Comparative models and simulations of a RG58 coaxial cable using mathematical method, CST Cable Studio, DWS (spicy SWAN)

1. Copyright Piero Belforte
Dec 24th 2013
RG58 coaxial cable: A comparison among Analytical
models, DWS BTM models, TDR measures and CST
2013 Cable Studio simulations
A 1m long RG58 coaxial cable, has been mathematically
modeled by Spartaco Caniggia including both skin and dielectric
losses in frequency domain, calculating the Inverse Fourier
Transform to get the time domain step response of S-parameters
S11 and S21.
The method was applied for a 25ps and 5ps ramp input.
Ramp stimulus rise time choice has to take into account the error
introduced with respect the required ideal step stimulus
theoretically required to apply the BTM (Behavioral Time
Domain, Hp seminar 1993 PB -New modeling & simulation
environment) method supported by DWS:
Prediction of rise time errors of a cascade of behavioral cells
The responses have been converted in piecewise linear (pwl)
BTM models for the DWS simulator and simulated for different
cable lengths using the chain utility of DWS. DWS supports file
description of S-parameters behaviors but pwl approximation is
mandatory to get fast simulations. Simulation time depends
inversely on total number of breakpoints. Usually 10-20
breakpoints are enough for each S-parameter to get a good
accuracy/speed trade off.
1

2. Copyright Piero Belforte
Dec 24th 2013
A comparison between the 5ps and 25ps input BTM model is
reported here:
https://www.ischematics.com/webspicy/report.py?RCODE=2856
8183274204325605as#.UrlzaMRWGSo
Here a comparison between the output of a 10m cable with a
100ps ramp input obtained as a cascade of 10 cells and its
analytical response
The waveforms are practically coincident, confirming the validity
of both the analytical method and of the BTM model. Pwl BTM
models run very fast on DWS allowing the user to simulate
circuits containing several basic cells in seconds.
The BTM model related to 1 m long cable was then used in
several Spicy SWAN circuits to compare the results with cellular
(micro-behavioral) BTM models previously optimized to match
the actual TDR (CSA 803) measures reported here:
TDR measurement of RG58 coaxial cable S-parameters
2

3. Copyright Piero Belforte
Dec 24th 2013
As example here two links to Spicy SWAN simulation reports of
these configurations:
https://www.ischematics.com/webspicy/report.py?RCODE=2811
2485416218536178as#.UrlyL8RWGSo
https://www.ischematics.com/webspicy/report.py?RCODE=2156
5334337162836476as#.UrhMssRWGSo
From previous comparisons on a 2m long cable, it seems that the
rising edge of the S21 is faster than the actual cable response.
The S11 peak is also higher (about twice) with respect the actual
cable. From these results it seems that both skin effect and
dielectric losses are underestimated in the mathematical model.
This conclusion seems confirmed by a direct comparison with a
open ended 7m long cable TDR (CSA 803) response.
The simulation report of this configuration is reported here:
https://www.ischematics.com/webspicy/report.py?RCODE=1687
3485375207814476as#newwin
And in the 3 following figures the direct comparison with the
actual measurements is shown:
3

4. Copyright Piero Belforte
Dec 24th 2013
4

5. Copyright Piero Belforte
Dec 24th 2013
CST 2013 CABLE STUDIO simulations
The 1m long RG58 was modeled and simulated using CST's Cable
Studio version 2013.
To minimize the errors due to model bandwidth, a 40Ghz
bandwidth for the model was chosen. Both skin and dielectric
losses were taken into account. These choices increase the
simulation time: more than 1 hour was required for a 10ns
window using a maximum time step of 1ps to run a single
simulation. 4 CPU (I7) cores were engaged during the simulation
task (50% of the full CPU processing power). The simulations
were carried out for both a 25ps and a 5ps ramp input.
In the 4 following figures several result comparisons are
reported.
5

