辅导ELEC4401、讲解Modelling留学生、讲解JAVA编程语言、JAVA辅导
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Revision: Date:
2.2 8/5/2018
Title:
ELEC4401-2019 Project –Modelling and
Analysis of Power Planes and Power Supply
Systems
Author(s):
Antonio Cantoni
Document History:
Revision Date Comments
1.0 12/10/2006 Initial Draft
1.1 8/3/2013 Minor Corrections
1.2 3/2/2017 Submission information added
2.0 4/3/2018 Adapted to include GUI Tool
2.1
2.2
7/5/2018 Added board dimensions in P4.1
Added lumped model parameters.
Department of Electrical, Electronic
and Computer Engineering Table of Contents
A.Cantoni 2018 i of i
Table of Contents
1 Introduction ............................................................................... 1
1.1 IMPORTANT NOTE ......................................................................................2
1.2 Individual Report .............................................................................................2
1.3 Project Report Organisation .............................................................................2
2 Summary of Software tools ....................................................... 3
2.1 Coordinate System for Port Location ...............................................................4
3 Investigations ............................................................................ 5
3.1 The impact of the dimension of power ground plane pair on Port Impedances..6
3.2 Adding Lumped Loads to Power Planes ...........................................................6
3.3 Stitching Power Planes Structures ....................................................................7
3.4 Modelling Complete Distribution Systems .......................................................9
4 References ................................................................................ 12 Introduction
? A.Cantoni 2013,2018 1 of 12
1 Introduction
The objective of this project is to gain experience in aspects of the design of one part of
an electronic system. Specifically, the project is concerned with the power supply
distribution system which is comprised of the DC regulator and one or more zones
created using power planes on a printed circuit board. The modelling and analysis of
this type of system involves both circuit theory and electromagnetic theory. In this
project, software tools based on the results obtained from these two areas will be used to
investigate the effect of various options that arise in design of the power supply
distribution system. The options are related to the use of zones to reduce coupling
among sub-circuits and the use of a range of decoupling components such as ferrite
beads and capacitors of various types (high frequency and low frequency capacitors) .
Approximate analytical modelling of parts of a power supply distribution system is
certainly possible and indeed necessary in order to appreciate what the key parameters
are and how these impact performance. However, validation of the approximate analysis
with models of higher accuracy is often required. These more accurate models usually
do not lead to closed form parametric results and also are not amenable to complete
systems that are quite complex. In this case, we turn to software tools which make
evaluation of quite complex systems possible and undertake numerical studies. This
project is concerned with numerical studies of aspects of a power supply distribution
system using software tools derived from circuit theory and electromagnetic theory.
This document provides an introduction to the software tools and then proposes a
number of scenarios that you should investigate using the tools. The proposals are
identified as Px.y. Each proposal requires you to investigate some particular
characteristic for number of scenarios or for parameters specified within some limits.
For example, investigate the effect of the size of a zone on the impedance at a port on
the zone. It is up to you to decide the level of detail to be pursued in the investigation
and the range of parameter values within the given limits that should be used. Your
report should be written strictly with hindsight and should not present an exhaustive or a
purely chronological study, but rather, you should isolate the key effects and identify
broad trends that you have seen in your numerical studies and support these conclusion
with selected and small number of numerical results. Introduction
A.Cantoni 2013 2 of 12
1.1 IMPORTANT NOTE
The software tools that will be provided for you to carry out the project described in this
document consist of MATLAB PCBStructure Tools and a PSImpedance Tool that
provides a GUI interface to the MATLAB PCBStructure Tools through a user friendly
GUI interface to define and analyse power supply distribution systems.
You are permitted to use these tools as a student enrolled in the unit ELEC4401 at
UWA for the purpose of carrying out the project described in this document. You are
required to acknowledge the source of the tools in any report you write that has results
obtained by using the software tools provided.
You are not permitted to distribute the software in any manner.
You are not permitted to use the software for any commercial work without
written permission of the owners of the software.
1.2 Individual Report
This project should be the work of individual students. Collaboration is accepted, but
copying and plagiarism is not. The results presented should be produced by individuals
using the tools and the report must be written by each individual student and express his
personal view.
1.3 Project Report Organisation
Your report should use the proposal/investigation labels Px.y as section headings so that
it is clear where each proposal/investigation is covered in the report. Keep the text brief
and do not replicate what is already in this project description document but use
referencing where required. Do not include large amounts of MATLAB code or Tool
use descriptions in the main body of the report place this type of information in an
Appendix and keep it brief.
