PCB METAL PLANE MODELVALIDATION vs MEASURED TDR. 250X250X1.3mm MICRO-BEHAVIORAL 2D MODEL (10X8 array of LOSSY TRANSMISSION LINES)

1. Piero Belforte 1993 – rev. 2009
MODELLING AND SIMULATION OF
P.C.B. POWER AND GROUND
DISTRIBUTION PLANES
In circuits with very fast edges,
power and ground planes cannot be
considered ideal, zero-impedance
elements. Current pulses injected
by a switching driver at any point
on the plane generate a voltage
noise that propagates along the
plane.
The
circular
wave
propagating from the injection
point is reflected by both lumped
component discontinuities (e.g.
decoupling capacitors) and plane
boundaries, which act like open
terminations causing a total
reflection of the incident wave.
The result is a deterioration of
signals which will impair data
transmission. These effects can be
taken into account only by
including accurate models of the
ground and power planes in the
simulation.
Normally it is very difficult to
simulate these planes, not just from
the standpoint of modeling, but
more importantly because plane
models generally have a great
many
inductors
and/or
transmission lines, and simulators
such as Spice cannot handle these
efficiently.
DWS,
however,
simulates such models very
quickly.
Figure 1 shows a 2-layer metal
plane under investigation and its
crossection. If a TDR step (50 ps
rise time or less) is injected into
a metal layer using the other layer
as reference, a response such as
shown in Fig.2 is obtained.
For slow edges, the plane acts as a
two-plate capacitor of capacitance
where A ( A = 0.05 m2 ) is the
behavior of the two planes (DUT
plane and reference plane). The
detail of the waveforms shows a
P
y
t
hH
t
Y
X = 250mm
Y = 200mm
P = 25mm
t = 0.035 mm
h = 1.3 mm
TDR injection point
50
x
X
Fig. 1: Two-layer metal plane.
A
C 
0 r h
metal plane area, h ( h=1.3 mm )
the dielectric thickness and r (r=
4.7) the relative permittivity of the
dielectric. The overall time
constant is 50*C where 50 ohm is
the value of TDR reference
impedance. The overall curve
shows the general capacitive
significant noise due to TDR step
reflections at the open boundaries
of the plane. Changing the
injection
point
alters
this
waveforms. Almost any injection
point can be used as long as it
corresponds to the point used in the
simulation for model extraction by
parameter optimization.
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#RHO
0.80 #
0.60 #
0.40 #
0.20 #
0.00 #
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-0.40#
-0.60#
-0.80#
-1.00#
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00 100.00
TIME[nS]
Fig. 2: TDR response of the 2-layer metal plane
Copyright
Piero Belforte
1993-2012

2. 0.0 
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METAL PLANE MODELING
Two different approaches can be
used to implement the model: an
"unbalanced" or a "full-floating"
model. The "unbalanced" model
uses one of the two planes as an
ideal reference plane. In this case,
the propagation effects are
assigned to the second plane, that
is, quantized in both x and y
directions using a constant pitch of
approximately 25 mm. The latter is
then replaced by an array of ideal
transmission lines placed at the
edges of the mesh. (Fig. 3a)
This structure is useful for
modeling packages or p.c. boards
having only one metal plane. The
ideal plane used for reference will
consist of
the p.c. board
supporting the package or the
metal shield of the enclosure
containing the p.c. board.
As shown in Fig. 1, TDR pulse
is injected at an arbitrary point in
the actual plane. In the "full-
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Simulated
Measured
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0.00
5.00
10.00
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25.00
30.00
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45.00 50.00
TIME[nS]
Fig. 4: Lossless Plane Model Validation.
maintaining the same impedance
and propagation time values. The
resulting model is shown in Fig.
3b. This model can be used to
simulate coupling between two or
more metal planes for multilayer
structures.
shown in fig.4.The overall
behavior of the result approaches
the measured waveform but the
actual reflection noise is more
damped
than
its
simulated
counterpart. This damping effect
due to skin effect losses on copper
planes has a good noise limitation
effect so that ignoring it can be too
conservative.
LOSSY MODEL
MODEL VALIDATION
Starting
from
the
preceding
2Z0, TD
Z0, TD
Td = 120 ps
50 ohm
Z0 = 13.35 ohm
a
S11=0, S21=pwl, 2Z0
S11=0, S21=pwl, Z0
where pwl is:
50 ohm
1
2-port
S-parameter
B
A = 0.97
t = 300ps
B
A
tB
t
b
Fig. 3: Discrete approximation of TL model for a metal plane
a) Unbalanced model b) full-floating model
floating" model, both planes are
given a discrete representation and
used to simulate the propagation
effects. In this case the lines of the
"unbalanced" model are replaced
by balanced transmission lines,
DWS is used to validate the array
model simulating the TDR setup.
Simulation runs very fast, even if
178 transmission lines are required
to model the metal plane. The
result of model simulation is
considerations, a new version of
the 2-D model is created replacing
each ideal line with a lossy
counterpart represented by a 2-port
S-parameter block.