6. Copyright Piero Belforte
Dec 24th 2013
6

7. Copyright Piero Belforte
Dec 24th 2013
7

8. Copyright Piero Belforte
Dec 24th 2013
Conclusions.
1) Mathematical methods can be a quick way to get fast BTM
models of coaxial cables. Dielectric and skin effect losses seem
underestimated unless corrective coefficient is introduced to
take into account the actual physical structure of cables (tinned
copper wires, stranded conductors, braided shield etc., see the 2
following figures).
8

9. Copyright Piero Belforte
Dec 24th 2013
In particular tinned copper conductors can show a complex skin
effect due to 1-10 um thick tin surface. Tin has a resistivity that is
about 7 times greater than copper. At 1Ghz skin depth for
copper is about 2um so the resistivity used as input parameter of
predictive methods should be selected between copper and tin
values. The optimum resistivity value should be set by fitting the
S11 behavior with actual measurement.
Skin depth calculator
Even dielectric permittivity of the insulator should be adjusted to
perfectly match the measurements with particular reference to
cable delay. An adjustment of 50-100ps has been required to
match the 5ns delay of the 1 m long sample. This 1m long cable
requires a 5ps (or less) rise time input stimulus to get accurate
results on S21 response.
9

10. Copyright Piero Belforte
Dec 24th 2013
2) CST Cable Studio 2013 provides results comparable to
mathematical method. Losses seems underestimated even if less
than for the analytical approach for dielectric losses. Long
simulation times are required (1hour with 4 I7 CPU cores).CST
results are potentially utilizable to derive fast BTM models for
DWS even if also in this case some correction on input
parameters is required for better matching of measurements.
3) All predictive methods used so far (numerical simulation
including 3D field solvers and analytical methods based on
frequency domain expressions of losses) suffer of bandwidth
limitations. This means that there is a lower limit of physical
length of cable to be characterized and to related input ramp rise
time. This limit is in the region of 1m for the RG58 under analysis
corresponding to a 5ps rise time of the input ramp approximating
the ideal step response. For example here a comparison between
DWS and Simbeor about the prediction of S-parameters for a
5cm long RG58 is shown:
10

11. Copyright Piero Belforte
Dec 24th 2013
A direct time-domain mathematical expression of S-parameters
could overcome the bandwidth (rise time) limitation issue.
4) BTM models extracted from actual TDR measurements are the
most realistic because they take into account all actual cable
behaviors including impedance micro discontinuities.
In this case the TDR measurement setup has to be de-embedded
to get accurate results. With TDR rise times in the order of 20ps
(CSA803) the minimum cable length to be characterized is in the
order of 1-2 m or more .
BTM pwl models run very fast (seconds) on DWS (Spicy SWAN)
using picosecond range simulation time steps even for long
cables. Only one CPU core is engaged on multi-core CPUs for each
DWS task, minimizing the power consumption.
Pwl S-parameters models are numerically very stable, so that
even a not perfect matching between S11 and S21 is allowable to
get numerically stable results.
Obviously this modeling method can be applied to all types of
cable and interconnnections.
Here a Spicy SWAN simulation report related to a trifilar cable:
https://www.ischematics.com/webspicy/report.py?RCODE=3853
1030073586323447as#.UrxsasRWGSo
5) Accurate micro-behavioral BTM models for DWS can be
derived from previous methods (Analytical and CST) and/or from
circuital cellular models (Spice, DWS) applying corrections to
11

12. Copyright Piero Belforte
Dec 24th 2013
match the actual measurements. Here an example of this
procedure applied to optimize some breakpoint of a 18.3cm BTM
cell derived from a vector-fitting RL-TL model. The optimization
process automatically de-embeds cell parameters (breakpoints)
from TDR setup effects because the optimized configuration
includes the measurement setup.
Optimization of coax cable BTM cell breakpoints
This procedure could be performed automatically by a suitable
optimization program.
6) Hybrid micro-behavioral models can be also developed mixing
in the same basic cell S-parameter behavioral blocks and circuital
elements.
This Hybrid technique has been utilized to match the S21 rising
edge of a 1.83m long cable within the 5 cm RL-TL cell by
replacing the lossless Transmission Line of the elementary cell
with a lossy TL (LTL). The RL-TL using an ideal TL is not able to
take into account dielectric loss effect on S21 rise time.
Only one parameter ( S21 ramp rise time, 3ps) is required to
match the actual measurement by taking dielectric losses into
account.
https://www.ischematics.com/webspicy/report.py?RCODE=5761
0115134168853871a#.UrqxucRWGSo
In this way a fast mixed circuital/behavioral model is obtained
with a "short" spatial definition step (5cm).
12

