2b r
where b is the width of the unit-cell and c is the speed of light.
Figure 3.9: The equivalent model of the unit-cell of the UC-EBG structure
32
Chapter 4
The Common-Mode Filter
using the EBG Structure
4.1
The Structure of the Common-Mode Filter
In this thesis project, the goal of the common-mode filter is operated to resonate at 937.5 MHz for four differential pairs in chorus and takes little space
on the PCB. In industrial implementations, the size of the EBG structure
is a challenging. A typical HIS-EBG structure will become large due to the
dimension of the enlarged patches and the length of the extended via to shift
the resonant frequency to the lower frequency range. Hence, to design a
compact EBG structure is a important task for us in the project.
As mentioned in chapter 3, the resonant frequency can be shifted to lower
band by increasing the inductance and capacitance. A short summary is
given as follows and is listed in Table 4.1.
Capacitance Aspect
The equivalent capacitance is mainly dominated by the patches. It increases
by enlarging the dimension of the patch or inserting a high dielectric constant
material into PCB. However, it is difficult to implant in the project because
it will take too much space on the PCB and cost expensive.
Inductance Aspect
On the other side, vias are responsible for the equivalent inductance of the
HIS-EBG structure. Two of the manners to increase the inductance are to
narrow the diameter of vias and to extend the length of vias. The length
of via extension gives significant inductance increment but it occupies more
33
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
layers on the SCXB to add up the height between the patch and the ground
plane. Hence, the etching of spiral on patches is proposed to solve the problem. The common-mode filter in the project is applied on the technique.
Table 4.1: The summary of the design concept for the common-mode filter
Action
Concerns
Inductance Increment
Height of Via Extension
More Layers Needed
Capacitance Increment
Dimension of Enlarged Patches
More Space Needed
Inserting High DK Thin Film
More Expensive
4.1.1
General Description
The EBG structure is implemented in SCXB that the non-related components had been removed from the PCB. Figure 4.1 is the top view layout
of the test board with the common-mode filter. The common-mode filter
is put beneath four differential pairs: Diff.1, Diff.2, Diff.3 and Diff.4. Each
differential pairs connects to the connectors for the VNA measurement. The
four differential pairs transmit the signal parallel in the system.
4.1.2
The EBG Structure with the Double Spirals
Figure 4.2 is the proposed common-mode filter. The rectangular patch is
connected to two spiral shape and the center of the spiral shape is shorted
to ground by via. The four differential pairs are routed above the rectangular patch. In the proposed EBG structure, the via is moved to side edge
instead of putting in the centre of the patch. It gives the available space
for positioning four differential pairs. Also, the resonant frequency is shifted
to lower band compared to the tradition HIS-EBG structure with the same
dimension. The common-mode filter is cascaded by three unit cell of the proposed EBG structure. The more cascaded unit cells can achieve the deeper
resonant notch and wider the bandgap slightly. The -10 dB power blocking
is enough for common-mode noise rejection. Hence, the case of the three
cascaded unit cells is trade-off between the total dimension and the depth of
the notch.
34
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.1: The proposed common-mode implanted on the test board
4.1.3
The PCB Stack-UP
The stack up of the test board is shown in Figure 4.3. The differential pairs
are routed on the first layer which is also known as microstrip coupled lines.
The common-mode filter is put below the four differential pair. The patch of
the EBG structure is on the second layer. The height between the first and
second layer is 0.1 mm. The patch of the EBG structure is connected to the
ground plane on sixth layer. The space under the patch of the EBG structure,
from the third, fourth to fifth layer, is left out. The height between the patch
of the EBG structure and the ground plane is 0.4 mm. The impedance of
every differential pair in differential mode is 100 Ω. The width of every
differential line is 0.15 mm and the conductor-to-conductor spacing is 0.15
mm. Also, the distance between every differential pairs is about 4 to 5 times
of the line width that is around 0.6 mm to 0.75 mm.
4.1.4
The Specification of EBG Structure with Double
Spiral
The specification of the unit cell is shown in Figure 4.4. The rectangular
shape is (W1, W2) = (4.5, 1.8) mm. The spiral shape is (L1, L2, L3, L4, L5,
L6, L7, L8, L9, g) = (2.2, 1.1, 4.3, 0.9, 4.1, 0.7, 3.9, 0.3, 2.2, 0.1) mm and
the line width of the spiral is 0.1 mm. The diameter of the via is 0.25 mm.
