1

CST coaxial cable models for

SI simulations: a comparative

study

Piero Belforte, Spartaco Caniggia

March 24th 2013

2

Outline

• Introduction

• S parameters in frequency domain

• S parameters in time domain

• Comparison between measurements and

simulations

• Ultra Wide Band (UWB) source

• Proposal for efficient and accurate simulation of

lossy cables

• Conclusion

3

Introduction

• The task of this report is to show that some important

signal integrity (SI) problems arise when Cable Studio

(CS) is used to simulate high-speed digital signal

transmission with lossy lines (cables or traces in PCB)

[1]

• An 1.83-m RG58 coaxial cable is modeled by CS and

commercial programs: MC10 [2] and DWS , based on

Digital Wave Network equivalent of the electrical network

[3].

• Simulations are compared with measurements

• It is shown that CS doesn’t provide good results

• A method is proposed to solve the SI problems with

CST Cable and Design studio.

4

S parameters in frequency domain

5

S parameter computation

• Cable: RG58

• Length: 5cm

• Frequency range: 0-10GHz

• Characteristic Impedance Z0: 49.94Ω

• Only ohmic losses are taken into account because dielectric losses with tanδ=0.0002 at 100MHz (Polyethylene) doesn’t give significant changes.

• SPICE simulation performed by MicroCap10 (MC10) because of good TL models [2]

• DWS (Digital Wave Simulator) analysis because of speed (50X MC10), accuracy and time-domain scattering parameters.

• Comparison among CST Cable Studio, CST MWS, MC10 and DWS (Digital Wave Simulator)

6

Equivalent circuit used by MC10 (SPICE) for theoretic S11

& S21 computation (analytic approach)

rs

ts

εr

2rw

Coaxial cable

geometry

50Ω

50Ω

For details, see [1, clause 11.2.3]

5-cm RG58: Z0=49.94Ω

File:S_LOSSYTL_ANALYTICAL_10GHZ.CIR (MC10)

Permittivity=2.3, Loss

angle tanδ=0.0002

Insulator outside: thickness=0.5mm,

permittivity=3, Loss angle tanδ=0.02 Solid shield screen type

7

CST cable studio for S11 & S21

computation

Equivalent circuit to compute S

parameters by CST DESIGN

STUDIO

50 Ω 50 Ω

RG58: length=5 cm,

Z0=49.94Ω

File: Ex_coax_S_5cm.cst

8

3D RG58 model by MWS

Meshcells=41,515 Waveguide port

Time domain solver: adaptive mesh refinement was used

9

S11

• S11 computed by Cable Studio 2010 &

2012 provide the same results

• S11 computed by MWS and MC10 provide

similar results and about some dB lower

•Level differences are due to impedance

mismatching

• Resonance frequencies are slightly higher

for MWS (lower cable delay)

Cable Studio (CS) 2012

Cable Studio (CS) 2010

MWS Studio 2012

MC10 2012

10

S21

Cable Studio (CS) 2012

Cable Studio (CS) 2010

MWS Studio 2012

MC10 2012,DWS 8.4

RL-TL model

• S21 computed by MC10 is the lowest curve

(more losses)

• S21 computed by CST 2012 is too higher

than CST 2010 (less losses)

• S21 computed by MWS is in the middle

between MC10/DWS and Cable studio 2012

and close to cable studio 2010

MWS

MC10,DWS

CS

11

Comments on computation of S

parameters

• S11 computed by MWS and MC10/DWS provide similar values both in time domain and frequency domain

• S11 computed by Cable Studio 2010 & 2012 are about 15dB higher than MWS and MC10/DWS due to characteristic impedance mismatching

• S21 computed by Cable Studio 2012 provides much less losses than those computed by Cable Studio 2010

• S21 computed by Cable Studio 2010 is close to MWS

• CST should investigate the last two items

12

S parameters in time domain

13

Lossy line matched at both ends

Typical source and load voltage waveforms for an interconnect matched

at both ends: lossless TL (dashed line), frequency-dependent lossy TL

(solid line) [1, Fig.7.3]

When TL has characteristic impedance different from the loads, distortions occur

Definitions of S

parameters in time

domain:

•S11=VS-1

•S21=VL

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Voltage computations in time

domain

• Cable: RG58

• Length: 1.83m

• Line terminations: 50Ω

• Source: step waveform with rise time tr=0.1ns

• Frequency range: 0-10GHz

• Characteristic Impedance Z0: 49.94Ω

• SPICE simulation performed by MC10 [2]

• DWS simulations performed by DWS 8.4 [4]

• Comparison between CST & SPICE results

• DWS results are the same of MC10

15

Coaxial cable structure

50 Ω

50 Ω

Z0=49.94 Ω Length:1.83m

V1 V2

Vsource=2 V

trise=0.1 ns

Ramp

Source

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Circuit and model used in MC10 and DWS (RL-TL

approach)

