1.
Comparison of timedomain Sparameters of RG58 cable
computed by: Theory, CST,
SPICE, DWS
S. Caniggia, P. Belforte
February 04, 2014
1
2.
Outline
•
•
•
•
•
•
•
•
•
Introduction
Sparameter definition in time domain
Simulations of a 18.3cm RG58 coaxial cable
S11&S21 computed by analytic approach (theory)
Cable Studio 2013 results as source of a BTM of a 1.83m RG58 coaxial cable used in DWS
Analytical method results as source of a BTM of a 10m
RG58 coaxial cable used in DWS
Conclusions
Appendix: Dielectric losses (Tanδ)
References
2
3.
Introduction
•
•
•
•
•
•
In this report, the sixth of a series devoted to lossy lines [1,2,3,7,8],
several approaches for computing timedomain step responses of a
lossy line are outlined and compared.
The methods used are: MWS of CST, CS of CST, RLTL model for
SPICE & DWS, Theory.
The purpose is to pinpoint the advantages and drawbacks of each
approach for simulating lossy lines.
The feasibility of deriving BTM models to be used by DWS is
analyzed. Long lossy lines can be simulated by DWS in seconds
using a cascade of shorter line segment characterized as Behavior
Transmission Model (BTM) by parameters S11 & S21 in time
domain (7,9).
These S parameters can be computed by CS or theory and can be
used as models for DWS. If a piecewise linear (pwl) approximation
is used for behaviors, a dramatic speedup of simulations can be
obtained
A typical RG58 coaxial cable is used as line sample for the study.
4.
Methods for time domain simulations of lossy lines [4]
Three methods can be used to simulate lossy lines in transient. The choice depends
on which simulator should be used for a simple or complex line structure.
1.
Behavioral Transmission line Model (BTM) block, based on timedomain step
responses of lossy line Sparameter to be used within the Digital Wave
Simulator (DWS) [1,2,3,7,8,9] to get quick simulations.
2.
Vector fitting technique (VFT) [4,6] to set, starting from analytical expression
of losses, an equivalent circuit for a cascade of RLGCTL (lossless) segments of
line electrically short to be used with a SPICElike circuit simulator such as
MC10 [1,2,3,4,6] or DWS for faster (12 order of magnitude) simulations
[1,2,3,7,8] .
3.
Model Order Reduction (MOR) technique to set, starting from S parameters,
an equivalent circuit of the line (complex net of RLGCTL) for the frequency
range of interest to be used by CST circuit simulator [1,2,3,7,9].
Note:
•
The lossy line can be both a cable or a PCB trace.
•
VTF and MOR should be used for the frequency range of interest.
•
CST is particularly suitable for complex line structures such as multiconductor
lines with shields.
•
DWS allows the use of hybrid BTM and circuital models [8]
5.
Flow chart for direct transient simulation of lossy lines by using
three different methods: SPICE, CST, DWS [4].
Define the line (a,p,σ,μ,Rdc,tanθ,Kp) and compute the perunitline parameters: Zi, L0, C0, Gd
unit cell
RL
TL
Segmented line
Full line
Which
model ?
GC
One block: measured or
computed Sparameter line in
time domain
S11
One block
complex RLGCTL net
Zi, L0,C0, Gd
VFT technique
Modeling
Cascade of unit cells to
form a block (SPICElike
Sim.)
MOR technique
S21
Which
technique?
S technique
Modeling
Modeling
One RLGCTL block
One BTM block
(DWS)
(SPICE in CST)
Cable block in schematic
Simulated waveforms with several loadings
(passive/active, linear/nonlinear)
7.
Sparameter definition for twoport network [5]
I1
a1
I2
+
+
Z01
b1
V1
Two port network

V2

a2
b2
Z02
With n=1,2:
Normalized
incident wave
Vn
an
Z0n
Vn (Vn Vn  ) Z0n (a n b n )
1
1
In
(Vn Vn  )
(a n b n )
Z0n
Z0n
Vn
bn
Z0n
Normalized
reflected wave
b1 S11 S12 a1
b S
S22 a 2
2 21
7
8.
Sparameter physical interpretation [5]
a1
a2=0
Z01
+
Source applied
to Port 1

b1 S11a1
b 2 S21a1
a1
Port 2 matched
Two port network
b1
Z02
b2
S11 is just the input reflection coefficient when the
output is matched.
S21 is the ratio of waves to the right at output and input
under this condition.