Also, the gap between unit cells of the HIS-EBG is 0.2 mm. The commonmode filter is cascaded by three unit-cells of the EBG structure. The total
dimension of the common-mode filter is 14 × 6.5 mm2 .
35
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.2: The top view of the common-mode filter
Figure 4.3: The stack up of the common-mode filter on the test board
4.2
4.2.1
Analysis Methods for the Common-Mode
Filter
S-parameter Measurement
The scattering parameter of common-mode filter is measured by 12-port vector network analyzer (VNA). The illustration of the set up is shown in Figure
4.5. Every differential line is connected with Rosenberg Connector.
The 16-port vector network analyzer is not available for the project. To
build the 16-port network (.s16p), it is required to divide the differential
36
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.4: The specification of the EBG patch
pairs into three groups and then perform measurement of the 3 groups separately. Then, the measurement data from 3 groups will be combined to 16
ports network. The three groups of the measurement are shown in Table 4.2
During every measurement, the unused differential pair should be terminated
by 50 Ω to avoid the standing wave influencing the measurement data. Afterwards, the three s-parameter sets, each are .s12p, .s12p and .s8p files are
combined to create the 16-port network file.
4.2.2
Pseudo Common-Mode Signal Environment
As mentioned in chapter 1, there are three reasons to cause the commonmode noise on differential line. In the case, the major origin is from the
ground bounce noise. The ground bounce noise (external electromagnetic
field) induce equal and in-phase signal on the eight transmission lines.
However, the s-parameter is calculated by setting other ports to be matched.
It is not the driven state of the common-mode noise; also, it is not correct to
analyze the common-mode noise by seeing it on each differential pairs separately. Hence, all the differential pairs need to be connected to one common
port at both sides. The common port is likely a ground bounce noise generator.
37
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.5: The set up of the VNA measurement
Table 4.2: The three groups in the measurement
Group 1
VNA
Ch1
Ch2
50 Ω
50 Ω
Ch3
Ch4
Ch5
Ch6
Diff1
Diff1
Diff2
Diff2
Diff3
Diff3
Diff4
Diff4
p
n
p
n
p
n
p
n
Group 2
VNA
Ch7
Ch8
50 Ω
50 Ω
Ch9
Ch10
Ch11
Ch12
VNA
Ch1
Ch2
Ch3
Ch4
50 Ω
50 Ω
Ch5
Ch6
Diff1
Diff1
Diff2
Diff2
Diff3
Diff3
Diff4
Diff4
p
n
p
n
p
n
p
n
Group 3
VNA
Ch7
Ch8
Ch9
C10
50 Ω
50 Ω
Ch11
Ch12
VNA
50 Ω
50 Ω
Ch1
Ch2
Ch3
Ch4
50 Ω
50 Ω
Diff1
Diff1
Diff2
Diff2
Diff3
Diff3
Diff4
Diff4
p
n
p
n
p
n
p
n
VNA
50 Ω
50 Ω
Ch5
Ch6
Ch7
Ch8
50 Ω
50 Ω
Phase Shift Adjustment
Another important point is to adjust the phase shift of the trace length in the
front of the common-mode filter and vice versa, for the back of the commonmode filter. The trace model of the coupled line is put into the circuit. A
certain length is added for each differential pairs whereby the four differential
pairs with common-mode filter can be integrated as one system. The setup
of the pseudo common-mode noise is shown in Figure 4.6.
Summary: Analysis Procedure
Step 1 : to measure the s-parameter data of the proposed common-mode
filter that is a 16-port network
Step 2 : to adjust the phase shift of the trace length to the front and the
38
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.6: The schematic of the common-mode noise environment
back of the common-mode filter
Step 3 : to convert the 16-port network (.s16p) into 4-port network (.s4p)
and set the port reference impedance as 12.5 Ω
Step 4 : to analyze the 4-port network by mixed-mode s-parameter
39
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
4.3
Experiment Results
The performance of the modified common-mode filter is shown and discussed
in the section. The s-parameter of the common-mode filter is measured; also,
it is transferred to mixed-mode parameter for analysis. The common-mode
signal (Scc21), differential signal (Sdd21) and the mode-conversion signal
(Scd21, Scd12) are shown in the section.