Your report must be composed using appropriate document composition tools for text,
equations and plotting. Scanned handwritten material is not allowed.
Your report must be submitted online by the due date as specified in LMS. Summary of Software tools
A.Cantoni 2013 3 of 12
2 Summary of Software tools
This project uses a set of software tools that have been developed in MATLAB and
JAVA to analyse power distribution systems for multi-layered PCBs. The tools allow
for the creation of software structures that represent physical power distribution
structures. Specifically, the tools allow for the creation of rectangular power ground
plane (P/G) distribution structures that can be interconnected to form arbitrarily shaped
structures. Lumped impedances can be connected to the structures at specified ports.
These lumped impedances may be used to model bulk decoupling, high frequency
decoupling or the behaviour of the dc supply. Distribution structures can be
interconnected directly or can be interconnected by means of a series impedance. The
series impedance allows for the addition of supply filtering components such as ferrites
or inductors used to interconnect supply zones.
Multiple supply layers in a PCB stack-up can be modelled by creating separate
structures for the different VCC/GND pairs and interconnecting them at ports to
simulate the effect of stitching vias.
Figure 1 (a) physical system (b) model using software tools
The tools allow for the analysis of power distribution systems by predicting the supply
input or transfer impedance at arbitrary ports over the frequency spectrum of the circuit.
For example, in Figure 1(a) the input impedance of the supply planes at IC1 may be
IC2 Summary of Software tools
A.Cantoni 2013 4 of 12
desired. This impedance will provide an estimate of the noise induced on this supply
node in response to a switching current produced by IC1. Further, the transfer
impedance between the supply nodes of IC1 and IC2 may be desired. This impedance
will give an indication of the noise voltage appearing at the supply pins of IC2 due to
the switching of IC1.
Use may use either or both MATLAB PCBStructure Tools and the PSImpedance
Tool to carry out your project.
Details on the MATLAB PCBStructure Tools can be found in [1].
Details on the PSImpedance Tool can be found in [2].
Make sure you clearly understand the limitations of the tools and the assumptions made
to develop the models used by the tools.
2.1 Coordinate System for Port Location
A rectangular plane pair is defined as shown in Figure 2 with three
parameters( , , , ) a b d h , the extent along the x axis, the extent along the y axis and the
board thickness and copper plane thickness respectively. Note that the lower left hand
corner of a board is located at the origin of the coordinate system. The location of a port
for impedance observation and for loading of the planes is specified in terms of the
x y, coordinates.
As an example, two ports, p and q located at ? x y p p , ? and ? x y q q , ? with a port radius of
vr are shown Figure 2. Investigations
A.Cantoni 2013 5 of 12
Figure 2 Board and Port Location
3 Investigations
For all investigations use the following electrical parameters for the power planes:
0 Free space dielectric constant. 8.854188e-120
Free space permeability constant. 1.256637061e-6
r Relative dielectric constant of insulator
between the copper planes
4.42s Conductivity of copper planes. 5.76*1e6
tan G Loss tangent of copper planes. 0.002
h Thickness of copper planes. 35e-6
d Thickness of insulator between copper
planes.
0.25e-3
vr Via radius. 0.5e-3
Table 1
Thickness h Investigations
A.Cantoni 2013 6 of 12
3.1 The impact of the dimension of power ground
plane pair on Port Impedances.
P1.1 Investigate the impact of the length and width of the planes on the impedance of
a single port on a plane. Consider planes with dimensions 0.3m x 0.3m, 0.15m x 0.3m
and 0.05m x 0.3m. You should choose no more than five locations for location of the
port on the planes.
3.2 Adding Lumped Loads to Power Planes
Lumped loads, such as decoupling capacitors are added to the power ground plane
structures to control impedance at ports and trans-impedance between ports.
0 0.05 0.1 0.15 0.2 0.25 0.3
example0-1.m: Simple Power Ground Plane
Figure 3 Port labelling. Two observation ports with one loaded port, port 2-1. Investigations
? A.Cantoni 2013 7 of 12
P2.1 For the board shown in Figure 3 investigate the effect on the impedance at port 1-1
and 1-2, when a capacitor with parameters C nF R L ? ? ? ? 100 30 m , 1 nH in the
model shown in Figure 4 is added at port 2-1.
Figure 4 Capacitor Lumped Impedance Model
The (x,y) locations of the ports are shown in Table 2.
