1. PB FM 1990-2009
AN-01
DWS APPLICATIONS
PASSIVE COMPONENT MODELING
BASED ON REFLECTOMETER
MEASUREMENT
The speed of digital systems is
showing up the limits of the
standard modeling based on
lumped circuit parameters.
Interconnections few centimeters
long can be critical for the integrity
of signals if the rise time is smaller
than a nanosecond because of
reflections, dispersion and skin
effect. For example, a signal with a
subnanosecond rise time, and a
bad-designed board
interconnection few centimeters
long can invalidate the correct
performance of the design.
These problems require the
introduction of new concepts about
modeling techniques, based on
distributed models that can take all
the undesirable effects into
account.
According to the problem, several
models are available, with
different complexity:
1) Lumped LC model.
This model (Fig.1a) is the simplest
one and takes only the
characteristic impedance and the
propagation delay into account,
while losses can be modeled
through series or parallel resistors
(Fig.1b). This model cannot take
skin effect and dispersion
phenomena into account and may
be only used when the propagation
delay is shorter than the transition
time of the signal.
2) Distributed LC model.
In this case (Fig.1c), if the delay of
a single cell is smaller than the
transition time of the signal, there
is a partial modeling of skin effect
and dispersion phenomena during
the propagation of the signal.
Losses are modeled through series
and parallel resistors distributed in
each cell of the chain. Drawbacks
of this model are the large number
of cells that are necessary in order
to model the interconnection with
accuracy and the simulation time
that increases considerably.
3) Transmission line model.
This model (Fig.1d) is similar to
the previous one, where a
transmission line characterized by
Z0 (characteristic impedance) and
Td (propagation time) replaces the
LC element. A transmission line
is, for definition, a wide-band
circuit, that means that the input
waveform is transferred to the
output after the delay Td without
modifications1. Losses can be
modeled using resistors, as
discussed before2. As well as the
previous model, the number of
elements required to model a lossy
interconnection with accuracy can
increase very fast and the relatively
small propagation time of the
single pieces of transmission line
complicates the problem so that,
very often, the problem is not yet
1 If the line is terminated on its
characteristic impedance.
2 Or ladder RL for skin effect modeling.
Z0 Td Z0 Td
S11,S21
a) b)
c)
d) e)
(S22,S12)
Fig. 1: Interconnection models: a) lumped LC, b) lossy lumped, c) distributed LC,
d) Distributed lossy TLM, e) behavioral.

2. PB 1990-2009
solvable with conventional SPICE-
derived simulators.
The DWS simulation engine, not
only allows designers to simulate
the models already presented, but
also, thanks to a new
methodology, allows them to
use both standard models
and behavioral descriptions
based on REFLECTOMETER
MEASUREMENTS in time
domain (BTM - Behavioral Time
Modeling).
Using a reflectometer (TDR -
Time Domain Reflectometer) it is
possible to make a wide-band
characterization of one or two
port3 devices by means of the
measure of their scattering
parameters S11, S22, S21 e S12.
These models are very useful
where sections of interconnection,
pieces of coaxial cable, packages,
etc. can be characterized
experimentally. Usually, an
accurate electrical modeling of
passive devices is not possible,
because of their complicated
geometries. The utilization of field
simulators for the extraction of the
parameters of the cross section
shows a lot of troubles (first of all
the input description) and can't
take into account the
discontinuities that sometimes are
present along the device (for
example connectors). The
measures are directly utilizable
by the simulator giving the
3Models with more than two ports will be
soon available.
simulations a high degree of
realism. Standard component
libraries are already available, and
the user can easily create new
models with the utilities offered by
the graphic environment DWV
(DWS Waveform Viewer). This
methodology is also usable after
the prototyping phase in order to
verify the behavior of the
prototype in all the situations by
replacing the pre-layout models
(with lumped or distributed
parameters) with the measure-
based models. As a consequence it
is possible to use the simulation
tool for investigating the signal
waveform where it is not possible
to measure it, for example inside
the package.