3. 0.0 
during post-layout checks included
in
the
POST-LAYOUT
environment.
In
this
case
distribution
plane
model
parameters are extracted from p.c.
board crossection data while power
pin and decoupling capacitors are
automatically connected to the
right nodes of the plane model.
Obviously this process causes a
quantization error that is negligible
if the array pitch has been selected
on the basis of bandwidth (time
resolution) requirements. In case of
more
complicated
physical
structures like gridded planes a
model optimization versus the
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0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00 50.00
TIME[nS]
Fig. 5: Measure and simulation of the lossy model.
For an accurate model, it is
necessary to adjust the model so
that the simulation of the
experimental setup fits the actual
TDR curve. This is a simple
parameter
extraction process,
adjusting the model parameters A
and
tB
inside
the
PWL
representation
of
the
S21
transmission coefficient of the
transmission lines of the mesh.
After a few trials, the optimized
parameter values are obtained as
shown in Fig.5. Correspondence
between
measurement
and
simulation is very good, including
damping effects. The addition of
two parameters determines a slight
slow down of simulation runs in
comparison with the lossless
model.
Imax=50mA
tr=tf=1ns
76
10nF
25mm
50mm
36
Cdec
10nF
125mm
Fig. 6: Analyzed situation
from simulations are shown in
Fig.7.
MODEL EXTENSIONS
actual
TDR
measure
is
recommended to get best results.
MULTILAYERED
STRUCTURES
More realistic situations can be
investigated using accurate device
and interconnect models connected
to the 2-D plane model. This task
can be carried out automatically
An extension to multilayered
structures can be obtained by
creating a stack of the models
50mV
BOUNCE NOISE
EVALUATION
The lossy model can be utilized to
evaluate the amount of switching
noise in actual operation. A
simplified test situation is shown
in Fig.6. The two-layer rectangular
p.c. board, a set of decoupling
capacitors and a noise source
consisting of a trapezoidal current
pulse are connected as shown in
Fig.6 . The effect of decoupling
capacitor placement on noise
amplitude at various positions
inside the p.c. board can be easily
analyzed. Some results coming
a)
0mV
V(36)
-50mV
50mV
a)
0mV
V(76)
-50mV
50mV
b)
0mV
V(36)
-50mV
50mV
b)
0mV
-50mV
40.00
V(76)
50.00
60.00
70.00
80.00
90.00 100.00 110.00 120.00 130.00 140.00
TIME[nS]
Fig. 7: Simulation of switching noise effects
a) Cdec on node 76, b) Cdec on node 36

4. shown in Fig.3. The first layer can
be modeled using both balanced
and unbalanced transmission lines,
while the upper layers are
represented only by balanced
models (Fig. 8a and 8b). In this
way
the
coupling between
superimposed metal planes is taken
into account implementing a quasistatic approximation of planecoupling effects.
Under steady state conditions, the
multilayered structure acts as a
capacitive divider. Depending on
the fineness of the mesh, a ground
plane model may consist of several
hundreds or even thousands of
transmission lines. However, since
DWS handles transmission lines
and BTM S-parameters blocks
very efficiently, this does not result
in overly long simulation times.
For example, simulating a p.c.b.
including interconnect models,
IBIS models, and
power
distribution planes containing
about 20,000 transmission lines
takes few seconds on a current PC.
Exploiting its unique performance
DWS is able also to simulate
conventional models, composed
tens of thousands of inductances
and resistances, generated by
commercial 3D Field Solvers.
Balanced transmission line
t1
t2
t3
t4
h1
h2 H
h3
Unbalanced transmission line
a)
Balanced transmission line
t1
t2
t3
b)
Fig. 8: Multilayered structures: a) mixed balanced and unbalanced model, b) full balanced model
h1
h2
H