Port x (m) y (m)
1-1 0.1 0.1
1-2 0.25 0.05
2-1 0.2 0.15
Table 2
P2.2 For the board shown in Figure 3 investigate the effect on the impedance at port 1-1
and 1-2, if the capacitor has parameters C nF R L ? ? ? ? 100 30 m , 5 nH in the
model shown in Figure 4 .
3.3 Stitching Power Planes Structures
Two rectangular structures can be combined to form a lager structure. This is achieved
by defining a string of matching ports along the edges of the P/G structures and then
joining the ports together. Investigations
A.Cantoni 2013 8 of 12
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Figure 5 Power ground plane with two ports that is not segmented
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Figure 6 Two supply zones joined using large ports Investigations
A.Cantoni 2013 9 of 12
P3.1 For the board shown in Figure 6 investigate the effect on the impedance at the
observation ports due to stitching of two planes to approximate the single plane.
The (x,y) locations of the ports are shown in Table 3.
Port x (m) y (m)
1 0.1 0.1
2 0.35 0.05
Table 3
3.4 Modelling Complete Distribution Systems
Figure 7 shows an example of a complete power distribution system. The system
includes an L-shaped power zone that is connected to a square power zone by means of
a bridge. The location of the power supply (PS), bulk decoupling (BD) and high
frequency decoupling (HFD) are illustrated. A ferrite bridge (FB) is used to connect the
two power zones together as shown. The sizes of the three boards can be determined
from dimension x,y dimension shown in Figure 7.
Figure 7 Example of a complete Distribution System Investigations
A.Cantoni 2013 10 of 12
The lumped impedance models for the elements used on the boards are as follows:
Figure 8 Capacitor Lumped Impedance Model
HFD - High Frequency Decoupling Capacitor Lumped Impedance Model
C nF L nH R m 100 1 30
BD -Bulk Decoupling Capacitor Lumped Impedance Model
C F L nH R m 100 50 100
Figure 9 Power Supply Lumped Impedance Model
PS- Power Supply Lumped Impedance Model
L H R m 6.4 20
FB-Ferrite Bead Lumped Impedance Model
Figure 10 Ferrite Bead Lumped Impedance Model
0.68 1.26 410 800 R C pF L nH R S ? ? ? ? ? ? Investigations
? A.Cantoni 2013 11 of 12
P4.1 Investigate the impedance at port 1 and the transfer impedance between port 1-1
and port 1-2 under the following conditions:
a) PS - only power supply and planes with FB a short circuit.
b) PS and BD - power supply, bulk decoupling and planes with FB a short circuit.
c) PS, BD and HFD - power supply, bulk decoupling, high frequency decoupling
and planes with FB a short circuit.
d) PS, BD, HFD, and FB - power supply, bulk decoupling, high frequency
decoupling, FB and planes.
The (x,y) locations of the ports on Board 1 are shown in Table 4. Note that location of a
port is relative to the origin of each power plane system, i.e. relative to the lower left
hand corner of each rectangular plane.
Port x (m) y (m)
P1 0.07 0.22
PS 0.03 0.02
BD 0.06 0.05
FB 0.195 0.05
HFD1 0.04 0.20
HFD2 0.04 0.04
Table 4
The (x,y) locations of the ports on Board 2 are shown in Table 5.
Port x (m) y (m)
P2 0.05 0.03
FB 0.005 0.05
HFD4 0.02 0.02
Table 5 References
A.Cantoni 2013 12 of 12
The (x,y) locations of the ports on Board 3 are shown in Table 6.
Port x (m) y (m)
HFD3 0.08 0.13
Table 6
4 References
[1] Joe Trinkle, Matthew Wood and Antonio Cantoni, "MATLAB Tools for Power
Ground Plane Analysis- ELEC4401", V1.3, on LMS at UWA.
[2] Antonio Cantoni, "A Tool for Power Distribution Analysis in Electronic Circuits
Comprised of Multiple Interconnected Structures Including Power Planes", V1.0,
ELEC4401, LMS at UWA.
[3] “Impedance Expressions for Unloaded and Loaded Power Ground Planes”, Trinkle,
J.; Cantoni, A.; IEEE Transactions on Electromagnetic Compatibility, Volume 50, Issue
2, May 2008 Page(s):390 – 398.
[4] “Comparison of methods for calculating the loading effect of capacitors on power
ground planes”, Trinkle, J.; Cantoni, A.; EMC-Zurich 2006. 17th International Zurich
Symposium on Electromagnetic Compatibility, 2006, Feb. 27 2006-March 3 2006
Page(s):97 – 99.