V1 Z01I1
2 Z01
V1 Z01I1
b1
2 Z01
When Z01=Z02=Z0 (the characteristic impedance of the two port network
representing a cable), and the source is a step of amplitude 2V: 1+S11 and S21
are the V1 and V2 voltages respectively.
8
9.
Port signals in MWS
•
•
•
•
MWS stimulates the network by means of a gaussian pulse having
a flat bandwidth up to the maximum frequency defined by the user.
Port signals: (i1), (o1,1), (o2,1) of MWS have the meaning
respectively of incident (a1), reflected wave at port1 (b1) and
reflected wave at port2 (b2).
Better results can be obtained by using waveguide ports instead of
discrete ports when possible: less oscillations in reflected wave b1.
To find equivalent circuit of a DUT it is better to use the option in
MWS “S parameters without normalization to fixed impedance”
instead of “…with…”: resonance peaks are avoided. These
resonances are due to mismatch between port and waveguide
which could be: coaxial cable, microstrip, etc.
•
Integrating (o1,1) & (o2,1) waveforms in time domain, we get the
response at port1 (1+S11) and port2 (S21) of a step pulse with rise
time tr determined by the maximum frequency.
•
The source pulse is obtained by integrating (i1) of MWS.
9
10.
S parameters in time domain
Typical source and load voltage waveforms for an interconnect matched
at both ends: lossless TL (dashed line), frequencydependent lossy TL
(solid line) [6, Fig.7.3]
Definitions of S
parameters in time
domain:
•VS=1+S11
•VL=S21
When TL has characteristic impedance different from the loads, distortions occur
10
11.
Simulations of a 18.3cm RG58
coaxial cable
11
12.
Sparameters calculations
•
•
•
•
•
•
Timedomain Sparameters computation from incident and reflected
waves provided by MWS is shown.
S11 and S21 timedomain step responses with matched line at both
ends are computed integrating the waveforms provided by MWS
when using waveguide ports.
Comparison with RLTL model used by MC10 (SPICE) or DWS
[1,2,3] and 2DTL model of Cable Studio (CS) [3] is given.
CS 2013 takes into account also proximity effects [3].
The accuracy of models has been evaluated by comparison with
actual TDR measurements of a 1.83m RG58 coaxial cable [2,3,7,8].
The lack of dielectric losses in the RLTL model is somewhat
compensated by the overestimation of skin effect [3].
12
14.
Input signal in MWS
Gaussian (40GHz)
Step source
Integration of
gaussian
normalized to
maximum value
of the integral
Tr=23ps
14
Rise time tr between 1090% is about 23ps as used in TDR measurements
15.
Port signals of RG58 in MWS
i1
o21
ns
o11
ns
Integrating o11
and o21 and
normalizing the
results to the
maximum value
of the gaussian
integral, we get
respectively S11
and S21 as
response of a
step with tr=23 ps
15
16.
Cable studio (CS) structure
Step source with 40GHz
bandwidth imported from
MWS (see previuos slide)
Ohmic losses only
16
17.
MC10 (SPICE) structure
The equivalent RL circuit was
obtained by VFT applied to
compact expressions for
coaxial cable without factor ½,
see Eq.7.57 of [6]
Step source
with tr=25ps
S11=VTin
S21=VTout
Cascade of 100 1.83mm unit RLTL cell
17
19.
Input (1+S11) and output (S21) line waveforms
Line length= 18.3 cm
1+S11
S21
MWS
waveforms
ps
Remark: MC10 and CS provide similar waveforms
19
20.
S11
Volt
MC10&DWS
MWS: solid
CS: dot
MWS&CS
MC10: dash
ps
• MC10 & DWS with RLTL cells compute the
same waveforms [10]
• MWS & CS provide about similar waveforms
with less losses (lower values than DWS & MC10)
20
21.
1+S11 and S21
Volt
1+S11
MC10
MWS: solid
MWS&CS
CS: dot
MC10: dash
MWS&CS
MC10
S21
DWS
1+S11
ps
• MC10 & DWS compute the
same waveforms [10]
• MWS & CS compute similar
waveforms with about half losses
S21
• S11 of CS & DWS show some
slight segmentation due to 37cell discretization
21
22.
1+S11 and S21 with and without dielectric
losses
MC10
CS
CS
MC10
•Solid MC10 RLTL without dielectric losses
•Dash CS 2013 without dielectric losses
•Dot CS 2013 with dielectric losses (Tanδ=0.8m)
Dielectric losses introduce just a slight difference in this
portion of the waveform
22
23.
