partial element equivalent circuit (peec)dipanjan/e8_202/e8202-cem_12.pdf · 4 • a. e. ruehli,...
TRANSCRIPT
![Page 1: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/1.jpg)
Partial Element Equivalent Circuit (PEEC)
E8-202 Class 12
Dipanjan Gope
![Page 2: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/2.jpg)
2
Grading Scheme
Time Frame Assignment Grading
Sep 6 HW 1 15
Sep 24 HW2
Oct 8 HW 3
Oct 11 Midterm 1 15
Nov 5 HW 4 5
Nov 20 Midterm 2 15
Dec 5 Final Exam 30
Dec 10 Final Project 20
![Page 3: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/3.jpg)
3
• 2D vs 2.5D vs. 3D Formulations
• Electrostatic Formulation: Capacitance matrix extraction
• Magnetostatic Formulation: Inductance matrix extraction
• Electric Field Integral Equation (EFIE): S-parameter extraction
• Partial Element Equivalent Circuit (PEEC) Method
• Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE)
• PMCHWT Formulation: Dielectric modeling
• Parallelization techniques
Module 2: Method of Moments
![Page 4: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/4.jpg)
4
• A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE Trans. Microwave Theory and Techniques, vol. MTT22 (3), pp. 216-221, March 1974.
References
![Page 5: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/5.jpg)
5
What does PEEC do?
Lumped Circuit Elements e.g. R; L; C; V; I
Distributed Circuit Elements e.g. Transmission Line
~r dt t
KVL; KCL Maxwell’s Equations
Elem
en
ts
Def
init
ion
Eq
uat
ion
s So
luti
on
SPICE Port Model + SPICE PEEC
r dt t
![Page 6: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/6.jpg)
6
SPICE Review
• Sparse Tableau Analysis (STA) - IBM ASTAP simulator
• Modified Nodal Analysis (MNA) - SPICE simulators
![Page 7: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/7.jpg)
7
Stamps Revisited
Resistor
Current Source
Voltage Source
Some excerpts from UW class notes by Prof. Richard Shi and Guoyong Shi
![Page 8: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/8.jpg)
8
Stamps Revisited
Capacitor
N+
N-
N+ N- RHS
N+ C/h -C/h (C/h)V(t-h)
N- -C/h C/h -(C/h)V(t-h)
Inductor
N+
N-
N+ N- I-branch RHS
N+ 1
N- -1
Branch 1 -1 -L/h -(L/h)I(t-h)
![Page 9: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/9.jpg)
9
Stamps Revisited
VCVS
CCCS
Some excerpts from UW class notes by Prof. Richard Shi and Guoyong Shi
N+ N- NC+ NC- ik
N+ 1
N- -1
NC+
NC-
ij 1 -1 E -E
![Page 10: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/10.jpg)
10
' '
' ' ' '( )( , ) ( , ) ( ) ( , ) ( )i
v v
J rE r j G r r J r dv G r r q r dv
j
Circuit Model Element Identification
• KVL: Voltage = R I + sLp I + Q/sC
• RHS Term 1: Resistance
• RHS Term 2: Partial Inductance
• RHS Term 3: Coefficients of Partial Potential
PEEC: Equation
![Page 11: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/11.jpg)
11
Basis Function
Current
Charge
![Page 12: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/12.jpg)
12
Partial vs Loop Inductance
Loop Partial
122211 2LLLL
![Page 13: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/13.jpg)
13
Vc2
CCVS
Vc1
Unit Cell
' '
' ' ' '( )( , ) ( , ) ( ) ( , ) ( )i
v v
J rE r j G r r J r dv G r r q r dv
j
dldarfa
dvrfa
a lv
)(1
)(1
Testing Function
![Page 14: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/14.jpg)
14
Vc2 CCVS
Vc1
Resistance Term
dldaJ
adv
J
aa lv
11
dldaa
I
adv
J
aa lv
11
a
lIdv
J
av
1
![Page 15: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/15.jpg)
15
Vc2 CCVS
Vc1
Inductance Term
v va a
dvdvGaa
jGJdvdvja
'1
'1
''
'
v v
vvp dvdvGaa
L '1
''
'
![Page 16: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/16.jpg)
16
Vc2 CCVS
Vc1
Capacitor Terms
2121111 QpQp
211
1211
11
1Q
p
pQ
p
dt
dQ
p
p
dt
dQ
dt
d
p
2
11
1211
11
1
211
121
1
11
1cc i
p
pi
dt
d
p
![Page 17: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/17.jpg)
17
Ge
om
etry
C
on
du
cto
r
4km
k m k m
k mp k m
k m k ma a l l
dl dlL da da
a a r r
+ - + -
R1 N1 N2 1.202mOhms
L1 N2 N3 5.887nH
C1 N1 0 1.702pF
K12 L1 L2 1.282nH 0.054ns
F12 N4 0 V1 0.124 0.032ns
PEEC Stick Example
![Page 18: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/18.jpg)
18
Vc2 CCVS
Vc1
Basic Dielectric Modeling
Vc2 CCVS
Vc1
vv
i dvrqrrGj
dvrJrrGjj
JrE ')'()',(')'()',(
)1(),(
'0
l
AC 0)1(
![Page 19: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/19.jpg)
19
Integral Equation Solution to Maxwell’s Equations
Special Meshing for PEEC Cells
Transformation to PEEC Circuit Elements
SPICE Circuit Elements Other SPICE Type Models
SPICE Like Circuit Description
MNA Delay Diff. Eq. (DDE) Circuit Solver
Voltages, Currents, Electric and Magnetic Fields
PEEC Flow
![Page 20: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/20.jpg)
20
• Orthogonal, No-retardation
• …
• Orthogonal, with-retardation
• …
• Orthogonal, with-dielectric and retardation
• Non-orthogonal, with dielectric, retardation
• ….
PEEC History
![Page 21: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/21.jpg)
21
Volumetric formulation ideal for on-chip cases
• No thickness discretization necessary
DC to daylight solution
• Charge and current decoupled at DC
“Stamps” provide interface between techniques Multi-purpose solver (.tran / .ac / .cap / .ind)
PEEC: Advantages
![Page 22: Partial Element Equivalent Circuit (PEEC)dipanjan/E8_202/E8202-CEM_12.pdf · 4 • A. E. Ruehli, “Equivalent circuit models for three-dimensional multiconductor systems” IEEE](https://reader036.vdocuments.us/reader036/viewer/2022070908/5f8b668815540e58e1022dd6/html5/thumbnails/22.jpg)
22
Dense Matrix: Expensive LU (Gaussian Elimination)
• Can we use EM properties to expedite solution? Volume formulation unsuitable for “thick” structures
• Can we get similar stamps for surface-based/hybrid form?
PEEC: Drawbacks
Addressed in later research