Revision: Date:
2.2 8/5/2018
Title:
ELEC4401-2019 Project –Modelling and
Analysis of Power Planes and Power Supply
Systems
Author(s):
Antonio Cantoni
Document History:
Revision Date Comments
1.0 12/10/2006 Initial Draft
1.1 8/3/2013 Minor Corrections
1.2 3/2/2017 Submission information added
2.0 4/3/2018 Adapted to include GUI Tool
2.1
2.2
7/5/2018 Added board dimensions in P4.1
Added lumped model parameters.
Department of Electrical, Electronic
and Computer Engineering Table of Contents
A.Cantoni 2018 i of i
Table of Contents
1 Introduction ............................................................................... 1
1.1 IMPORTANT NOTE ......................................................................................2
1.2 Individual Report .............................................................................................2
1.3 Project Report Organisation .............................................................................2
2 Summary of Software tools ....................................................... 3
2.1 Coordinate System for Port Location ...............................................................4
3 Investigations ............................................................................ 5
3.1 The impact of the dimension of power ground plane pair on Port Impedances..6
3.2 Adding Lumped Loads to Power Planes ...........................................................6
3.3 Stitching Power Planes Structures ....................................................................7
3.4 Modelling Complete Distribution Systems .......................................................9
4 References ................................................................................ 12 Introduction
? A.Cantoni 2013,2018 1 of 12
1 Introduction
The objective of this project is to gain experience in aspects of the design of one part of
an electronic system. Specifically, the project is concerned with the power supply
distribution system which is comprised of the DC regulator and one or more zones
created using power planes on a printed circuit board. The modelling and analysis of
this type of system involves both circuit theory and electromagnetic theory. In this
project, software tools based on the results obtained from these two areas will be used to
investigate the effect of various options that arise in design of the power supply
distribution system. The options are related to the use of zones to reduce coupling
among sub-circuits and the use of a range of decoupling components such as ferrite
beads and capacitors of various types (high frequency and low frequency capacitors) .
Approximate analytical modelling of parts of a power supply distribution system is
certainly possible and indeed necessary in order to appreciate what the key parameters
are and how these impact performance. However, validation of the approximate analysis
with models of higher accuracy is often required. These more accurate models usually
do not lead to closed form parametric results and also are not amenable to complete
systems that are quite complex. In this case, we turn to software tools which make
evaluation of quite complex systems possible and undertake numerical studies. This
project is concerned with numerical studies of aspects of a power supply distribution
system using software tools derived from circuit theory and electromagnetic theory.
This document provides an introduction to the software tools and then proposes a
number of scenarios that you should investigate using the tools. The proposals are
identified as Px.y. Each proposal requires you to investigate some particular
characteristic for number of scenarios or for parameters specified within some limits.
For example, investigate the effect of the size of a zone on the impedance at a port on
the zone. It is up to you to decide the level of detail to be pursued in the investigation
and the range of parameter values within the given limits that should be used. Your
report should be written strictly with hindsight and should not present an exhaustive or a
purely chronological study, but rather, you should isolate the key effects and identify
broad trends that you have seen in your numerical studies and support these conclusion
with selected and small number of numerical results. Introduction
A.Cantoni 2013 2 of 12
1.1 IMPORTANT NOTE
The software tools that will be provided for you to carry out the project described in this
document consist of MATLAB PCBStructure Tools and a PSImpedance Tool that
provides a GUI interface to the MATLAB PCBStructure Tools through a user friendly
GUI interface to define and analyse power supply distribution systems.
You are permitted to use these tools as a student enrolled in the unit ELEC4401 at
UWA for the purpose of carrying out the project described in this document. You are
required to acknowledge the source of the tools in any report you write that has results
obtained by using the software tools provided.
You are not permitted to distribute the software in any manner.
You are not permitted to use the software for any commercial work without
written permission of the owners of the software.
1.2 Individual Report
This project should be the work of individual students. Collaboration is accepted, but
copying and plagiarism is not. The results presented should be produced by individuals
using the tools and the report must be written by each individual student and express his
personal view.
1.3 Project Report Organisation
Your report should use the proposal/investigation labels Px.y as section headings so that
it is clear where each proposal/investigation is covered in the report. Keep the text brief
and do not replicate what is already in this project description document but use
referencing where required. Do not include large amounts of MATLAB code or Tool
use descriptions in the main body of the report place this type of information in an
Appendix and keep it brief.