4.3.1
Resonant Frequency Error Correction
Problem Description
In the experiment, the resonant frequency of the common-mode filter shifts
to lower band than the designed one from simulation. The measured resonant
frequency is at 736 MHz. It is 201.5 MHz lower than the desired frequency
band. The reasons why the fabricated board does not match to simulation
result were:
• The difference in dielectric constant of the material
• The compression process during the fabrication
Stratagem
To obtain the desired resonant frequency, we adjust the inductance from the
EBG patch. As shown in Figure 4.7, one point on the spiral shape is directly
shortened to ground. It is likely to divide the inductance from the total
spiral shape and make it be a parallel inductor circuit. The inductance of the
structure is decreased. Hence, the common-mode filter further approaches
the desired resonant frequency which is at 937.5 MHz. Figure 4.8 shows the
test board with the modified common-mode filter.
Figure 4.7: The illustration of the resonant frequency tuning strategy
40
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.8: The test board with the modified common-mode filter
Predicted Result After Adjustment
Figure 4.9 shows the predicted result after tuning process in HFSS simulation. The solid line is the Scc12 from the pre-modified board. The first step
is to build the simulated model in HFSS to be identical with the measured
result. Hence, the dielectric constant is set to 5.2 which is the blue dash
line. Afterwards, the spiral shape is modified for adjusting the inductance
and making the common-mode filter shift to the desired frequency which is
the red dash line.
Figure 4.9: The simulation of Scc21 for modified case comparison with
pre-modified board
41
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
4.3.2
The Common-Mode Signal of the 10GBASE Ethernet
Insertion Loss (Scc21)
The measured and simulated common-mode signal of the common-mode filter
is shown in Figure 4.10. The solid line is the measured common-mode signal
(Scc21) and the dash line is the simulated common-mode signal (Scc21) in
HFSS. The reasonably good agreement between the measurement and simulation is seen. The sweep frequency of the measurement is from 600 MHz
up to 1.5 GHz with 3.998 MHz resolution.
The stopband is at the desired frequency range which is 937.5 MHz. It fits to
the goal of the project. The center stopband frequency of the common-mode
is at 921.7 MHz. Also, the lower cut-off frequency is 893.7 MHz and the upper
cut-off frequency is 1014 MHz. The bandwidth is 120.3 MHz that is defined
by the power of Scc21 < -10 dB. It is a narrow bandwidth common-mode
filter; however, it is able to apply on the issue board. The undesired noisy
spectrum of the board which is at frequency 937.5 MHz is in the stopband
range.
Figure 4.11 shows the measured common-mode signal (Scc21) up to 20 GHz.
The sweep frequency of the measurement is from 10 MHz up to 20 GHz
with 3.998 MHz resolution. There is a deep notch at 921.7 MHz. Also, the
common-mode signal (Scc21) is lower than -10 dB after 6 GHz.
The Impact of Characteristic Impedance of Differential Lines
The implemented common-mode filter is designed for 4 parallel differential
pairs. The common-mode signal (Scc21) is down to -33 dB at the resonant
frequency. However, Scc21 is influenced by characteristic impedance of differential pairs. Figure 4.12 shows the Scc21 for 4 differential pairs system
and one differential pair system. In the case of one differential pair, the Scc21
is -3.6 dB and the effect of common-mode filter almost lost. The reason can
be discussed in the view of characteristic impedance of differential pairs.
The LC resonator is like a series element in the network. Hence, the network
of common-mode signal can be described as two-port network of a series
element with impedance Zs between two transmission lines with the characteristic impedance Z0 . It is shown in Figure 4.13. Accordingly, the S21 can
42
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.10: The measured Scc21 in comparison with HFSS simulation for
the common-mode filter
Figure 4.11: The measured Scc21 in the wide frequency range 10 MHz to 20
GHz
43
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
be written in
2Z0
Zs + 2Z0
S21 =
(4.1)
The characteristic impedance for four differential pairs is quarter of the one
for one differential pair that can be interpreted by
0
Z
Z0 = (Z0 //Z0 //Z0 //Z0 ) = 0
4
0
0
0
0
0
where Z0 is the characteristic impedance for one differential pair.
