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

66