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1
Comparison of time-domain S-
parameters of RG58 cable
computed by: Theory, CST,
SPICE, DWS S. Caniggia, P. Belforte
February 04, 2014
2
Outline
• Introduction
• S-parameter definition in time domain
• Simulations of a 18.3-cm RG58 coaxial cable
• S11&S21 computed by analytic approach (theory)
• Cable Studio 2013 results as source of a BTM of a 1.83-m RG58 coaxial cable used in DWS
• Analytical method results as source of a BTM of a 10-m RG58 coaxial cable used in DWS
• Conclusions
• Appendix: Dielectric losses (Tanδ)
• References
Introduction
• In this report, the sixth of a series devoted to lossy lines [1,2,3,7,8], several approaches for computing time-domain step responses of a lossy line are outlined and compared.
• The methods used are: MWS of CST, CS of CST, RL-TL 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.
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 time-domain step responses of lossy line S-parameter 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 RLGC-TL (lossless) segments of line electrically short to be used with a SPICE-like circuit simulator such as MC10 [1,2,3,4,6] or DWS for faster (1-2 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 RLGC-TL) 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 multi-conductor lines with shields.
• DWS allows the use of hybrid BTM and circuital models [8]
Flow chart for direct transient simulation of lossy lines by using
three different methods: SPICE, CST, DWS [4].
Cascade of unit cells to
form a block (SPICE-like
Sim.)
Simulated waveforms with several loadings
(passive/active, linear/non-linear)
Which
model ?
One block: measured or
computed S-parameter line in
time domain S11
S21
TL RL
GC
unit cell
VFT technique
Which
technique?
Modeling
Zi, L0,C0, Gd
Define the line (a,p,σ,μ,Rdc,tanθ,Kp) and compute the per-unit-line parameters: Zi, L0, C0, Gd
Full line Segmented line
Modeling
One BTM block
(DWS)
MOR technique
S technique
Cable block in schematic
Modeling
One RLGC-TL block
(SPICE in CST)
complex RLGC-TL net
One block
6
S-parameter definition in time
domain
7
Two port network
+ +
- -
I1 I2
V1 V2
a1 a2
b1 b2
0n
nn
Z
Va
0n
nn
Z
Vb
)ba(Z
1)VV(
Z
1I nn
0n
-nn
0n
n
)ba(Z)VV(V nn0n -nnn
2
1
2221
1211
2
1
a
a
SS
SS
b
b
S-parameter definition for two-port network [5]
Normalized
incident wave
Z01 Z02
Normalized
reflected wave
With n=1,2:
8
S-parameter physical interpretation [5]
Two port network
a1 a2=0
b1 b2
+
-
Z01 Z02
Source applied
to Port 1
Port 2 matched
1111 aSb
1212 aSb
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.
01
10111
Z2
IZVa
01
10111
Z2
IZVb
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.
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.
10
S parameters in time domain
Typical source and load voltage waveforms for an interconnect matched
at both ends: lossless TL (dashed line), frequency-dependent lossy TL
(solid line) [6, Fig.7.3]
When TL has characteristic impedance different from the loads, distortions occur
Definitions of S
parameters in time
domain:
•VS=1+S11
•VL=S21
11
Simulations of a 18.3-cm RG58
coaxial cable
12
S-parameters calculations
• Time-domain S-parameters computation from incident and reflected waves provided by MWS is shown.
• S11 and S21 time-domain step responses with matched line at both ends are computed integrating the waveforms provided by MWS when using waveguide ports.
• Comparison with RL-TL model used by MC10 (SPICE) or DWS [1,2,3] and 2D-TL 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 1.83-m RG58 coaxial cable [2,3,7,8].
• The lack of dielectric losses in the RL-TL model is somewhat compensated by the overestimation of skin effect [3].
