A comparative study on modeling techniques of coaxial cables.

1. CST coaxial cable models for
SI simulations: a comparative
study
Piero Belforte, Spartaco Caniggia
March 24th 2013
1

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
2

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.
3

4. S parameters in frequency domain
4

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)
5

6. Equivalent circuit used by MC10 (SPICE) for theoretic S11
& S21 computation (analytic approach)
For details, see [1, clause 11.2.3]
50Ω 5-cm RG58: Z0=49.94Ω
50Ω
File:S_LOSSYTL_ANALYTICAL_10GHZ.CIR (MC10)
Insulator outside: thickness=0.5mm,
Solid shield screen type permittivity=3, Loss angle tanδ=0.02
εr rs
Permittivity=2.3, Loss Coaxial cable
angle tanδ=0.0002 geometry
2rw 6
ts

7. CST cable studio for S11 & S21
computation
RG58: length=5 cm,
50 Ω Z0=49.94Ω
50 Ω
File: Ex_coax_S_5cm.cst
Equivalent circuit to compute S
parameters by CST DESIGN
STUDIO
7

8. 3D RG58 model by MWS
Waveguide port Meshcells=41,515
Time domain solver: adaptive mesh refinement was used
8

9. S11
• S11 computed by Cable Studio 2010 &
2012 provide the same results
• S11 computed by MWS and MC10 provide
Cable Studio (CS) 2012 similar results and about some dB lower
Cable Studio (CS) 2010 •Level differences are due to impedance
mismatching
MWS Studio 2012
• Resonance frequencies are slightly higher
MC10 2012
for MWS (lower cable delay)
9

10. S21
MWS CS
MC10,DWS
• S21 computed by MC10 is the lowest curve
(more losses)
Cable Studio (CS) 2012 • S21 computed by CST 2012 is too higher
than CST 2010 (less losses)
Cable Studio (CS) 2010
• S21 computed by MWS is in the middle
MWS Studio 2012 between MC10/DWS and Cable studio 2012
MC10 2012,DWS 8.4 and close to cable studio 2010
RL-TL model
10

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
11

12. S parameters in time domain
12

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]
Definitions of S
parameters in time
domain:
•S11=VS-1
•S21=VL
When TL has characteristic impedance different from the loads, distortions occur
13

14. 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
14

15. Coaxial cable structure
Z0=49.94 Ω Length:1.83m
50 Ω
Ramp 50 Ω
V1 V2
Source
Vsource=2 V
trise=0.1 ns
15

16. 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,]
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]
Step
signal
V1=VS V2=VL
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
16
section, see Fig.7.22 of [1]

17. Circuit and cable model used in CST
Vinit: 0.0
Vpulse: 2.0
Tdelay: 1e-9
Trise: 0.1e-9
Thold: 100e-9 RG58 model with
Tfall: 0.1e-9 length 1.83 m
Ttotal: 200e-9
File: Ex_coax_S_1_83_10GHz.cst
10GHz
Skin effect only
17

18. Voltages V1 & V2 (cst 2010)
MC10 (SPICE) CST
V1 V2 V1 V2 Samples 5001 in
Samples 1001 in
transient1 task
transient1 task
ns ns
? ?
V1 V1
V2 V2
ns ns
MC10 and CS have the same losses except the oscillations provided by 18
CST 2010 that should not occur

19. 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
19

20. With 1-GHz model computed by CST 2012
Oscillations
increase!
20

21. 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
21

22. 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
22

23. Comparison between
measurements and simulations
23

24. 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.
24

25. CST model (Step source)
Vinit: 0.0
Vpulse: 2.0
Tdelay: 1e-9
Trise: 0.1e-9 50-Ω RG58 model with length
Thold: 100e-9
Tfall: 0.1e-9 1.83 m (very high accuracy,
Ttotal: 200e-9 ohmic losses in CS)
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)
25

26. DWS (4) cable cell on Spicy SWAN (5)
(Due to DWS sim speed, even a .5mm cell has been tried)
26

27. 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)
27

28. RG58 CU (TASKER) specs
28

29. Measurement set-up (CSA803)
29

30. Measurements with cable open at far-end voltage
1.2
V1
The measurements were
performed by Piero Belforte
0 on two commercial 1.83-m
RG58 cables: Tasker and
Reflected edge GBC.
ns
-1 50
1.2
V1
Comparison of the
Tasker reflected edge of the
GBC
two cables: very little
differences.
ns
0 4
30

31. VP1:voltage at cable input
V1
CST 2012
Measurement
MC10
ns DWS
(including TDR
setup)
V1
ns
31

32. VP1 voltage details
V1
ns
• There is good agreement on reflected edge among RL-TL
model using both MC10 and DWS simulators (DWS is CST 2012
50X faster than MC10) and measurements. Note that
dielectric losses were neglected in the RL_TL model and Measurement
actual cables have stranded conductors (not solid) MC10
• CS reflected edge is affected by not acceptable 32
DWS
oscillations

33. S-parameters measurements and comparison with
366 RL_TL model in the actual setup (DWS)
S21 S21
S11 S11
33

34. 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)
34

35. DWS BTM (Behavioral Time Model) of
1.83m cable using Spicy SWAN
1 cells
S from
measurements 1V
366 cells
50 ns
of RL-TL
1V 0.035
BTM
BTM
RL-TL
12 ns
RL-TL
50 ns 35

36. 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
36

37. Ultra Wide Band (UWB) source
37

38. 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.
38

39. 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]
Model
Validation
39

40. CST model (UWB source)
Imported file:
New_uwb_input_by2.txt
RG58
Ohmic losses
File: Ex_coax_UWB.cst
40

41. 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.
41

42. Proposal for Signal Integrity of
lossy cable
42

43. 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
43

44. Flow chart
Define the cable
Define an unit-cell cable
Vector fitting
unit cell 2D/3D S-parameter unit cell
to set RL
TL network computation S1
RL Which
1
RL solution ? S2
1
RL-TL Model S-parameter Model (DWS)
(SPICE, DWS)
Cascade of unit cells
Results obtained by SPICE or DWS
time domain simulations 44

45. 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.
45

46. 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
46