1. Piero Belforte
Spartaco Caniggia
June 04, 2013
1
TDR measurements and
simulations of RGU 58 coaxial
cable S-parameters

2. Outline
Introduction
Measurement setup
Spicy Swan (DWS) simulations
MC10 (SPICE) simulations
Cable studio (CST 2012&2013) simulations
Frequency-domain S parameters of 5-cm RG58
Conclusions
References

3. Introduction
The purpose of this document is to compare
measurements and circuit simulations of input (S11) and
output (S21) waveforms in time domain of a lossy line.
The line under investigation is an 1.83-m RG58 coaxial
cable.
It is shown the validity and limit of the model RL-TL [1],
[2], [3] used for simulations by using two commercial
circuit simulators: Spicy Swan (DWS) [4] and MC10
(SPICE) [5]
Results computed by Cable Studio 2013 using 2D-TL
model of CST 2013 [6] are also reported.

4. Measurement setup

5. TDR setup: CSA 803 and RG58 cable fixture
5

6. Detail of SD24 head and cable connection fixture
Cable connection to SD24 ports is achieved by means of two 60mm long
SMA semirigid cables soldered to a reference ground plane (FR4 pcb).
Cables under test inner conductors are connected together by means of
short soldered splices.
6

7. S11/S22 (measure)
Heavy distributed impedance discontinuities (up to more than 50mrho pp) are
pointed out by the measurement.
The cable is not symmetrical (S11 not equal to S22) due to these discontinuities
7

8. S21 (measure)
8

10. OPTIMIZED SETUP MODEL(1) : Spicy SWAN schematic
This model utilizes an ERFC approximation of TDR waveform taking into
account SMA fixture effects.
Connection splices are modeled by two equal TL (TSOLD1,TSOLD2).
RG58 CU cable is modeled as a cascade of 366 X 5cm RL-TL cell.
10

11. SETUP DISCONTINUITIES (soldered splices between semirigid fixture )
can be used as TIME MARKERS.
Comparing the measured S11 (red) to the simulated one (blue) the exact
matching of marker position is achieved adjusting the value of TD of
elementary RL_TL cell of the model. A slight reduction from nominal 25.3ps
to 24.75ps was needed for perfect match
11

12. FIRST SPLICE MODEL OPTIMIZATION
Z0 and Td of TL model of the splice (TSOLD1) are optimized to match
the first peak of actual measure . The same parameters are assigned to
the second splice (TSOLD2)
12

13. Actual SD24 TDR HEAD (CSA 803) waveform
The following is the actual waveform generated by Ch1 and observed on Ch2. The
connection is made using a wideband 40cm SMA cable. In this way the step
dispersion due to the fixture of RG58 cable is taken into account.
The resulting risetime is 22.5ps between 20% and 80%, while the observed risetime
at Ch1 (generator) is 17ps.
13

14. Normalized TDR waveform (0-2rho)
This is 19-breakpoints PWL approximation of the previous SD24 waveform.
The step amplitude has been normalized between 0 and 2rho for utilization
in the simulative DWS model (model 2)
14

15. OPTIMIZED SETUP MODEL(2)
This is the Spicy SWAN schematic of the simulative model (2) using the pwl
approximation of TDR step generator (VTDR).
Splice models parameters are optimized ,and the RG58 elementary RL-TL
cell delay is optimized as well. The sim time step has been chosen to be 1/10
of elementary cell delay (Tstep=2.475ps) to minimize overall delay errors.
15