13
MWS structure
Meshcells=545,472
•Frequency range: 0-40GHz
•Waveguide ports
Cable parameters:
• Dielectric=2.3, tangent delta=0
• Lossy metal: 5.8e7 S/m
• Geometry in mm: length=183; wire
radius=0.395, shield radius=1.397; shield
thickness=0.127
14
Input signal in MWS
Rise time tr between 10-90% is about 23ps as used in TDR measurements
Tr=23ps
Gaussian (40GHz)
Step source
Integration of
gaussian
normalized to
maximum value
of the integral
15
Port signals of RG58 in MWS
i1 o21
o11
ns
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
16
Cable studio (CS) structure
Step source with 40GHz
bandwidth imported from
MWS (see previuos slide)
Ohmic losses only
17
MC10 (SPICE) structure
Cascade of 100 1.83-mm unit RL-TL cell
S11=VTin
S21=VTout
Step source
with tr=25ps
The equivalent RL circuit was
obtained by VFT applied to
compact expressions for
coaxial cable without factor ½,
see Eq.7.57 of [6]
18
DWS (Spicy SWAN [12 ]) circuits
RL-TL5mmx37=185mm
185-mm RG58 from CST
19
Input (1+S11) and output (S21) line waveforms
Line length= 18.3 cm
Remark: MC10 and CS provide similar waveforms
ps
1+S11
S21
MWS
waveforms
20
S11
ps
Volt
MWS: solid
CS: dot
MC10: dash
• MC10 & DWS with RL-TL cells compute the
same waveforms [10]
• MWS & CS provide about similar waveforms
with less losses (lower values than DWS & MC10)
MC10&DWS
MWS&CS
21
1+S11 and S21
DWS 1+S11
S21
• MC10 & DWS compute the
same waveforms [10]
• MWS & CS compute similar
waveforms with about half losses
• S11 of CS & DWS show some
slight segmentation due to 37-
cell discretization
ps
1+S11
S21
Volt
MWS: solid
CS: dot
MC10: dash
MC10
MC10
MWS&CS
MWS&CS
22
1+S11 and S21 with and without dielectric
losses
MC10
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
CS
CS
23
CS 2012: Adding dielectric losses
(tanδ=0.8m)
Ohmic losses 1+S11
S21
sec
Volt
Ohmic + dielectric losses
1+S11
S21 sec
Volt •There are slight
differences in this
portion of the
waveform
•The
segmentation
effect is
eliminated
24
CS 2013: Adding dielectric losses
(tanδ=0.8m)
Ohmic losses
1+S11
S21
sec
Volt
Ohmic + dielectric losses
1+S11
S21
sec
Volt
•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
25
Input and output line voltages
VS
VS
VS
VL
VL
VL
MC10
MWS 2013
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 (=Vin-1) 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
will be estimated.
26
Comments on simulations
• MC10 & DWS by using RL-TL 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
RL-TL 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.
S11&S21 computed by analytic
approach (Theory)
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 RL-TL model.
• MathCad code professional 2001i is used for analytic computations.
• The comparisons are performed among: RL-TL model (RL-TL), Cable Studio ohmic losses (cs), Cable Studio ohmic+dielectric losses (cs_d), analytic results with all losses (Theory).
Line structure & input signal
tr (10%-90%)
Vs=2V
LenZocoax
Zocoax
Vsin (1+S11) Vl (S21)
rw: wire radius
rsh
: internal shield radius
dcoax
: shield thickness
Coaxial cable
Source signal: tr=25ps
Skin effect (compact expressions)
• 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 RL-TL waveforms are in agreement with theory without factor ½
because vector fitting technique (VFT) was applied starting from these expressions.
½ factor
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
Dielectric losses and line parameters
Dielectric losses
Line parametrs
For more details, see chapter 7 of [6]
Output rise time comparison (Len=18.3cm)
MC, CS, CS_d
Theory
• 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
ps
ns
S11&S21 computed with factor ½
(Len=18.3cm)
Theory
cs_d
cs_d
• Good agreement
between cs_d and
theory
• S11 of theory is
slightly lower
S11&S21 computed without factor ½
(Len=18.3cm)
RL-TL
RL-TL
Theory
•Very good agreement
between RL-TL model
and theory
•The reason is that the
RL-TL model was
obtained by VFT using
compact skin effect
expressions for coaxial
cable without factor ½.
ps
ns
S11 computed with factor ½ (Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
CST provides slightly lower values
S21 computed with factor ½ (Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
Both methods provide the same values
1+S11 computed without factor ½
(Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
Theory provides more than doubled values for S11
S21 computed without factor ½ (Len=1.83m)
Theory
Cable studio
(Bandwith=10GHz)
Theory computes slight lower rising edge values
after the 80% of its DC level
Comments on analytic approach
• Good agreement between CS and theory waveforms considering all losses.
• RL-TL 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 RL-TL and justifies the good agreement with the measured waveform tails as shown in [2,3].
• The S21 rising edge coming from the RL-TL 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 1.83-m RG58 coaxial cable
used in DWS
Used BTM procedure
• The S11 and S21 computed by cable studio (CS) 2013 for a 18.3-cm of RG58 (0-40GHz) 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 0-10GHz.
43
CS VS&VL (cable length=18.3cm, model:0-
40GHz,tandelta=0.0)
S-parameter
waveforms do not
seem influenced
by the tr, apart the
oscillations in S11
A fixed time step of
0.1ps has been used
for CS simulation tasks
1+S11
S21
1+S11
tr=25ps
tr=1ps
44
CS VS&VL (cable length=18.3cm, model:0-
40GHz,tandelta=0.8m)
1+S11
tr=25ps
tr=1ps S11 waveform
does not seem
influenced by the
tr, apart the
oscillations in S11
A fixed time step of
0.1ps has been used
S21
1+S11
S21
45
VS&VL (cable length=18.3cm, model:0-
40GHz,tandelta=0.8m): extended time scale
tr=25ps Time step=1ps
Samples=4001
1+S11
S21
Zoom
46
VL edge detail (cable length=18.3cm, model:0-
40GHz,tandelta=0.8m)
tr=25ps
tr=1ps •S21 rising edge is
strongly influenced
by input tr
• Waveform from
1ps stimulus can
be used to extract
BTM models using
the PWL technique
Time step=0.02ps
Samples= 8001
Time step=0.1ps
Samples= 4001
S21
S21
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 semi-automatic way.