-40
-20
0
20
[mrho]
40
0 10 20 30 40 50 60 70 80 90 100
TIME[nS]
30
S11
1
2
3
4
5
6
7
0.0
0.2
0.4
0.6
0.8
1.0[rho]
10 12 14 16 18 20 22 24 26 28
TIME[nS]
S21
1
2
3
4
5 6 7
a)
b)
Fig. 3: Measure and PWL extraction of the S11(a) and S21(b).
-40
-20
0
20
[mrho]
40
0 10 20 30 40 50 60 70 80 90 100
TIME[nS]
S11
A
B
C
D
E
Fig. 2: Measured TDR response of the parameter S11 for a coaxial cable
* Coaxial cable: TDR and TDT simulation for model validation
*
******************************************************************
*
*
* Coaxial cable description using S-parameters with PWL extraction
*
BCOAX 20 0 30 0 S11=PWL ( 0.0NS -3.26e-02 18.6NS -1.99e-03 19.2NS 3.23e-02
+ 20.4NS 2.49e-02 25.8NS 1.7e-02 47.2NS 8.42e-03 96.6NS 2.5e-03) Z0=50 TD=0
+ S21=PWL ( 0.0NS -1.53e-03 0.2NS 1.33e-01 .44NS 6.6e-01 .64NS 8.19e-01
+ 1.12NS 8.99e-01 2.2NS 9.42e-01 17.6NS 9.975e-01) Z0=50 TD=9.15NS
*
*
* termination resistor
*
RLOAD 30 0 50
*
*
*
* TDR step generator: a 2V step shows the result equivalent in RHO scale.
*
VTDR 20 0 PWL ( 0.0PS 0.0 3.25NS 0.0 3.28NS 2 ) 50
*
*
* analysis
*
.TRAN TSTEP=30P TSTOP=100N A(VTDR, 20) V(30) LIMPTS=1000
.END
Fig. 4: Simulation file (DWS syntax) used for model validation.

3. PB 1990-2009
SCATTERING PARAMETERS
The measurement of the time-
domain scattering parameters (or S-
parameters) during the
characterization of circuital parts
allows the user to quickly define
accurate models, also for high
frequency applications. One of the
advantages of this technique is the
wide band of the measure (10-
20GHz) and the termination
required at the ports of the network
under test, usually 50 . Other
measurement techniques require
sometimes creating shorts or open
circuits in the network, that are
conditions usually difficult to
realize for high frequency.
The S-parameter technique is based
on the measurement of reflected
or transmitted voltage waves when
the device is stimulated by an
incident wave. Simple bipoles,
whose model presents only one
port, are modeled by only one
scattering parameter S(t).
The relationship between the
reflected wave b and the incident
wave a is:
b(t) = S(t) * a(t)
where S(t) is the impulse response
of the one-port device obtainable
from TDR measure and the symbol
* means time-convolution operator.
Two-port devices require four
scattering parameters but only two
measures are enough if the device is
both symmetrical and reciprocal
(because the others are identical),
or only three in the case the device
is not symmetrical. Some
applications are presented in the
following.
COAXIAL CABLE
One of the characteristics of coaxial
cables is the uniformity of the
electrical parameters along it: for
this reason the cable may be
modeled by a reciprocal (S21 =
S12) and symmetrical (S22 = S11)
two-port element. Fig. 2 shows a
typical measured TDR response of
the parameter S11 for a section of
micro coaxial cable 2 meters long
with a characteristic impedance of
50 . The response is displayed
with the graphic environment DWV
after the measure has been captured
from the measure set-up. The
vertical scale is expressed in m (it
is reminded that = 0 is equivalent
to a 50 resistance, = 1 an
open circuit and = -1 a short).
The peak A is a parasitic effect
due to the end of the launch cable,
in the point where it is jointed with
the device under test. The section B
shows the reflection during the
40
10 12 14 16 18 20 22 24 26 28 30
TIME[nS]
0 10 20 30 40 50 60 70 80 90 100
TIME[nS]
-40
-20
0
20
0.0
0.2
0.4
0.6
0.8
1.0[rho]
[mrho]
S11
S21
measure
model
a)
b)
Fig. 5: Comparison between simulations and actual responses: a) S11, b) S21.
a)
b)
Fig. 6: PWL extraction of the scattering parameters S11(a) and S22(b).

4. PB 1990-2009
propagation of the incident wave4
along the cable.