Therefore, the characteristic impedance for four differential pairs system is
smaller than the one for one differential pair system. According to Equation
4.1, Scc21 of four differential pairs system is smaller as well.
Figure 4.12: The effects of common-mode filter for one and four differential
pair(s)
Electric Field Distribution
Figure 4.14 shows electric field distribution in common-mode at the resonant frequency at 921.7 MHz. The differential lines are driven by 1 volt in
same phase. The common-mode mode is similar to the mode of a signal-end
trace that the electric filed strongly couples to the ground plane. Hence, it is
44
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.13: The two-port network with series element
obviously shown in the figure that the distribution of the electric field concentrates on the ground plane embedded the common-mode filter. Further,
the distribution of the electric field on the common-mode filter is dissipating
while transmitting. It means the common-mode filter stops the transmission
of the common-mode noise.
Figure 4.14: The electric field of the common-mode filter in common-mode
at first resonant 921.7 MHz
4.3.3
The Power Radiation of a Shielded Cable Connected the CM-Filter
The power radiation measurement shows the amount of common-mode noise
is indeed reduced. The measurement is operated in reverberation chamber.
The feature of reverberation chamber is giving a fast method to measure the
total power radiation of the cable under test. The demonstration of measurement set-up is shown in Figure 4.15.
45
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
The cable under test (CUT) is assembled in chamber room 1 and the input
signal source is assembled in chamber room 2. In chamber room 1, the received antenna is active and is able to receive radiation power from the cable
under test.
The input source is 1 mW power driven by power generator. The 1 mW
is input into chamber room 2 and then connected to 3-ports power splitter.
The power from two output of power splitter is linked to one differential
pair. In the reference case, the differential pair is directly connected to the
differential cable connection board which is assembled the specific connector
for cable under test. In other hand, in the experiment case, the differential pair is first connected to the one channel of differential pair embedded
by common-mode filter. The cable under test is Densi shield cable which
contains 8 differential pair. In the experiment, one differential pair is used
and injected common-mode current by power generator. The other unused
differential pairs are matched with 50 Ω terminations.
The CUT is driven by common-mode signal which is 1 mW in the reverberation chamber. As shown is Figure 4.16, the power radiation is reduced
within the bandgap range from 880 MHz to 970 MHz. It further proves that
the common-mode current is reduced by the common-mode filter.
Figure 4.15: The demonstration of the power radiation measurement in the
reverberation chamber
46
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.16: The power radiation of the shielded cable driven by commonmode signal with/without the common-mode filter
4.3.4
The Differential Signal of the 10GBASE Ethernet
Insertion Loss
The measured differential signals (Sdd21) are shown in Figure 4.17. The
performance of differential signal is analyzed separately. The differential signals only have transmission losses due to dielectric material. The power of
differential signals is larger than -3 dB until 3 GHz. Several minor notches
are shown above 6 GHz from connectors. As shown below, the proposed
common-mode filter does not degrade the differential signaling.
Eye Diagram
The eye diagram is an useful tool to examine the quality of the digital signal
at a specific bit rate with the rising/falling time. Every bits of the digital
signal will overlay on the top of each others. The figure of the overlaid bits
is called eye diagram. The more eye height and eye width it has, the better
digital signal performance it is [28].
On the SCXB, the 10GBASE Ethernet is applied the 8b/10b encoding tech47
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.17: The measured Sdd21 for each differential pairs in wide frequency
range
nique. For this reason, the bit sequence transmits in 10Gbps×(10/8) = 12.5
Gbps. Next, the Ethernet is composed of four differential pairs so that each
differential pairs transmits signal in (12.5 Gbps/4) = 3.125 Gbps. The input bit sequence runs at 3.125 Gbps of which rising time is 50 ps and the
falling time is 50 ps. Figure 4.18 shows the reference case that Sdd21 of
differential lines without common-mode filter. The eye diagram of the case
using common-mode filter with and without FFE (Feed Forward Equalizer)
are shown in Figure 4.19. It is simulated by the measured s-parameter of the
differential pairs with common-mode filter. Figure 4.20 shows the eye diagram of the differential pair connects with TSR-491-602 cable model which
length is 500 mm.
In conclusion, the performance of the differential signal is good. The eye
height and eye width are both large. It further accessed that the quality of
the differential signal is not degraded by the common-mode filter.
