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Task 2: Modeling and Simulation of Conducted and Radiated EMI from HPM and UWB Sources on PCBs and ICs. A. C. Cangellaris and E. Michielssen ECE Department Center for Computational Electromagnetics University of Illinois at Urbana-Champaign. EMI to connectors & packages. Antennas Cracks - PowerPoint PPT Presentation
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June 2002 1
Illinois
Task 2: Modeling and Simulation of Conducted and Radiated EMI from HPM and UWB Sources on PCBs and ICs
A. C. Cangellaris and E. Michielssen ECE Department
Center for Computational ElectromagneticsUniversity of Illinois at Urbana-Champaign
June 2002 2Illinois
Accurately “propagate” the spurious signals (noise) through the packaging hierarchy (printed circuit boards, cards, connectors, interposer, package…) to the die.
HPM/UWBSources
AntennasCracks
AperturesCables
Propagationto interior
InternalCoupling
EMI to connectors &
packages
Internal fields as radiated EMI
Circuits
Spuriousbehavior
Objective
June 2002 3Illinois
Major Obstacle: Tackling System Complexity
Courtesy of Qualcomm
June 2002 4Illinois
EM Complexity– Geometric complexity and distributed nature of the
packaging hierarchy (“coupling path”)– Broad frequency bandwidth of the interfering signal– Non-linearity of the terminations
Tackling Complexity– Hierarchical approach to the modeling of
electromagnetic interactions• From lumped models, to transmission-line models, to
quasi-3D full-wave models, to 3D full-wave models Abstracting Complexity
– Systematic order reduction of numerical models of the coupling path
– Equivalent circuit representation of the coupling path for its seamless incorporation in network-oriented non-linear circuit simulators
System Complexity translates to EM Complexity
June 2002 5Illinois
Integrating Substrate
(PCB, MCM, …)
Packageddigital & analogdevices
Conducted& radiated
EMI
Radiated EMIVirtual couplingports
Physical coupling ports (e.g., connectors, cables…)
EM Modeling & Simulation
Model Order ReductionSynthesis
V
V
Network representation
of thecoupling
path
Sourcerepresentationof conductednoise at thephysical ports
Equivalent sourcerepresentation ofradiated EMI coupling
Non-linearlumped circuits
SUMMARY OF MODELING OBJECTIVE
June 2002 6Illinois
Specific Subtasks
Task 2.1 Development of a coupling path modeling methodology
Task 2.2 Development of a (EMI) source modeling methodology
Task 2.3 Non-linear Transient Simulation of the hybrid lumped-distributed non-linear network
June 2002 7Illinois
Subtask 1: Modeling of the Coupling Path
Printed Circuit Board
Package
Chip
IBM Corporation
June 2002 8Illinois
Our modeling approach is hierarchical– EM-Physics driven “divide and conquer” approach
Use suitable EM modeling approach for individual blocks– RLC models for short interconnect at chip & package level– Multi-conductor Transmission Lines (MTL)
• Balanced interconnects at the board level– Quasi-3D EM Modeling for PCB power delivery network– Full-wave modeling
•Unbalanced interconnects at the board level•Coupling through cables•RF/microwave packages & boards
Reduction of EM models to non-linear network simulator (e.g. SPICE)
– Direct model order reduction– Equivalent circuit synthesis
Subtask 1: Modeling of the Coupling Path (Cont)
June 2002 9Illinois
Block Diagram of EM Modeling Flow
June 2002 10Illinois
1
1( ( 1, ) ( , ))
( ( , 1) ( , ))
( , )z y y
x x
j xE H i j H i j
y H i j H i j
i j
( , ) ( , ) ( , 1)
( , ) ( , ) ( 1, )
z z
z z
x
y
j y
j x
H i j E i j E i j
H i j E i j E i j
Quasi-3D Modeling of Power Delivery Network
EM field between power/ground plane pairs exhibits, approximately, a two-dimensional variation• Use simple 2D FDTD Three-dimensional features (vias, pins,slots, voids, etc) require locally 3Dmodels to capture the correct physics
June 2002 11Illinois
I
V
-1
-1
( ) ( )( ),
( ) ( )
The multiport transfer function is:
( ) ,
( )
T
T
T
s ss s
s s
s s s where
s s
T
G D E C 0 EFU V = F X
D R H 0 L H
Y
C 0G -DV = F A + B FU( ) A = B =0 LD R
= F A + B F
The resulting discrete EM model
• Direct time-domain simulation is possible if desired• Could be synchronized with time-domain IE solver
• Alternatively, model order reduction of the transfer function using an Arnoldi-based subspace iteration method (PRIMA)
is used for the generation of a compact multiport
June 2002 12Illinois
11 1
1
( )
1 1
1 1
Nk k
k k
N NNk k
k k
R R
s
M M
k k
M M
k k
s P s P
R Rs P s P
Y
Multi-port representation of the reduced-order model is in terms of rational functions
Form compatible with circuit simulators that support rational function models (e.g. H-Spice, ADS)
Equivalent circuit synthesis is possible also
June 2002 13Illinois
0
0
01
For a passive, reciprocal multi-port, its admittance (or impedance)
matrix may be cast in the following form:
where it is:
Re{ } 0, 1,2, .