CS 2012: Adding dielectric losses
(tanδ=0.8m)
Volt
Ohmic losses
1+S11
S21
sec
Volt
Ohmic + dielectric losses
1+S11
S21
sec
•There are slight
differences in this
portion of the
waveform
•The
segmentation
effect is
eliminated 23
24.
CS 2013: Adding dielectric losses
(tanδ=0.8m)
Volt
Ohmic losses
1+S11
S21
sec
Volt
Ohmic + dielectric losses
1+S11
•The
segmentation
effect is
eliminated also
for ohmic losses
• There is a slight
increase of losses
due to proximity
effect in CST
2013 vs 2012
S21
sec
24
25.
Input and output line voltages
VS
VL
MC10
VS
VL
MWS 2013
VS
VL
CS 2013
•For MC10 a ramp has
been used
•For MWS and CS the
time integral of a
gaussian (40GHz BW)
has been used.
• S11 (=Vin1) and S21 (=Vout)
should be computed with an input
step of about 1ps rise time to
approximate the ideal step
response.
• A non zero rise time input could
give some inaccuracy when using
these responses to get a BTM
model [11].
• In the following slides this error
25
will be estimated.
26.
Comments on simulations
•
•
•
•
•
•
MC10 & DWS by using RLTL model compute the same waveforms
and are used as reference being validated experimentally [1,2,3].
MWS & CS provide similar waveforms with less losses respect to
RLTL model, as verified in [1,2].
MWS waveforms evolves more rapidly than CS towards dc values
for high values of time.
S11 of DWS shows a small ringing due to finite number of cell
segmentation.
This effect can be eliminated by using more unit cells (example 100
as done with MC10).
DWS simulations are very fast (50+ times faster than MC 10) at
equal cell number.
26
27.
S11&S21 computed by analytic
approach (Theory)
28.
Analytic method
•
•
•
•
•
•
The method used for computing S11 & S21 in time domain is outlined in
[4] and with more details in chapter 7, subparagraph 7.1.5.2 of [6].
A linear ramp of tr=25ps for a cable length of 18.3cm and tr=100ps for
1.83m are used as input .
Tangent delta (θo) is set to 0.8m, see Appendix.
Skin effect is computed by Eq.7.57 of [6] by using a factor ½ for
comparison with CS and without the factor ½ for comparison with RLTL
model.
MathCad code professional 2001i is used for analytic computations.
The comparisons are performed among: RLTL model (RLTL), Cable
Studio ohmic losses (cs), Cable Studio ohmic+dielectric losses (cs_d),
analytic results with all losses (Theory).
30.
Skin effect (compact expressions)
½ factor
• In [5], Ziwcoaxb and Zishcoaxb expressions for a coaxial cable, are reported without the
factor ½, while for a round wire the factor ½ should be used.
•It will be shown that cs waveforms are in agreement with theory using factor ½
(round wire) while RLTL waveforms are in agreement with theory without factor ½
because vector fitting technique (VFT) was applied starting from these expressions.
31.
Skin effect impedances (Ohm/m)
•ZiSkinw Internal wire
impedance computed as round
wire, see chapter 7 of [6] for
the expressions.
•Ziwcoaxb Internal wire
impedance computed by
compact expression with ½
factor.
•Zishcoaxb Shield impedance
computed by compact
expression with ½ factor.
• ZiSkin= Ziwcoaxb+ Zishcoaxb Total
impedance of the cable
ZiSkinw and Ziwcoaxb provide the same values
See also the results reported in [3] for the 18.3cm RG58 cable
32.
Dielectric losses and line parameters
Dielectric losses
Line parametrs
For more details, see chapter 7 of [6]
33.
Output rise time comparison (Len=18.3cm)
MC, CS, CS_d
ps
Theory
ns
• Good agreement
nevertheless a
ramp and not a
gaussian shape has
been used
• A delay of 22ps
has been introduced
into theorical result
for comparison
reasons
34.
S11&S21 computed with factor ½
(Len=18.3cm)
cs_d
cs_d
Theory
• Good agreement
between cs_d and
theory
• S11 of theory is
slightly lower
35.