48
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.18: The eye diagram of a differential pair in 100 mm without the
common-mode filter
Figure 4.19: The eye diagram of a differential pair with the common-mode
filter (a) without FFE (b) with FFE
49
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.20: The eye diagram of a differential pair applied with the commonmode filter connected to the 500 mm TSR-491-602 cable (a) without FFE
(b) with FFE
50
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Electric Field Distribution
Figure 4.21 shows the electric field distribution of the differential signal at
the resonant frequency 921.7 MHz. The driven signal of the differential
pair is 1 volt with out of phase. As mentioned, the differential signal is
strongly coupled to another trace of the pair. Hence, the electric field mainly
distribute on the differential pair as shown in the figure. Hence, there is no
baleful influence for the differential signal from the common-mode filter.
Figure 4.21: The electric field of the common-mode filter in differentialmode at the first resonant 921.7 MHz
4.3.5
The Mode-conversion of the 10GBASE Ethernet
Figure 4.22 shows the mode-conversion signal Scd12 and Scd21. Mode conversion shows the signal from differential signal to common-mode signal and
vice versa. As seen in the figure, the mode conversion is below -20 dB from
10 MHz to 20 GHz. Hence, the filter does not lead to bad effect on the issue.
51
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.22: The measured Scd21 and Scd12 in wide frequency range
4.4
Parametric Analysis
In this section, the parameters of the common-mode filter are discussed. As
mentioned, the EBG structure can be regarded as LC resonator. Also, the effective value of the capacitance and inductance are varied with the dimension
of unit-cell of the EBG structure. The dimension of the rectangular patch,
turns of spiral inductor, gap distance between unit-cells and the height of the
unit-cell are discussed and analyzed by simulation tool HFSS in the section.
4.4.1
The Effect of the Patch’s Size and the Spiral
Turns
The resonant frequency of the common-mode filter is decided by the dimension of the EBG structure. The upper side of stopband (fH ) is determined
from the cavity resonance which is derived from
fH =
1
√
2π LC
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CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
The capacitance (C) is mainly contributed by the dimension of the rectangular patch; also, the inductance (L) is mostly dominated by the spiral arms.
The vias also contribute inductance for the model but the amount is lesser
comparably.
The simulated model is shown in Figure 4.23. The dimension of the rectangular patch is w1 × w2 where w2 is 3.6 mm and w1 is swept from 1.3 mm to
11 mm. The total length of spiral is (x + y + 2x + 2y + x)N where x is 0.6
mm, y is 0.2 mm and N is the number of turns. The width of the spiral is
0.1 mm.
According to the formula of plate capacitor
C=
A
d
where A is the area of metallic plate and d is the distance between the two
metallic plates, the capacitance increases as the area enlarges. As shown
in Figure 4.24, the capacitance becomes large as the width (w1) increases;
further, the resonant frequency shifts to lower band.
On the other hand, the inductance of a spiral inductor increases with the
number of turns (N ). It can be seen from Figure 4.24 that the resonant
frequency shifts to lower band as the number of turns increases.
Figure 4.23: The simulated model of the common-mode filter
53
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.24: The resonant frequency for common-mode signal versus the
dimension of the unit-cell
4.4.2
The Effect of the Width of the Rectangular Patch
The depth of common-mode signal (Scc21) is related to the width of rectangular patch (w2). Figure 4.25 shows the simulated model of which the width
(w1) of the rectangular is 1.3 mm , 4.3 mm and the gap distance (g) between
each unit-cells is 0.2 mm. The trend of sweeping w2 is shown in Figure 4.26.
As seen from the result, the Scc21 becomes large at the center frequency
as the width (w2) of the rectangular increases. The resonant cavity for the
patch can be seen as shunt LC resonator. Also, the impedance of the LC
resonator is
1
1
1
=
+
Zeq
XL XCP atch
Therefore, once the capacitance (CP atch ) is increase, the equivalent impedance
becomes smaller. Further, the Scc21 tends to be larger that is known from
Equation 4.1.