13. Copyright Piero Belforte
Dec 24th 2013
Micro-behavioral technique has been also successfully utilized in
the past (Piero Belforte 1993-2009) to get fast and accurate DWS
models of p.c.b. power distribution metal planes:
1993-P.C.B. power/ground distribution plane models
2009 Micro-behavioral models of FR4 laminates
and to lossy coupled traces of p.c. boards:
2009-micro-behavioral models of lossy coupled lines
http://www.youtube.com/watch?v=r8MJrkzqRL0 (set 480p for
best viewing)
Micro-behavioral techniques have the advantage of "scaling
down" the length of the elementary cell with respect the original
measure. In this way even sub-multiple lengths of the original
measured cable can be simulated mitigating the bandwidth
limitation of both analytical and simulative methods. A simple
TDR measurement at one-port only with other ports left open is
required to optimize the micro-behavioral model (pwl
breakpoints).
7) A Hybrid cell structure can be also utilized to model the long
waveform tail of both S11 and S21. A single RC cell with negative
parameters values added to the BTM 2-port block is enough to
create the long tail in the truncated behavior of BTM cells. The
following figure shows an example of the correction effect of the
13

14. Copyright Piero Belforte
Dec 24th 2013
added RC cell (-0.1 ohm in parallel to -10uF) for a 10 m long cable
modeled as cascade of 10 BTM cells (100ps ramp input stimulus).
8) Complex structures including metal planes and coaxial cables
can be simulated in seconds using measure-derived BTM models
leading to high-reality results:
https://www.ischematics.com/webspicy/report.py?RCODE=2461
7017134125327611as#.UrxeTMRWGSo
14

15. Copyright Piero Belforte
Dec 24th 2013
8) Actual cables are affected by impedance discontinuities that
are not included in predictive models. Only measure-derived
BTM models can take into account in a simple way these
additional effects still holding fast simulation speed(seconds)
even for long cables. The distributed micro-reflections of
reflected wave (S11) cause and additive random noise that
affects bidirectional transmission configurations. In the
following example this effect is clearly visible:
https://www.ischematics.com/webspicy/report.py?RCODE=5073
5623343426046486a#.UrxpOsRWGSo
15

16. Copyright Piero Belforte
Dec 24th 2013
This kind of simulations is out of reach of conventional models
and simulators.
9) DWS is the most accurate and fast simulation engine for
circuital (RLC-TL), behavioral and hybrid s-parameters models.
Several order of magnitude simulation time speedup factors can
be obtained over conventional NA simulators:
DWS vs Microcap10 comparative benchmarks
16

17. Copyright Piero Belforte
Dec 24th 2013
2012 - DWS vs Microcap 10 time trial (set HD option for best
viewing)
10 ) Actual measurements are always needed to validate the
models even for "simple" geometries like coaxial cables.
17

18. Copyright Piero Belforte
Dec 24th 2013
Useful WEB links
Hp seminar 1993 PB -New modeling & simulation environment
http://www.ischematics.com/
https://www.cst.com/
DWS concepts
https://www.facebook.com/SpicySchematics
2007- J. SCHRADER- WIRELINE EQUALIZATION BOOK
2013_PB_TDR MEASUREMENTS ON RG58 COAXIAL CABLE
CST 2013-S.Caniggia-Modeling interconnects and pdn of pcb
Skin effect depth calculator
18

19. Copyright Piero Belforte
Dec 24th 2013
2013-Linkedin discussion on PDNs
http://www.simberian.com/
19