48
VS&VL (cable length=1.83m, model:0-10GHz,
tandelta=0.8m, tr=25ps)
Cascade of
10 BTM cells
with DWS
S11 & S21
waveforms are in
good agreement
CS 2013
1+S11
ns
V
1+S11
S21
ns
V
49
VL (S21) edge detail (cable length=1.83m, model:0-
10GHz, tandelta=0.8m, tr=25ps)
ns
V
S21 Cascade of
10 BTM cells
with DWS
CS 2013
• S21 waveforms are in good agreement
• S21 rising edge computed by 10 BTM seems to be a little lower
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. 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].
2. 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 (100-cell for a 183mm long cable) and the simulation time of CS.
3 BTM model accuracy depends on the number and placement of the breakpoints chosen for the pwl behavior. Normally 20-30 breakpoints are enough to get a good speed/accuracy trade off.
4 An impressive DWS vs speedup factor (3 to 4 orders of magnitude) is obtained for “long” cables using chain of BTM cells
Analytical methods used to extract
a 1-m unit cell BTM to simulate a
10-m RG58 coaxial cable with
DWS
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 1-m 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 10-meter cable.
Signals & line voltages for 1-m of RG58
S21
S11
Data used as input for BTM
Tr=25p
s
Tp
Data used as input for BTM
Time period Tp should be large enough to reach with approximation the dc values of S11
Signals & line voltages for 10-m 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
S21 (vl) rising edge (10-m 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
S21 (vl) rising edge of a 10-m cable: detailed view
with equalized delays for edge comparison
Edge computed by Theory
Edge computed by DWS using 10 BTM cells with tr=25ps
Edge computed by DWS using 10 BTM cells with tr=5ps
As expected [11], better agreement is obtained
by using tr=5ps as input for the 1m basic cell
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.
BTM model from theoretical responses: key points
As for the BTM model extracted from Cable Studio simulations,
some key points have to be pointed out:
1. The S21 rising edge should be computed by IFFT using an
enough short rise-time ramp as input (e.g. 5ps for 1-m cable) to
limit the rise time error of the BTM cells cascade [11].
2. 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.
3. The BTM model extracted taking into account previous points is
very fast and achieves a good accuracy level.
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=9.54361271247e-012 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 100-cell 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 100-cell
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 10-50X 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 20-cm unit cell
and 5ps for a 1-m 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.
• RL-TL 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 RL-TL model with the exception of S21 rising edge. A closer result with the measurement is shown in [2] and [3]. An improved RL-TL hybrid circuital-BTM 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 two-step 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].
Appendix:
Dielectric losses (Tanδ)
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
The dielectric loss tangents for some materials commonly used in coaxial cables are:
Material
tanD at 100 MHz tanD at 3 GHz
Air 0.0 0.0
PTFE 2E-4 15E-4
PolyEthylene, DE-3401 2E-4 3.1E-4
Polyolefin, irradiated 3E-4 3E-4
Polystyrene 1E-4 3.3E-4
Polyvinal formal (Formvar) 1.3E-2 1.1E-2
Nylon 2E-2 1.2E-2
Quartz, fused 2E-4 6E-5
Pyrex Glass 3E-3 5.4E-3
Water, distilled 5E-3 1.6E-1
For simulation we have used Tanδ=8e-4 (used in CST as default value)
http://cp.literature.agilent.com/litweb/pdf/genesys200801/elements/substrate_tables/t
ablelosstan.htm
64
Tandδ (coax Belden)
Tandelta
From: H. Johnson, M. Graham, “High-Speed Signal Propagation”, Prentice Hall, 2003
For RG58, a tanδ between
1.12e-3 and 2.12e-3 are given
(values higher than the previous
table for polyethylene)
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 with1.83-m RG58 cable”, April 5th 2013
[3] Piero Belforte, Spartaco Caniggia, “TDR measurements and simulations of RGU 58 coaxial cable S-parameters”, June 04, 2013 TDR measures and simulations of RG58 cable
[4] Spartaco Caniggia, “Modeling interconnects and power distribution network in PCBs, CST workshops, Milano, 26-11-2013
[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 High-Speed Digital Systems”, John Wiley & Sons, 2008
References (2)
[7] Piero Belforte “ TDR mesurements of RG58 coaxial cable S-
parameters”, 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 high-
performance 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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