matrices
)
n
(
a d
Qq q
q
q q
a as s
s
p q
s
Q
p p
C
H G C G
, 0,1, 2,..., , are real and
positive semi-definite
Re{ } 0, 1,2, .
0<Im{ }Im{ } Re{ }Re{ } , 1, 2, .
q
q
q q q q
q Q
a q Q
a p a p q Q
G
Passive synthesis through Foster forms
June 2002 14Illinois
Equivalent circuit for a two-port
June 2002 15Illinois
Two-port sub-circuit for use in H-SPICE
June 2002 16Illinois
3 ports 10 ports 36 ports
H-SPICE 0.7 sec 5.73 sec 21.2 min
Equivalent 2.3 sec676.55
sec>12
hours
3 ports 10 ports 36 ports
H-SPICE 25.9 KB 53.4 KB 172 KB
Equivalent 308.2 KB 269 MB >2 GB
Elapsed Simulation Time
Transient Data File Size
The advantages of the direct use of the rational function macro-model in the simulator
The secret is in the recursive convolution that is utilized for the interfacing of the macro-model with the rest of the circuit
June 2002 17Illinois
|Z21| From H-SPICE
8 cm X 4 cm, 4 layer board. A 2mm gap is present all the way across the top ground plane. A total of 58 pins are used.
Top view
Cross-sectional view
Application to a 4-layer PCB
June 2002 18Illinois
H-SPICE calculation of the transient response. Switching occurs at port 1 while port 2 is terminated with 50ohm. Voltage at port 1 is depicted by the solid line. Voltage at port 2 is depicted by the dotted line.
Application to a 4-layer PCB (cont’d)
June 2002 19Illinois
Intel 4-layer test board
1st layer: Power plane
2nd layer: Ground plane
3rd layer: Ground plane
4th layer: Power plane
Validation study in progress
June 2002 20Illinois
Samples of the generated mesh
June 2002 21Illinois
Generated multi-port for switching noise simulation in SPICE
June 2002 22Illinois
Rational function multi-port & equivalent circuit synthesis from raw data
Data either from measurements or EM field solvers Step 1: Rational function fitting
– Process guarantees stability but not passivity
– Check fitted multi-port for passivity• If not passive, constrain fitting using Foster
constraints
•Repeat fitting
June 2002 23Illinois
Validation of rational function fitting
PCB interconnect test structures courtesy of Intel
June 2002 24Illinois
Validation of fitting (cont’d)
Measured |Y61|* Synthesized |Y61|
(*) Measurements courtesy of Intel Corporation
June 2002 25Illinois
EM modeling flow for the coupling path established
Quasi-3D EM Model for power delivery network completed
– Validation in progress– Further enhancements include:
• Incorporation of hooks for balanced MTLs• Incorporation of hooks for matrix transfer functions in
Foster form Capability for SPICE-compatible broadband
multi-port macro-model generation in place
Task 2.1 Summary
June 2002 26Illinois
Subtask 2.3: Non-linear Transient Simulation
Full wave modeling of printed circuit boards (PCBs) with fine geometric features, finite (and possibly inhomogeneous) dielectrics, and nonlinear loads and circuits
Interfaces with SPICE solvers and models
Physics-oriented nonlinear transient simulator
17.5 cm
4.5 cm
25 cm
25 cm
10 cm
1 cm
20 cm
30 cm
30 cm
15 cm
15 cm
1 cm
June 2002 27Illinois
Introduction (cont.)
Time Domain Integral Equation (TDIE) based Marching-on-in-time (MOT) solvers
Have been known to the acoustics and electromagnetics communities since the sixties.
Compared to frequency domain solvers, they can solve nonlinear problems directly.