S11&S21 computed without factor ½
(Len=18.3cm)
•Very good agreement
between RLTL model
and theory
RLTL
RLTL
ps
Theory
ns
•The reason is that the
RLTL model was
obtained by VFT using
compact skin effect
expressions for coaxial
cable without factor ½.
36.
S11 computed with factor ½ (Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
CST provides slightly lower values
37.
S21 computed with factor ½ (Len=1.83m)
Theory
Both methods provide the same values
Cable studio
(Bandwith=10GHz)
38.
1+S11 computed without factor ½
(Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
Theory provides more than doubled values for S11
39.
S21 computed without factor ½ (Len=1.83m)
Theory
Theory computes slight lower rising edge values
Cable studio
after the 80% of its DC level
(Bandwith=10GHz)
40.
Comments on analytic approach
•
•
•
•
Good agreement between CS and theory waveforms considering all
losses.
RLTL model overestimates the losses due to the lack of .5 factor in
skin effect compact expressions used to get the equivalent RL circuit
by Vector Fitting Technique.
This difference compensates the lack of dielectric losses in the model
RLTL and justifies the good agreement with the measured waveform
tails as shown in [2,3].
The S21 rising edge coming from the RLTL model is too fast due to
lack of dielectric losses and can be compensated using a DWS
RL_LTL hybrid model as shown in [8]
41.
Cable Studio results as source of a
BTM of a 1.83m RG58 coaxial cable
used in DWS
41
42.
Used BTM procedure
•
•
•
•
The S11 and S21 computed by cable studio (CS) 2013 for a 18.3cm of RG58 (040GHz) have been used as sources to get the
Behavioral Transmission Model (BTM) in DWS.
The waveforms obtained from a 1ps ramp input are used in the
BTM model as PWL approximations and not directly as ASCII file
(both ways provided by DWS) to speed up the simulations .
For comparisons, a ramp of 25ps is also considered.
DWS has been used to compute VS&VL voltages obtained from a
cascade of 10 BTM with a ramp input. The waveforms are compared
with those computed by CS 2013 using a model valid in the range 010GHz.
43.
CS VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.0)
tr=25ps
1+S11
A fixed time step of
0.1ps has been used
for CS simulation tasks
tr=1ps
1+S11
S21
Sparameter
waveforms do not
seem influenced
by the tr, apart the
oscillations in S11
43
44.
CS VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.8m)
tr=25ps
1+S11
A fixed time step of
0.1ps has been used
S21
tr=1ps
1+S11
S21
S11 waveform
does not seem
influenced by the
tr, apart the
oscillations in S11
44
45.
VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.8m): extended time scale
1+S11
tr=25ps
S21
Time step=1ps
Samples=4001
Zoom
45
46.
VL edge detail (cable length=18.3cm, model:040GHz,tandelta=0.8m)
tr=25ps
S21
Time step=0.1ps
Samples= 4001
tr=1ps
S21
Time step=0.02ps
Samples= 8001
•S21 rising edge is
strongly influenced
by input tr
• Waveform from
1ps stimulus can
be used to extract
BTM models using
46
the PWL technique
47.
PWL generation
PWL generation: The CS output waveform is digitized by extracting the time and
amplitude values at user chosen points (see small circles along the waveform).
The manual choice is performed with the aim of minimizing the number of points
but still achieving a good accuracy .This can been accomplished by a graphic
digitizer program due to the availability of the image files. In case of ASCII files
compatible with the .g format of DWS, a DWV viewer feature is provided to
quickly accomplish this task in a semiautomatic way.
48.
VS&VL (cable length=1.83m, model:010GHz,
tandelta=0.8m, tr=25ps)
V
1+S11
CS 2013
Cascade of
10 BTM cells
with DWS
S21
ns
V
1+S11
S11 & S21
waveforms are in
good agreement
ns
48
49.
VL (S21) edge detail (cable length=1.83m, model:010GHz, tandelta=0.8m, tr=25ps)
V
CS 2013
S21
Cascade of
10 BTM cells
with DWS
ns
• S21 waveforms are in good agreement
• S21 rising edge computed by 10 BTM seems to be a little lower
49
50.
Comments on BTM results
•
The S11 waveform obtained by DWS from a chain of 10 BTM
cells derived from CS is in good agreement with the one obtained
by CS for the total length of the cable
The S21 edge obtained by a cascade of 10 BTM cells seems to
be slightly faster than the one obtained by a CS for the total length
of cable
There are some key points to be taken into account in using the
cascade of BTM cells :
•
•
1.
2.