Coaxial cable matched at both ends and modeled as a

cascade of 610 3-mm RL-TL cells including the skin effect,]

V1=VS V2=VL

Step

signal

Remark: the cascade of RL-TL cells provides the same S11 and S21 in

frequency domain computed by the analytic approach used in the previous

section, see Fig.7.22 of [1]

RL-TL model: RL parameters

were computed by vector

fitting technique starting from

analytic expressions for ohmic

losses, see [1, clause 7.2.1.3]

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Circuit and cable model used in CST

RG58 model with

length 1.83 m

Skin effect only

10GHz

Vinit: 0.0

Vpulse: 2.0

Tdelay: 1e-9

Trise: 0.1e-9

Thold: 100e-9

Tfall: 0.1e-9

Ttotal: 200e-9

File: Ex_coax_S_1_83_10GHz.cst

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Voltages V1 & V2 (cst 2010)

MC10 (SPICE) CST

V1 V2

V1 V2

V1 V2

V1 V2

ns ns

ns ns

Samples 1001 in

transient1 task

Samples 5001 in

transient1 task

? ?

MC10 and CS have the same losses except the oscillations provided by

CST 2010 that should not occur

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Voltages V1 & V2 (cst 2012)

MC10 (SPICE) CST

• CST cable studio 2012 provides

less losses than MC10 and CS 2010,

as evidenced by frequency

computation of S parameters.

• Oscillations remain

• Using normal or very high accuracy

the results do not change

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With 1-GHz model computed by CST 2012

Oscillations

increase!

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DWS 37-cell model vs CST MWS: S11

•It can be noted that MWS

computes about half

losses than DWS.

•S11 of MWS was

obtained calculating the

integral of the reflected

wave (o1,1) as response

to a step source.

DWS

MWS

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Comments on computation of V voltages

• V1: the voltages at source end computed by MC10 (SPICE)/DWS and CST 2010 are in good agreement.

• V2: the voltages at load end computed by SPICE/DWS and CST 2010 are in good agreement except for the oscillations in CST waveform.

• V1 and V2 computed by CST CS 2012 are not in agreement with MC10/DWS, less losses are computed by CST 2012 and unrealistic oscillations on V2 remain.

• CST should investigate these two last items

• Time domain S11 from CST MWS is lower (about half) of that from RL-TL model simulated with DWS as already noticed in return loss vs frquency

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Comparison between

measurements and simulations

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Comparison between

measurements and simulations

The measurements performed on 1.83-m RG58 cables are compared with three simulation methods:

1. CST cable studio.

2. MC10, based on SPICE [2] and using a cascade of 610 3-mm RT-TL unit cells.

3. DWS models using both 366 X 5mm RL-TL chain of cells and a 3660 X .5mm RL-TL chain inserted in actual CSA803 measurement setup.

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50-Ω RG58 model with length

1.83 m (very high accuracy,

ohmic losses in CS)

Vinit: 0.0

Vpulse: 2.0

Tdelay: 1e-9

Trise: 0.1e-9

Thold: 100e-9

Tfall: 0.1e-9

Ttotal: 200e-9

CST model (Step source)

Open

•V1 (or VP1) voltage at the input of the cable was computed and measured

•Dielectric losses are neglected for SPICE (MC10) and CS (Cable Studio 2012)

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DWS (4) cable cell on Spicy SWAN (5)

(Due to DWS sim speed, even a .5mm cell has been tried)

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Example of Spicy SWAN (DWS) circuit for S-parameter

cable characterization using a chain of cells

(Due to DWS sim speed, even a chain of 3660 X .5mm RL TL cells has been

utilized, getting practically the same results of the 366X 5mm cell model)

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RG58 CU (TASKER) specs

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Measurement set-up (CSA803)

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Measurements with cable open at far-end voltage

The measurements were

performed by Piero Belforte

on two commercial 1.83-m

RG58 cables: Tasker and

GBC.

Comparison of the

reflected edge of the

two cables: very little

differences.

V1

V1

ns

ns

-1

0

1.2

0

1.2

4

Reflected edge

Tasker GBC

50

31

VP1:voltage at cable input

V1

ns

V1

ns

CST 2012

Measurement

MC10

DWS (including TDR

setup)

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• There is good agreement on reflected edge among RL-TL

model using both MC10 and DWS simulators (DWS is

50X faster than MC10) and measurements. Note that

dielectric losses were neglected in the RL_TL model and

actual cables have stranded conductors (not solid)

• CS reflected edge is affected by not acceptable

oscillations

VP1 voltage details

V1

ns

CST 2012

Measurement

MC10

DWS

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S-parameters measurements and comparison with