16. * Netlist and simulation file
* Generated by: SPICY Schematics (ischematics.com)
* File: CSA803_RG58_1.83m_3
******************************************
* Author: Piero Belforte
* Date: March 28 2013
* Desc: CSA803 actual setup model for 1.83m RG58
* coax S-parameter measurement: actual SD24
* CSA 803 waveform (pwl) and optimized
* setup discontinuities.
******************************************
.CHAIN 366*RG58_RLT_5mm_OPT I:14; O:15
TTDR 2 0 7 0 Z0=50 TD=500p
TSOLD1 7 0 140001 0 Z0=100 TD=20p
TSOLD2 150366 0 8 0 Z0=100 TD=20p
R0 8 0 50
VTDR 2 0 PWL (0.00ps 0 11.50ps 0.03088 16.50ps 0.06504 21.50ps 0.12632
+ 27.00ps .248 31.25ps .3888 39.25ps .7632 47.50ps 1.23552
+ 54.25ps 1.59472 60.50ps 1.84672 66.00ps 1.9884 70.50ps 2.04816
+ 75.75ps 2.047 91.75ps 1.9 97.25ps 1.878 110.25ps 1.928
+ 119.00ps 1.957 139.25ps 1.928 162.00ps 2) 50
* {RS} N_5=1 N_S11=2 N_2=3 N_3=4 UN_2=140001 UN_3=150366 UN_5=7 N_S21=8
******************************************
* MODELS USED IN CIRCUIT
******************************************
**********************
* Spicy SWAN - Model File
* http://ischematics.com
* Author: Piero Belforte
* Date: Thu 04 Apr 2013 21:24:25 GMT
**********************
.CELL RG58_RLT_5mm_OPT 14 15
R2 22 23 .10527
L2 0 24 1.734p
R3 23 25 .035811
L3 0 26 3.151p
R4 25 27 .016176
L4 0 28 6.6198p
R5 27 29 7.3875m
L5 0 6 13.469p
R6 29 7 3.3826m
L6 0 4 25.327p
R7 7 5 1.6371m
L7 0 11 45.323p
R8 5 12 .8425m
L8 0 8 80.524p
R9 12 9 .41854m
L9 0 2 .11427n
R10 9 3 .35315m
L10 0 21 .40739n
R11 3 20 .11879e-3m
L11 0 19 18.906n
R1 14 22 .2224m
T0 20 0 15 0 Z0=49.942 TD=24.75p
AS2 22 23 24
AS3 23 25 26
AS4 25 27 28
AS5 27 29 6
AS6 29 7 4
AS11 3 20 19
AS7 7 5 11
AS8 5 12 8
AS9 12 9 2
AS10 9 3 21
.ENDC RG58_RLT_5mm_OPT
******************************************
* Simulations
* Note: This portion below is updated when you simulate
******************************************
.OPTIONS DELAYMETH=INTERPOLATION
.TEMP 27
.TRAN TSTEP=2.475e-12 TSTOP=50e-9 TSTART=0e-9 LIMPTS=5000
I(VTDR,2) A(VTDR,2) A(R0,8)
.END
16

17. Spicy SWAN (DWS) results of model (2)
The following are the plots of simulated S11 and S22 of previous setup.
This sim requires about 30s with about 20K points and 28K model elements.
17

18. The following slides show the differences between
measured and simulated waveforms including setup
effects.
18

19. The RL-TL cell model is practically symmetrical, while the actual cable is
not.
Actual cable S11/S22 values are under-estimated with respect model values due
to distributed impedance discontinuities.
Overall behavior after first reflection shows good agreement between model and
meaure
19

20. 20
measuremodel
Splice 1
discontinuity
Distributed impedance
discontinuities
The waveforms are not matched in time for better comparison.
Distributed impedance discontinuities on the actual cable are well
visible.

21. 21
model
measure

22. 22
model
measure

23. S21 edge comparison (model1)
In this slide the absolute delays are taken into account (Splice markers matched)
Measured 20%-80% risetime : 80ps vs 70ps of model. The measured waveform has a
slower foot but a faster edge in the upper part. This is due probably to dielectric losses
(slower foot). The faster upper part can be due to stranded conductors of the actual cable,
23
S21:measure
S21:model

24. S21 edge comparison (model2)
24
In this slide the splice markers are NOT exactly matched to superimpose the
waveforms.
The measured risetime is identical to that of the model (80ps), but the shape
differences of model 1 are confirmed: slower measured waveform foot and
faster upper portion of measured edges
Measure
Model

25. 25
measure
RL-TL model
5 Gbit/sec
10 Gbit/sec
WCED: Worst Case Eye Diagrams (from DWV: Digital Wave Viewer) :
YELLOW : 5Gbit/sec, RED: 10Gbit/sec
EYE CLOSURE and ISI JITTER are slightly higher in the measure due to
dielectric losses not taken into account in the model
EYE shapes are more symmetrical in the measure: this can be also due to
dielectric losses not taken into account in the model

26. 26
Removing Splices from the simulative model, the simulated eye diagram
gets more open and less similar to the eye calculated from actual measure
(including splice effects). The dielectric loss effect (not considered in the
model) symmetrizes the eye diagram.

