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

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

3. PB 1990-2009
[mrho]
40
SCATTERING PARAMETERS 20
S11 0
The measurement of the time- measure
-20
domain scattering parameters (or S-
parameters) during the -40 model
characterization of circuital parts 0 10 20 30 40 50 60 70 80 90 100
allows the user to quickly define TIME[nS]
accurate models, also for high a)
frequency applications. One of the [rho] 1.0
advantages of this technique is the
0.8
wide band of the measure (10-
20GHz) and the termination 0.6
required at the ports of the network S21
0.4
under test, usually 50 . Other
measurement techniques require 0.2
sometimes creating shorts or open 0.0
circuits in the network, that are 10 12 14 16 18 20 22 24 26 28 30
conditions usually difficult to b) TIME[nS]
realize for high frequency.
Fig. 5: Comparison between simulations and actual responses: a) S11, b) S21.
The S-parameter technique is based
on the measurement of reflected
b(t) = S(t) * a(t) or only three in the case the device
or transmitted voltage waves when
is not symmetrical. Some
the device is stimulated by an
where S(t) is the impulse response applications are presented in the
incident wave. Simple bipoles,
of the one-port device obtainable following.
whose model presents only one
from TDR measure and the symbol
port, are modeled by only one
* means time-convolution operator. COAXIAL CABLE
scattering parameter S(t).
Two-port devices require four
The relationship between the
scattering parameters but only two One of the characteristics of coaxial
reflected wave b and the incident
measures are enough if the device is cables is the uniformity of the
wave a is:
both symmetrical and reciprocal electrical parameters along it: for
(because the others are identical), 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
a) 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
b)
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
Fig. 6: PWL extraction of the scattering parameters S11(a) and S22(b).

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