Your report must be composed using appropriate document composition tools for text,
equations and plotting. Scanned handwritten material is not allowed.
Your report must be submitted online by the due date as specified in LMS. Summary of Software tools
A.Cantoni 2013 3 of 12
2 Summary of Software tools
This project uses a set of software tools that have been developed in MATLAB and
JAVA to analyse power distribution systems for multi-layered PCBs. The tools allow
for the creation of software structures that represent physical power distribution
structures. Specifically, the tools allow for the creation of rectangular power ground
plane (P/G) distribution structures that can be interconnected to form arbitrarily shaped
structures. Lumped impedances can be connected to the structures at specified ports.
These lumped impedances may be used to model bulk decoupling, high frequency
decoupling or the behaviour of the dc supply. Distribution structures can be
interconnected directly or can be interconnected by means of a series impedance. The
series impedance allows for the addition of supply filtering components such as ferrites
or inductors used to interconnect supply zones.
Multiple supply layers in a PCB stack-up can be modelled by creating separate
structures for the different VCC/GND pairs and interconnecting them at ports to
simulate the effect of stitching vias.
Figure 1 (a) physical system (b) model using software tools
The tools allow for the analysis of power distribution systems by predicting the supply
input or transfer impedance at arbitrary ports over the frequency spectrum of the circuit.
For example, in Figure 1(a) the input impedance of the supply planes at IC1 may be
IC2 Summary of Software tools
A.Cantoni 2013 4 of 12
desired. This impedance will provide an estimate of the noise induced on this supply
node in response to a switching current produced by IC1. Further, the transfer
impedance between the supply nodes of IC1 and IC2 may be desired. This impedance
will give an indication of the noise voltage appearing at the supply pins of IC2 due to
the switching of IC1.
Use may use either or both MATLAB PCBStructure Tools and the PSImpedance
Tool to carry out your project.
Details on the MATLAB PCBStructure Tools can be found in [1].
Details on the PSImpedance Tool can be found in [2].
Make sure you clearly understand the limitations of the tools and the assumptions made
to develop the models used by the tools.
2.1 Coordinate System for Port Location
A rectangular plane pair is defined as shown in Figure 2 with three
parameters( , , , ) a b d h , the extent along the x axis, the extent along the y axis and the
board thickness and copper plane thickness respectively. Note that the lower left hand
corner of a board is located at the origin of the coordinate system. The location of a port
for impedance observation and for loading of the planes is specified in terms of the
x y, coordinates.
As an example, two ports, p and q located at ? x y p p , ? and ? x y q q , ? with a port radius of
vr are shown Figure 2. Investigations
A.Cantoni 2013 5 of 12
Figure 2 Board and Port Location
3 Investigations
For all investigations use the following electrical parameters for the power planes:
0 Free space dielectric constant. 8.854188e-120
Free space permeability constant. 1.256637061e-6
r Relative dielectric constant of insulator
between the copper planes
4.42s Conductivity of copper planes. 5.76*1e6
tan G Loss tangent of copper planes. 0.002
h Thickness of copper planes. 35e-6
d Thickness of insulator between copper
planes.
0.25e-3
vr Via radius. 0.5e-3
Table 1
Thickness h Investigations
A.Cantoni 2013 6 of 12
3.1 The impact of the dimension of power ground
plane pair on Port Impedances.
P1.1 Investigate the impact of the length and width of the planes on the impedance of
a single port on a plane. Consider planes with dimensions 0.3m x 0.3m, 0.15m x 0.3m
and 0.05m x 0.3m. You should choose no more than five locations for location of the
port on the planes.
3.2 Adding Lumped Loads to Power Planes
Lumped loads, such as decoupling capacitors are added to the power ground plane
structures to control impedance at ports and trans-impedance between ports.
0 0.05 0.1 0.15 0.2 0.25 0.3
example0-1.m: Simple Power Ground Plane
Figure 3 Port labelling. Two observation ports with one loaded port, port 2-1. Investigations
? A.Cantoni 2013 7 of 12
P2.1 For the board shown in Figure 3 investigate the effect on the impedance at port 1-1
and 1-2, when a capacitor with parameters C nF R L ? ? ? ? 100 30 m , 1 nH in the
model shown in Figure 4 is added at port 2-1.
Figure 4 Capacitor Lumped Impedance Model
The (x,y) locations of the ports are shown in Table 2.