27. 27
S11
PWL-BTM model
RL-TL
S21
BTM
RL-TL
As can be pointed out from the plots the BTM is far more realistic than the
RL-TL model. It is also 10-50 times FASTER (sim time under 1sec).

28. Comments on Measurements & DWS simulations
 The used setup is effective for a 1.83m long cable characterization
 The TDR incident pulse rise time (22ps) is fast enough to achieve good waveform
resolution (80ps rise time at cable’s output)
 Actual cable shows sensible impedance discontinuities (S11)
 Actual cable is asymmetrical
 Theoretical cable delay is slightly overestimated
 RL-TL model gives good S11 estimate (without discontinuities)
 S21 edge risetime agreement is good (70-80ps)
 Dielectric losses have to be added to achieve better S21 waveform match (edge
foot too fast in the sim model)
 Skin effect losses are probably over-estimated (upper S21 edge too slow)
 EYE CLOSURE and ISI JITTER (5-10Gbit/sec) slightly higher in the measure due to
dielectric losses not taken into account in the model
 DWS is very effective in terms of accuracy and sim times (at least 50X faster than
MC10)
 BTM S-parameters modeling, supported by DWS, can take into account effects like
distributed discontinuities and asymmetries of actual cable with a further speed-
up factor of 10X to 50X (more than 3 orders of magnitude faster than MC10)
 MC10 shows accuracy problems in simulating RL-TL circuits [9]
28

30. MC10 simulation features
MC10 uses the model RL-TL of [1, section 7.2.1]
The RL network is the result of vector fitting
technique applied to Eq. 7.59 of [1] that are the same
of Eq. V.18 of [7].

31. ….
1+S11
S21
366 RL-TL unit cells

32. Z0coax=49.95
TDcoax=25.293ps (no
delay adaptation with
measurements)
This circuit was obtained from Eq. 7.57 of [1] by
vector fitting technique adopting 10 poles.
The model is valid up to 10 GHz, see Fig. 7.21 of [1]

33. Imported from TDR measurement

34. Good agreement with DWS results
Measured
MC10
Volt
ns

35. Good agreement
with DWS results
Measured
MC10
Measured
MC10
MC10 delay is
modified for
comparison with
DWS waveform
(see slide 23)
ns
ns
Volt
Volt

36. Comments on Measure & MC10 simulations
In this situation MC10 simulations are in good
agreement with DWS simulations nevertheless the
delay of the unit cell were not optimized to
measurements and despite MC10 issues with RL-TL
circuits [9].
To achieve good accuracy, it is very important to use
at least a maximum step time of 1ps or a fixed time
step of 2.53ps=1/10 of unit cell delay.

38. CS simulation features
Cable Studio 2013 takes into account both skin and proximity
effect at the same time while CS 2012 considers skin effect only.
The source is the PWL approximation of actual TDR waveform
(rise time tr=22.5ps, 20% and 80%) as used for DWS sims.
A cable model valid up to 10,000 MHz (instead of 40,000 MHz
as should be required by the input risetime) is used for saving
simulation time.
A fixed time step=2.5ps is used.
Dielectric losses has tanδ=0.8m (8e-4) at 100MHz, default value
in CST.
Setup impedance discontinuities are considered.