3
4
A fast (1ps) edge has to be used as input stimulus to extract the BTM
model of the unit cell. A slower rise time stimulus as 25ps would
introduce a significant error in computing the S21 edge [11].
A suitable bandwidth (e.g. 40Ghz) has to be set in CS to get an
accurate response to the 1ps input required for the BTM model.
This bandwidth determines the number of cascaded RLCTL cells of
the CS circuital model (100cell for a 183mm long cable) and the
simulation time of CS.
BTM model accuracy depends on the number and placement of the
breakpoints chosen for the pwl behavior. Normally 2030 breakpoints
are enough to get a good speed/accuracy trade off.
An impressive DWS vs speedup factor (3 to 4 orders of magnitude) is
obtained for “long” cables using chain of BTM cells
51.
Analytical methods used to extract
a 1m unit cell BTM to simulate a
10m RG58 coaxial cable with
DWS
52.
Procedure adopted for BTM cell extraction
•
•
•
The theoretical expressions previously shown in this report are used
to get approximated S11 and S21 step responses for a 1m RG58
cable. Two different ramps of tr=5ps and tr=25ps respectively are
used as input stimuli.
The computed waveforms are digitized to get the breakpoints for
build up the pwl BTM cell model
A chain of 10 equal cells is simulated by DWS to get the response of
a 10meter cable.
53.
Signals & line voltages for 1m of RG58
Tr=25p
s
S21
Data used as input for BTM
S11
Tp
Data used as input for BTM
Time period Tp should be large enough to reach with approximation the dc values of S11
54.
Signals & line voltages for 10m of RG58
Source signal: tr=100ps
Line voltages: input (vsin) & output (vl)
Tp
Time period Tp should be large enough to reach
with approximation the dc values of S11
55.
S21 (vl) rising edge (10m cable)
Edge computed by Theory
Edge computed by DWS using 10 BTM cells with tr=5ps
Edge computed by DWS using 10 BTM cells with tr=25ps
56.
S21 (vl) rising edge of a 10m cable: detailed view
with equalized delays for edge comparison
Edge computed by Theory
Edge computed by DWS using 10 BTM cells with tr=5ps
Edge computed by DWS using 10 BTM cells with tr=25ps
As expected [11], better agreement is obtained
by using tr=5ps as input for the 1m basic cell
57.
S11
reflections computed by Theory
reflections computed by DWS by using 10 BTM with tr=5ps
The difference after t=40ns is due to S11 behavior truncation after the first
40ns window. Beyond 40ns the analytical S11 response was not available
due to FFT issues. At least a 400ns window should be required.
58.
BTM model from theoretical responses: key points
1.
2.
3.
As for the BTM model extracted from Cable Studio simulations,
some key points have to be pointed out:
The S21 rising edge should be computed by IFFT using an
enough short risetime ramp as input (e.g. 5ps for 1m cable) to
limit the rise time error of the BTM cells cascade [11].
The reflection coefficient (S11) should be computed using an
input stimulus period enough large to allow a good
approximation of steady state (dc ) values. A tradeoff between
this period and IFFT computation time is required. Therefore, a
global tradeoff is needed to take into account accuracy
requirement for simulations, fast tr, and large period Tp for IFFT
computation.
The BTM model extracted taking into account previous points is
very fast and achieves a good accuracy level.
59.
Using Cable Studio: user considerations
•
•
•
•
•
•
•
•
•
•
The results of CS are strongly influenced by several options set by the user.
The effect of options on final results is not always clear to the user.
TLM (modal) option is required to get accurate results.
TLM produces circuital models including thousands of RLC and TL elements.
The unit cell TL delay can be a number like TD=9.54361271247e012 sec. This kind of
values requires to set short fixed time step (e.g. 100fs) to get reliable results from
CS simulations . Otherwise overall delay and behavior of a 100cell cascade can be
strongly affected.
The Bandwidth to be set to get the modal TLM directly affects the number of
cascaded cells in the cable model . For example a 40Ghz BW generates a 100cell
model for a 18.3 cm cable.
CS 2013/14 simulations at fixed step can require several minute on a multicore CPU.
DWS can achieve a 1050X speed up over CS to simulate complex TLM models
generated by CS [13 ].
To extract accurate BTM models for DWS, a rise time of about 1ps for a 20cm unit cell
and 5ps for a 1m unit cell is suggested as stimulus signal of the cable.