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CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.25: The simulated model with w2 is variable
Figure 4.26: The trend of sweeping w2 for the cases with w1 = 1.3 mm, 4.3
mm, g is 0.2 mm and N = 1
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CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
4.4.3
The Effect of the Gap Distance Between UnitCells
Figure 4.28 shows the simulated model of which w1 is 1.3 mm, w2 is 0.7 mm
and g is variable. The tendency of sweeping g is shown in Figure 4.28. Also,
insertion loss of common-mode signal (Scc21) is shown in Figure 4.29. The
depth of Scc21 is apt to be deeper when the gap distance (g) increase that
the capacitance from the gap (Cg ) is smaller.
Figure 4.27: The simulated model with g as variable
Figure 4.28: The trend of sweeping g for the cases with w1 is 1.3 mm, w2 is
0.7 mm and N = 1
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CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.29: The Scc21 of sweeping g for the cases with w1 is 1.3 mm, w2 is
0.7 mm and N = 1
4.4.4
The Effect of the Height of the EBG Structure
The simulated model which height (h1, h2) is variable, w1 is 4.3 mm, w2 is
0.7 mm, g is 0.2 mm, is shown in Figure 4.30.
Figure 4.30: The simulated model with h1, h2 as variable
57
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
The Height (h1) Between Diff. Lines and the Patch
Figure 4.31 shows the result of sweeping h1. Also, the insertion loss of
common-mode signal (Scc21) is shown in Figure 4.32. As seen from the
simulation results, the height between the differential lines and the patch
affects the lower-side of stopband (fL ). The lower-side of stopband (fL )
shifts to lower frequency once the height (h1) decrease which gives larger
capacitance. As mentioned in chapter 3, the equation 3.3 give a hint that
larger capacitance leads to lower lower-side of stopband (fL ). It coincides
with the simulated result.
Figure 4.31: The trend of sweeping h1 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1
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CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.32: The Scc21 of sweeping h1 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1
The Height h2 Between the Patch and the Ground Plane
Figure 4.33 shows the result of sweeping h2. Also, the common-mode signal (Scc21) is shown in Figure 4.34. The upper-side of stopband (fH ) is
determined by the cavity resonance of the patch. It is determined by
fH =
1
√
2π LC
As shown in the result, the upper-side of stopband (fH ) shifts to higher
frequency as the height (h2) between the patch and ground increases that
means the capacitance tend to be smaller.
59
CHAPTER 4. THE COMMON-MODE FILTER USING THE EBG
STRUCTURE
Figure 4.33: The trend of sweeping h2 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1
Figure 4.34: The Scc21 of sweeping h2 for the cases with w1 is 4.3 mm, w2
is 0.7 mm, g is 0.2 mm and N = 1
60
Chapter 5
Conclusion
The compact common-mode filter based on the HIS-EBG structure to suppress common-mode noise at 937.5 MHz is achieved. The design of the
common-mode filter is based on the EBG structure which prevents electromagnetic wave to propagate in a certain frequency range.
It is necessary to understand the causes and relevant knowledge of commonmode noise to design the common-mode filter. The main studies are summarized into three parts:
• The causes of the common-mode noise. Three major causes have been
studied. The first one is the asymmetrical coupled lines routed on the
PCB. The second one is the differing rising/falling time from driven
source. The third one is the external EM-field scattering on the PCB.
• The theories of the coupled lines. First of all, the principle of the
coupled lines has been studied. Also, the scattering parameter of a
network system has further understood. It is important to analyze the
characteristic of common-mode filter.
• The researches on the electromagnetic bandgap structure. The principle of the EBG structures has been studied. The applications in EMC
area and in power integrity are also well-studied. The proposed methods to improve the EBG structures are understood and also applied in
the project.
A common-mode filter using the EBG structure is designed and also simulated by full-wave simulator software (HFSS); further, it is implemented on
Ericsson’s SCXB and also measured by VNA (Vector Network Analyzer) as
well as RC (reverberation chamber). The parametric analysis of the commonmode filter is discussed. The further understandings of the common-mode
61
CHAPTER 5. CONCLUSION
filter are given. It shows the behavior difference while changing the dimensions.
The common-mode signal, Scc21 is suppressed within the bandgap with
bandwidth is 120.3 MHz that is defined by power level at -10 dB. Also,
the differential signal, Sdd21 is not affected and still has good reliability.
The advantages of the proposed common-mode filter is low profile and low
cost. It is constructed during the PCB fabrication process but it will take
more layers. Furthermore, it works well in high frequency ranges and does
not lead to degradations on the differential signal.
62
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