39. Permittivity εr=2.3
Tanδ = 0.8x10-3
at 100MHz
Fixed time step=2.5ps
1+S11
S21
Source
with
TDR
input file

40. ns
Measured CS with (dadot) and without
(dash) dielectric losses
Volt
•Loss effect is under estimated
•There is an offset of about 0.005

41. •Loss effect is under estimated
•There is an offset of about 0.005
Measured
CS with (dadot) and without
(dash) dielectric losses
ns
Volt

42. •Measure (solid)
•CS with (dadot) and
without (dash) dielectric
losses
MC10 delay
modified for
comparison with
DWS waveform
Losses are slightly
under estimated also
with tanδ=0.8m
Dielectric losses introduce a
delay of 0.4ns
ns
Volt
ns
Volt

43. •Measure (solid)
•CS with (dadot) and
without (dash) dielectric
losses
CS delay is modified for
comparison with DWS
waveform (see slide 23)
S21 is in good
agreement with the
measurement when
tanδ=0.8m is used
Dielectric losses introduce a
delay of 10ps (anticipation)
ns
Volt
ns
Volt

44. Comments on Measure & cs simulations
CS provides the expected wave shapes of the S parameters in time
domain.
It is very important to use the option: “allow modal models” in
“2D (TL) modeling settings” to avoid fast oscillations on the front
of S21.
For accurate results, the circuit should run with a fixed time step
(in this case 2.5ps)
For better results, the cable model should be valid up to 40,000
MHz instead of 10,000.
CS under estimates S11 also with ohmic and dielectric losses
(tanδ=0.8m) while S21 is in good agreement with measurements.
Better results are obtained with cs2013, that takes into account
proximity effect also, than cs2012

46. MC10 models
 This section is divided into two parts:
1. The model RL-TL as described previously for MC10
& DWS sims is compared with CS
2. The analytic model as described in [1, 7.2.1.1] with a
correction factor of ½ and using the exact
transmission line model for computing s parameters
as reported in[1, 11.2.3] is compared with CS and
MWS.

47. Part1: CST simulation features
The frequency range considered is: 0-10 GHz
MWS and Cable Studio (CS) S parameters are computed
by CST 2013 if not specified
Normal accuracy is used for 2D modeling of CS
Meshcells=71,944 computed by adaptive mesh refinement
are used for MWS

48. CS (no modal)
MWS
MC10
CS
CS 2010 (no
modal)
Ohmic losses
CS (Ohmic)
CS (ohmic+diel)
CS (diel)
Tanδ=0.8m
CS 2013
MC10 & MWS
CS

49. CS (no modal)
MWS
MC10
CS
CS 2010 (no
modal)
Ohmic losses
CS (Ohmic)
CS (ohmic+diel)
CS (diel)
Tanδ=0.8m
CST 2013
CS 2010, why ?
MC10
dB
MHz
MHz
dB
CS 2013

50. -0.026dB
(data sheet)
CS (Ohmic)
CS (ohmic+diel)
CS (diel)
Tanδ=0.8m
CS (Ohmic+diel)
Tanδ=0.8m
MC10 (Ohmic)
-0.023dB
MHz
dB
dB
MHz

51. Part 1: Comments on S parameters
Making reference to [2], [3], we have:
DWS, MC10, CS models consider a solid shield while the actual RG58
cable has a braided shield.
S11 with ohmic losses only: CS 2010 & 2013 no modal show coincident
waveforms; CS modal provides lower valued waveform; MC10 and
MWS are lower also and are very similar with slight higher resonances
for MWS when the frequency increases.
S11 computed by CS with different types of losses are practically the
same.
S21 with ohmic losses only: MWS, CS (no modal), CS (modal) compute
the same attenuation; Higher attenuation is computed by CS 2010 (no
modal) and close to MC10 as previously verified.
S21 computed by CS with dielectric losses (tanδ=0.8m) provides an
attenuation of 0.023 dB close to the nominal 0.026 dB at 1 GHz
reported in the data sheet of the RG58.
S21 computed by CS (ohmic+diel) is slight lower than MC10 up to 7
GHz.