The same rule of thumb should be utilized to extract BTM models from analytical
methods.
59
60.
Conclusions
•
•
•
•
•
•
•
•
Cable Studio computes the step responses of the cable in good agreement
with MWS and the analytic approach based on theory.
RLTL circuital model provides overestimation of losses because the VFT used
for getting the equivalent RL circuit was applied by using compact analytic
expression for coaxial cable without the factor ½ [6].
This factor compensates the lack of dielectric losses in the RLTL model with
the exception of S21 rising edge. A closer result with the measurement is
shown in [2] and [3]. An improved RLTL hybrid circuitalBTM model is shown
in [8].
A BTM cell model cannot be practically obtained by a 3D model (MWS)
because the number of mesh cells required by a source with rise time in the
order of 1 ps is too large for the computation.
A BTM cell can be obtained by a 2D model (CS) feasible with a good tradeoff
between the CS input bandwidth and the stimulus rise time.
The analytical approach is feasible to get the BTM model. A tradeoff is
needed between the required fast input rise time and large period value used
for the IFFT computation. A twostep modeling using two different theoretical
responses (fast edge & short period, slower edge & larger period) should give
the best results
DWS can be used with major speed benefits both for TLM (10 to 50X) and
BTM (up to 10000X) cable models
DWS can also utilize both hybrid ( BTM and TLM) and full BTM models
directly extracted or optimized to actual TDR measures [8].
60
62.
Typical Tanδ values
• The following tables are extracted from the
literature.
• They should be compared with the value
of Tanδ=0.8m used in this report.
63.
Tandδ
http://cp.literature.agilent.com/litweb/pdf/genesys200801/elements/substrate_tables/t
ablelosstan.htm
The dielectric loss tangents for some materials commonly used in coaxial cables are:
tanD at 100 MHz
tanD at 3 GHz
Air
0.0
0.0
PTFE
2E4
15E4
PolyEthylene, DE3401
2E4
3.1E4
Polyolefin, irradiated
3E4
3E4
Polystyrene
1E4
3.3E4
Polyvinal formal (Formvar)
1.3E2
1.1E2
Nylon
2E2
1.2E2
Quartz, fused
2E4
6E5
Pyrex Glass
3E3
5.4E3
Water, distilled
5E3
1.6E1
Material
For simulation we have used Tanδ=8e4 (used in CST as default value)
63
64.
Tandδ (coax Belden)
For RG58, a tanδ between
1.12e3 and 2.12e3 are given
(values higher than the previous
table for polyethylene)
Tandelta
From: H. Johnson, M. Graham, “HighSpeed Signal Propagation”, Prentice Hall, 2003
64
65.
References
[1] Piero Belforte, Spartaco Caniggia, “CST coaxial cable models for
SI simulations: a comparative study”, March 24th 2013CST
models for theRG58 coax cable
[2] Piero Belforte, Spartaco Caniggia,, “Measurements and
Simulations with1.83m RG58 cable”, April 5th 2013
[3] Piero Belforte, Spartaco Caniggia, “TDR measurements and
simulations of RGU 58 coaxial cable Sparameters”, June 04,
2013 TDR measures and simulations of RG58 cable
[4] Spartaco Caniggia, “Modeling interconnects and power
distribution network in PCBs, CST workshops, Milano, 26112013
[5] Ramo, Whinnery, Van Duzer, “Fields and wave in communication
electronics”, John Wiley, 3rd Edition
[6] S. Caniggia, F. Maradei, “Signal Integrity and Radiated Emission
of HighSpeed Digital Systems”, John Wiley & Sons, 2008
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[7] Piero Belforte “ TDR mesurements of RG58 coaxial cable Sparameters”, April11th 2013 TDR measurements of RG58 coax cable
[8] Piero Belforte “ RG58 coaxial cable: A comparison among Analytical
models, DWS BTM models, TDR measures and CST 2013 Cable
Studio simulations”, Dec. 24th 2013 Models and measurements for a
RG58 coax
[9] Piero Belforte “A new modeling and simulation environment for highperformance digital systems” HP Digital Symposium (1993)
[10] Piero Belforte “DWS vs MC10: a comparative benchmark” April 15th
2013 DWS vs MC10
[11] Piero Belforte “ Prediction of rise time errors of a cascade of equal
behavioral cells” May 2nd 2013 Rise time error prediction
[12] http://ischematics.com/
[13] SWAN sim of a CST2014 TLM cable model
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