366 RL_TL model in the actual setup (DWS)

S21 S21

S11 S11

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Actual S-parameter measurements:

considerations

• Actual cable (stranded conductors) shows significant

distributed impedance discontinuities

• S11(S22) in time domain shows larger values than

model

• Actual S11 and S22 are not identical (not symmetrical)

due to impedance discontinuities

• S21(S12) edge is slightly slower from 0 to 50% due

probably to dielectric losses

• S21(S12) edge is slightly faster from 50% to 100% due

probably to stranded conductors (lower skin effect losses

at high frequency)

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DWS BTM (Behavioral Time Model) of

1.83m cable using Spicy SWAN

366 cells

of RL-TL

1 cells

S from

measurements

BTM

RL-TL

50 ns

12 ns 50 ns

1 V

1 V 0.035

BTM

RL-TL

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Comments on measurements and

simulations

• MC10 (SPICE) and DWS open cable and S21 are in good agreement with measurements despite the stranded (not solid) conductors of actual cable.

• S11 of measurements takes into account slight distributed impedance mismatching along the cable therefore more accurate models should be needed for a high level of accuracy.

• Dielectric losses are much less important than ohmic losses and can be neglected for most applications

• CST cable studio provides not realistic oscillations (distorted waveforms) as verified by measurements

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Ultra Wide Band (UWB) source

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Coaxial cable with source an UWB

signal

• The same coaxial cable of previous

example was tested by using as a source

an ultra wide band (UWB) signal instead of

a step waveform.

• The signal is introduced into design studio

as imported file.

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MC9 model (UWB source)

Coaxial cable matched at both ends and modeled as a cascade of 610 cells

including the skin effect: comparison between measured (dashed line) and

computed (solid line) waveforms [1, chapter7]

Validation

Model

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CST model (UWB source)

File: Ex_coax_UWB.cst

Imported file:

New_uwb_input_by2.txt

Ohmic losses

RG58

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Comments on coaxial cable with

UWB source

• SPICE (MC10) runs in some minutes and

gives waveform on 50-Ω load in good

agreement with measurement

• CST runs with very long time and the

simulation was aborted.

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Proposal for Signal Integrity of

lossy cable

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Method • Define the cable by its geometrical and electrical parameters

• Choose between two unit-cell models: 1. RL-TL: the unit cell should be electrically short for the frequencies of

interest. It is modeled as a network of resistances and inductances to take into account the ohmic and electric losses (analytic expression in frequency domain) computed by vector fitting technique in series with an ideal transmission line (TL) as reported in chapter 7 of [1]. Simulator: SPICE with good TL model [2], DWS (50X faster) [3].

2. S-parameter: the unit cell should have a length to satisfy the rule that the rise-time excitation should be less than 1/10 the unit-cell delay. It is modeled by using S-parameters in time domain (2D or 3D computation) as defined in [1,3]. Simulator: DWS only [3]

• Model the line by a cascade of unit cells.

• Perform simulations in time domain by using SPICE [2] or DWS (more accurate and 50X faster) [3] to get the voltage or current waveforms.

Remark: the method can also be used for interconnections in PCB such

as microstrip and stripline traces

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Flow chart

Define the cable

RL-TL Model

(SPICE, DWS) S-parameter Model (DWS)

Cascade of unit cells

Results obtained by SPICE or DWS

time domain simulations

Which

solution ?

2D/3D S-parameter

computation

Vector fitting

to set RL

network

Define an unit-cell cable

S1

1 S2

1

TL RL

RL

unit cell unit cell

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Conclusion • The 2D (TL) modeling in CST CABLE STUDIO should be revised

because it provides unexpected oscillations on signals when the source is a step waveform.

• CST Cable Studio 2012 provides less losses than CST 2010.

• CST Cable Studio results are not in agreement with MWS, SPICE and DWS simulations and measurements.

• There are instability problems in CST when the source is an ultra wide band signal imported as external file.

• We suggest to use the method presented at the end of this document that consists of a cascade of unit-cable cells simulated by SPICE or DWS (50X faster).

• DWS supports fast simulations of both time domain s-parameter and RL-TL chain of cells.

• BTM (Behavioral Time Model) method supported by DWS is the fastest and most accurate if unit-cell S-parameters are taken from actual measurements.

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References

[1] S. Caniggia, Francesca Maradei, “Signal Integrity and Radiated

Emission”, John Wiley & Sons, 2008

[2] www.spectrum-soft.com

[3] P.Belforte “Time domain simulation of lossy interconnections using

wave digital networks” ISCAS 1982 Rome

[4] DWS (Digital Wave Simulator) user manual

http://www.slideshare.net/PieroBelforte1/dws-84-

manualfinal27012013

[5 ] Spicy SWAN : www.ischematics.com

http://www.slideshare.net/PieroBelforte1/spicy-swan-concepts-

16663767

[6] DWS and SWAN, ( Simulation by Wave Analysis) are trademarks of

Piero Belforte http://www.linkedin.com/in/pierobelforte