52. Part2: MC10,CST, MWS simulation features
The circuit for computing S parameters is the same of [1, 11.2.3,
pag. 421].
The cable is simulated by exact TL equations by using the per-
unit-line parameters Zpuls and Ypuls.
Eq. for the case of a round wire above a ground plane are used
for Zi(ω) of Zpuls=Zi(ω)+j ωLo instead Eq. of a coaxial wire.
The two types of Equations differs for a factor ½.
Eq.7.28 of [1, pag.174]) is used for Ypuls=ωCotanδ +jωCo
MWS considers both ohmic and dielectric losses
It is used a tanδ=0.8m for all frequencies

53. Zi(f) Exact eq. for a
round wire [1, Eq.7.8a]
rDC dc value fpr for a
round wire [1, Eq.7.6]
Zif(f) approximate eq.
for a round wire [1,
Eq.7.15], type 1
Ziwcoax(f) approximate
eq. for a round wire [7,
Eq.V.13], type 2
Ziwcoaxt(f)
approximate eq. for a
coaxial wire [7,
Eq.V.18] and [1, 7.59]
•Exact and approximate equations (Types 1&2)
for a round wire are in good agreement over
0.3MHz.
•Approximate equation for a coaxial wire used for
RL-TL model overestimates the losses over
0.03MHz.
Ω
MHz

54. •Cable studio: solid line with ohmic, dielectric (do), ohmic+dielectric (d)
•MC10: dashed line with ohmic, dielectric (do), ohmic+dielectric (d)
•MWS: dash-dot line
CS provides
higher S11
parameters

55. •Cable studio: solid line
•MC10: dashed line
•MWS: dash-dot line
Dielectric
Ohmic
Ohmic+dielectric
MHz
Very good agreement among the
different methods can be noted

56. Part 2: Comments on S parameters
When using expression for a coaxial wire cable that
differs from round wire by a factor ½, the ohmic
losses are overestimated.
S11: Cable Sudio computes parameters for every type
of losses about 20 dB higher than those given by MC10
using the analytic expressions for a round wire.
S21: Cable Sudio computes parameters for every type
of losses in good agreement with those given by MC10
using the analytic expressions for a round wire.
S11&S21: MWS computes parameters in good
agreement with MC10 using the analytic expressions
for a round wire.

57. Conclusions
For accurate circuit simulations of S-parameter cable in time domain,
the discontinuities introduced by the setup should be considered.
RL-TL model: it seems it overestimates ohmic losses and therefore in
part takes into account the dielectric loss effect. To be verified
considering the actual dielectric losses of the coaxial cable.
RL-TL model: it is valid up to 10 GHz in Spicy Swan (DWS) or MC10
and provides waveforms close to the measurements if a constant time
step equal at least 1/10 of the unit cell delay is used.
RL-TL model: S11 is under estimated in the time interval equal twice
the cable delay because the model does not take into account
discontinuity and dissymmetry along the cable.
RL-TL model: S21 front is slight faster than measurement up to 0.4 of
its maximum value because the model does not take into account the
dielectric losses.
 Cable studio (frequency domain): S11 is overestimated (about 20dB)
while S21 is in good agreement with those computed by MC10 by using
exact analytic expressions for lossy round wire for all types of losses.
Cable studio (time domain): S11 is underestimated for all the time
interval while S21 is estimated well with ohmic and dielectric losses
(tanδ=0.8m), and fixed time step=2.5ps.

58. References
[1] S. Caniggia, Francesca Maradei, “Signal Integrity and
Radiated Emission”, John Wiley & Sons, 2008
[2] P. Belforte, S. Caniggia, “CST coaxial cable models for SI
simulations: a comparative study”, March 24th 2013
[3] P. Belforte, S. Caniggia,, “Measurements and Simulations
with 1.83-m RG58 cable”, April 5th 2013
[4] Spicy SWAN : www.ischematics.com
[5] MC10: www.spectrum-soft.com
[6] Cable and Micro Wave Studio: www.cst.com
[7] M. D’Amore, “Compatibiltà Elettromagnetica”, Siderea,
2003 (in Italian)
[8] P. Belforte DWS versus Microcap 10: 10 RL-TL cell cascade
comparative benchmark
[9]
http://www.slideshare.net/PieroBelforte1/2013-pb-dws-vs-micro