Liu and Tesche (1976), Landt and Miller (1983), Djordjevic and Sarkar (1985), Deiseroth and Singer (1995), Orlandi (1996)
25 cm
25 cm
5 cm
17.5 cm
10 cm
1 cm
20 cm
4.5 cm6 cm 0.5
cm
varistorvaristor
June 2002 28Illinois
Introduction (cont.)
Now, we can / should be able to rapidly solve large -scale, nonlinear problems using the PWTD technology!!!
Unstable: … But recently many proposals have surfaced for stabilizing these schemes (Davies, Rao and Sarkar, Walker, Smith, Rynne,…);
Slow: … Computational complexity has prohibited application to analysis of large scale problems! … PWTD technology removes this computational bottleneck
However TDIE - MOT solvers have long been conceived as
O N NT S2c h
2( log )T S SO N N N
June 2002 29Illinois
( , )exc tE r( , )r tE r
Formulation - Problem Definition
Given an of 3-D inhomogeneous dielectric
bodies (V ), and 3-D arbitrarily shaped PEC surfaces, wires, and surface-wire junctions (S ),
Multiple linear / nonlinear lumped circuits connected to
a temporally bandlimited excitation
ckt 1
ckt m
interconnect geometry
S V
S V
lumpedlumpeddistributeddistributed
Solve for all transient currents and voltages
induced on the interconnect geometry
and the the circuits (ckt 1, …, ckt m)
radiated electric and/or magneticfields if required
S V
June 2002 30Illinois
2
0
, , ,t
r t t c dt tt
E r A r A r
,R r r
0 ( ) ( )( , ) ( , ) ( , ) ,
4 PEC DIEL
S V
t R c t R ct ds t dv t
R R
A r J r J r
Assume spatially-variable, frequency independent permittivity and free-space permeability in V, and thin wires in S .
0( , ) ( ( ) ) ( , )totalDIEL t t
t
J r r E r
(1)(1)
(2)(2)
Formulation – Time Domain Electric Field
( , )exc tE r
0 ( ) r
( , )r tE r
V
0
0 S
PECPEC
( ) rRadiated electric field:
June 2002 31Illinois
Expand current as1 0
( , ) ( ) ( ), , , ,S TN N
j qn n j
n j
S PEC DIEL
t I T t q s w sw d
N N N
J r f r
Surface and Volume Spatial Basis Functions
np
np
nV
nV
na
Formulation - MOT Algorithm
The temporal basis functions are local cubic polynomials
n
rnp
np
nT
nT
1
ˆns 1ˆns
nu 1nu nr
1nr1nr
kp
1A2A3A
rkT
June 2002 32Illinois
1
01
jexc
j j l j ll
Z I V Z I
unknownstested
incident field
previously computed
delayed interactions
immediate interactions
Construct a system of equations by applying spatial Galerkin testing at each time step.
for the j’th time step:
Formulation - MOT Algorithm (cont.)
June 2002 33Illinois
Formulation - Transient Circuit Simulator
SPICE-like transient circuit simulator
Performs linear and nonlinear large-signal analysis using Modified nodal analysisNonlinear equations solved using multi-dimensional
Newton Incorporates the following circuit elements: Independent/dependent voltage and current sources Resistors, inductors, capacitors Diodes, BJTs, MOSFETs, MESFETs
AC
DC
June 2002 34Illinois
Circuit behavior described by time-domain nodal equations (using trapezoidal rule for the jth time step)
0 1 1exc
j j j G V I G V
Formulation - Transient Circuit Simulator (cont.)