The vertical step is due to the
mismatch between the impedance
of the micro coaxial cable and the
reference impedance at the port 1
(50 ) and its value is about-30m
(corresponding to a Z0 of about
47.1 ). The slope of the B section
is a typical effect of the skin effect.
It is possible to note the
discontinuities due to small changes
of geometry that are detected as Z0
changes. The point C shows the
discontinuity at the far end of the
cable and the E amplitude at the
end of the D section (constituted by
the multiple reflections inside the
cable for skin effect) corresponds to
the ohmic resistance of the cable
(about 250 m in this example).
DWS is able to directly utilize the
samples captured from the measure,
but in order to avoid useless
increase of the simulation time, it is
useful to extract the most
significant part of the measure
using the PWLEXTRACT utility of
DWV: Fig.3a shows an example of
piecewise linear extraction with
only 7 samples.
Fig.3b shows the measure of the
S21 and its related PWL extraction.
The two-parameter descriptions are
then combined in a single DWS
statement representing the model of
4 In this case, the incident wave is a voltage
step with a rise time of 25ps.
the interconnection. It is possible
now to validate the model by means
of a simulation, for example, of the
same measure scheme. The listing
of the input file used for the
simulation is shown in Fig.4 and the
correspondent results are shown in
Fig. 5a e 5b: it is possible to point
out the good correspondence
between the simulation responses
versus the actual measure. The
models can be used in chains or sub
circuits, for modeling longer
sections of cable.
BACKPLANE CONNECTOR
This example shows a connector as
a typical asymmetrical device,
whose structure is very difficult to
model in terms of lumped
parameters because of its electrical
discontinuities. For this reason a
behavioral model is more accurate
and easy to build.
The model we are going to propose
takes the asymmetry of the device
(S22 not equal to S11) into account.
In this example, the device is
reciprocal (S21 = S12) so only a
transmitting measure is required.
Fig.6a shows a typical TDR
response during the measurement of
the parameter S11 (backplane side).
The response is displayed using the
graphic environment DWV after the
measure has been captured from the
measure set-up. The same picture
reports also the PWL extraction of
the most significant portion of the
measure. The approximation starts
after the first peak that is a parasitic
effect due to the end of the launch
cable, in the point where it is
jointed with the device under test,
and must be ignored. It is possible
to note the strong discontinuities
present in the device that are
detected as Z0 changes. Fig. 6b
shows the measure and its related
PWL extraction of the S22
parameter (board side).
The descriptions of the two
parameters plus a simple
description of the S21 parameter
are then combined in a single DWS
statement representing the model of
the connector. Fig. 7 shows a listing
of the model. It is possible now to
validate the model by means of a
simulation, for example, of the
same measure scheme used for the
S11 characterization.
CONCLUSION
A very accurate and easy-to-do
modeling approach has been
presented. The methodology is well
applicable for both passive and
active (see AN-02) devices. The
models are extracted from
measurements using the utilities of
the graphic environment DWV and
allow the DWS simulator to achieve
result accuracy, otherwise
impossible, still maintaining run
times orders of magnitude shorter
than those of traditional products.
**********************************************************
*** CONNECTOR MODEL ***
**********************************************************
.SUBCKT CONCTOR 1 2
* 1=backpanel side, 2=board side
*
* behavioural description
BCON 1 0 2 0
+ S11=PWL(0 -1.53e-03 50PS 3.72e-01 160PS -3.78e-01 240PS -2.61e-01
+ 280PS -9.34e-02 340PS -2.22e-01 400PS -1.67e-01 430PS -8.73e-02
+ 560PS -1.53e-03) Z0=50 TD=0
+ S21=PWL(0 0 50PS 1) Z0=50 TD=230PS
+ S22=PWL(0 2.91e-04 60PS -1.07e-01 110PS -7.93e-02 190PS -2.74e-01
+ 220PS -2.74e-01 280PS -1.23e-01 330PS -3.48e-01 400PS -3.48e-01
+ 510PS 2.7e-01 550PS 3.11e-02 560PS -2.69e-03) Z0=50 TD=0
*
.END CONCTOR
Fig. 7: Connector model description (DWS syntax).