Port x (m) y (m)
1-1 0.1 0.1
1-2 0.25 0.05
2-1 0.2 0.15
Table 2
P2.2 For the board shown in Figure 3 investigate the effect on the impedance at port 1-1
and 1-2, if the capacitor has parameters C nF R L ? ? ? ? 100 30 m , 5 nH in the
model shown in Figure 4 .
3.3 Stitching Power Planes Structures
Two rectangular structures can be combined to form a lager structure. This is achieved
by defining a string of matching ports along the edges of the P/G structures and then
joining the ports together. Investigations
A.Cantoni 2013 8 of 12
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Figure 5 Power ground plane with two ports that is not segmented
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Figure 6 Two supply zones joined using large ports Investigations
A.Cantoni 2013 9 of 12
P3.1 For the board shown in Figure 6 investigate the effect on the impedance at the
observation ports due to stitching of two planes to approximate the single plane.
The (x,y) locations of the ports are shown in Table 3.
Port x (m) y (m)
1 0.1 0.1
2 0.35 0.05
Table 3
3.4 Modelling Complete Distribution Systems
Figure 7 shows an example of a complete power distribution system. The system
includes an L-shaped power zone that is connected to a square power zone by means of
a bridge. The location of the power supply (PS), bulk decoupling (BD) and high
frequency decoupling (HFD) are illustrated. A ferrite bridge (FB) is used to connect the
two power zones together as shown. The sizes of the three boards can be determined
from dimension x,y dimension shown in Figure 7.
Figure 7 Example of a complete Distribution System Investigations
A.Cantoni 2013 10 of 12
The lumped impedance models for the elements used on the boards are as follows:
Figure 8 Capacitor Lumped Impedance Model
HFD - High Frequency Decoupling Capacitor Lumped Impedance Model
C nF L nH R m 100 1 30
BD -Bulk Decoupling Capacitor Lumped Impedance Model
C F L nH R m 100 50 100
Figure 9 Power Supply Lumped Impedance Model
PS- Power Supply Lumped Impedance Model
L H R m 6.4 20
FB-Ferrite Bead Lumped Impedance Model
Figure 10 Ferrite Bead Lumped Impedance Model
0.68 1.26 410 800 R C pF L nH R S ? ? ? ? ? ? Investigations
? A.Cantoni 2013 11 of 12
P4.1 Investigate the impedance at port 1 and the transfer impedance between port 1-1
and port 1-2 under the following conditions:
a) PS - only power supply and planes with FB a short circuit.
b) PS and BD - power supply, bulk decoupling and planes with FB a short circuit.
c) PS, BD and HFD - power supply, bulk decoupling, high frequency decoupling
and planes with FB a short circuit.
d) PS, BD, HFD, and FB - power supply, bulk decoupling, high frequency
decoupling, FB and planes.
The (x,y) locations of the ports on Board 1 are shown in Table 4. Note that location of a
port is relative to the origin of each power plane system, i.e. relative to the lower left
hand corner of each rectangular plane.
Port x (m) y (m)
P1 0.07 0.22
PS 0.03 0.02
BD 0.06 0.05
FB 0.195 0.05
HFD1 0.04 0.20
HFD2 0.04 0.04
Table 4
The (x,y) locations of the ports on Board 2 are shown in Table 5.
Port x (m) y (m)
P2 0.05 0.03
FB 0.005 0.05
HFD4 0.02 0.02
Table 5 References
A.Cantoni 2013 12 of 12
The (x,y) locations of the ports on Board 3 are shown in Table 6.
Port x (m) y (m)
HFD3 0.08 0.13
Table 6
4 References
[1] Joe Trinkle, Matthew Wood and Antonio Cantoni, "MATLAB Tools for Power
Ground Plane Analysis- ELEC4401", V1.3, on LMS at UWA.
[2] Antonio Cantoni, "A Tool for Power Distribution Analysis in Electronic Circuits
Comprised of Multiple Interconnected Structures Including Power Planes", V1.0,
ELEC4401, LMS at UWA.
[3] “Impedance Expressions for Unloaded and Loaded Power Ground Planes”, Trinkle,
J.; Cantoni, A.; IEEE Transactions on Electromagnetic Compatibility, Volume 50, Issue
2, May 2008 Page(s):390 – 398.
[4] “Comparison of methods for calculating the loading effect of capacitors on power
ground planes”, Trinkle, J.; Cantoni, A.; EMC-Zurich 2006. 17th International Zurich
Symposium on Electromagnetic Compatibility, 2006, Feb. 27 2006-March 3 2006
Page(s):97 – 99.