For m circuits, the nonlinear system of equations is
1 1 1 1,10 1 1
0 1 1,
0 1 1
excj jj
excj j j
exc mm m m mjj j
G V G VI
G V I G V
IG V G V
immediate interactions interactions from
previous time stepsourcesunknowns
previously computed
June 2002 35Illinois
1
01
01 1
0
0
jexcj l j ljv
l
j j excij j
V Z IIZ C
V G VCI G V
Formulation - Coupled EM / Circuit Equations
Combine the EM and circuit nodal equations into a single consistent system to be solved for EM and circuit unknowns at each time step
Coupling between the circuits and the interconnect structure is accounted for by matrices and
vC iC
SN CN
June 2002 36Illinois
Formulation - the MLPWTD Algorithm
SS
Level
Source block
Observer block
Direct(0) 1 2:
:
:
2( log )T S SO N N N1
01
j
excj j l j l
l
Z I V Z I
for typical PCB for typical PCB structuresstructures
June 2002 37Illinois
Analysis of Active Nonlinear Microwave Amplifier
Geometry
Objective Simulation Parameters
Characterize structure from 2-10 GHz
1468, 7096
8564, 512
5.0 ps
s v
s v t
N N
N N N
t
5080
110
70
31
90180
150
Input port
Output portDevice region
Ground plane
Dielectric constant = 2.33
2 220 0( , ) cos( )inc tt V t e V r
90 2 6 10 rad/s
116 , 6.82 10 st t
Excitation pulse
June 2002 38Illinois
MESFET Circuit Model
2 30 1 2 3( , ) ( ) tanh( )ds gs ds gs gs gs dsI v v A A v A v A v v
0( )1 /
gsgs c
c b
CC v
v
G0 .5
C gs0
1 .0
0.2 p F0.05 nH
Ids 0.6 p F
0 .7
0 .5 0.05 nH
0.1 nH
D
S
Vc
Amplifier : Nonlinear circuitry
June 2002 39Illinois
MOT results*
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1
-0.5
0
0.5
1
1.5
2
time (ns)
ampl
itude
(V
)
Input port voltage Output port voltage
Transient input/output waveforms
2 3 4 5 6 7 8 9 10-20
-15
-10
-5
0
5
10
15
20
Frequency (GHz)
dB
S21 - MOTS11 - MOTS21 - REFS11 - REF
* C. Kuo, B. Houshmand, and T. Itoh, “Full-wave analysis of packaged microwave circuits with active and nonlinear devices: an FDTD approach,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 819-826, May 1997.
Amplifier: Plane Wave Interference
June 2002 40Illinois
Geometry
Objective Simulation Parameters
Determine effect of shielding box on S-parameters
PEC shielding box(640x186x690mils
)
3288, 7096
10384, 700
6.25 ps
s v
s v t
N N
N N N
t
Amplifier + Shield: geometry
June 2002 41Illinois
2 3 4 5 6 7 8 9 10-20
-15
-10
-5
0
5
10
15
20
frequency (GHz)
dB
S21 - WITH SHIELDS11 - WITH SHIELDS21 - NO SHIELD S11 - NO SHIELD
Amplifier + Shield: S-parameters
June 2002 42Illinois
Amplifier + Shield: Plane Wave Interference
2 220 0( , ) cos( )exc tt t e E r E
0 ˆ ˆ500 500 V m E x y
ˆ6 ( )t t c z r
Transient response at transistor output
90 2 6 10 rad/s
118.68 10 s
k̂
excE
0 0.5 1 1.5 2 2.5 3-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Vol
tage
(V
)
Time (ns)
DG ONLY DG+PLANE-WAVE DG+PLANE-WAVE+SHIELD
June 2002 43Illinois
Transient response at transistor output
k̂
excE
2 220 0( , ) cos( )exc tt t e E r E
ˆ6 ( )t t c k r
90 2 4 10 rad/s
1/ 4 ns
145, 0i i
ˆ ˆ ˆ0.5736 0.8192 k x y
500 V/m, 500 V/mE E
Amplifier + Shield: Plane Wave Interference
June 2002 44Illinois
Transient response at transistor output
k̂
excE
2 220 0( , ) cos( )exc tt t e E r E
90 2 3 10 rad/s
3/14 ns
115, 45i i ˆ ˆ ˆ ˆ0.6409( ) 0.4226 k x y z
500 V/m, 500 V/mE E
ˆ6 ( )t t c k r
Amplifier + Shield: Plane Wave Interference
June 2002 45Illinois
2 220 0( , ) cos( )exc tt t e E r E
ˆ6 ( )t t c k r
Transient response at transistor output
90 2 6 10 rad/s
3/11 ns
k̂
excE
180, 0i i ˆ ˆk z
500 V/m, 500 V/mE E
Amplifier + Shield: Plane Wave Interference
June 2002 46Illinois
1) A MOT algorithm based on a hybrid surface/volume time domain integral equation has been developed for analysis of conducting/ inhomogeneous dielectric bodies,
2) This algorithm has been accelerated with the PWTD technology that rigorously reduces the computational complexity of the MOT solver to for typical PCB structures,
3) Linear/Nonlinear circuits in the system are modeled by coupling modified nodal analysis equations of circuits to MOT equations,
4) A nonlinear Newton-based solver is used at each time step to consistently solve for circuit and electromagnetic unknowns.
5) The proposed method can find extensive use in EMC/EMI and signal integrity analysis of PCB, interconnect and packaging structures with realistic complexity.
Task 2.3: Summary
2( log )T S SO N N N
2( )T SO N N