OutlineIntroductionMeasurement setupSpicy Swan (DWS) simulationsMC10 (SPICE) simulationsCable studio (CST 2012&2013) simulationsFrequency-domain S parameters of 5-cm RG58ConclusionsReferences
IntroductionThe purpose of this document is to comparemeasurements and circuit simulations of input (S11) andoutput (S21) waveforms in time domain of a lossy line.The line under investigation is an 1.83-m RG58 coaxialcable.It is shown the validity and limit of the model RL-TL ,,  used for simulations by using two commercialcircuit simulators: Spicy Swan (DWS)  and MC10(SPICE) Results computed by Cable Studio 2013 using 2D-TLmodel of CST 2013  are also reported.
Detail of SD24 head and cable connection fixtureCable connection to SD24 ports is achieved by means of two 60mm longSMA semirigid cables soldered to a reference ground plane (FR4 pcb).Cables under test inner conductors are connected together by means ofshort soldered splices.6
S11/S22 (measure)Heavy distributed impedance discontinuities (up to more than 50mrho pp) arepointed out by the measurement.The cable is not symmetrical (S11 not equal to S22) due to these discontinuities7
OPTIMIZED SETUP MODEL(1) : Spicy SWAN schematicThis model utilizes an ERFC approximation of TDR waveform taking intoaccount 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
SETUP DISCONTINUITIES (soldered splices between semirigid fixture )can be used as TIME MARKERS.Comparing the measured S11 (red) to the simulated one (blue) the exactmatching of marker position is achieved adjusting the value of TD ofelementary RL_TL cell of the model. A slight reduction from nominal 25.3psto 24.75ps was needed for perfect match11
FIRST SPLICE MODEL OPTIMIZATIONZ0 and Td of TL model of the splice (TSOLD1) are optimized to matchthe first peak of actual measure . The same parameters are assigned tothe second splice (TSOLD2)12
Actual SD24 TDR HEAD (CSA 803) waveformThe following is the actual waveform generated by Ch1 and observed on Ch2. Theconnection is made using a wideband 40cm SMA cable. In this way the stepdispersion due to the fixture of RG58 cable is taken into account.The resulting risetime is 22.5ps between 20% and 80%, while the observed risetimeat Ch1 (generator) is 17ps.13
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 utilizationin the simulative DWS model (model 2)14
OPTIMIZED SETUP MODEL(2)This is the Spicy SWAN schematic of the simulative model (2) using the pwlapproximation of TDR step generator (VTDR).Splice models parameters are optimized ,and the RG58 elementary RL-TLcell delay is optimized as well. The sim time step has been chosen to be 1/10of elementary cell delay (Tstep=2.475ps) to minimize overall delay errors.15
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
The following slides show the differences betweenmeasured and simulated waveforms including setupeffects.18
The RL-TL cell model is practically symmetrical, while the actual cable isnot.Actual cable S11/S22 values are under-estimated with respect model values dueto distributed impedance discontinuities.Overall behavior after first reflection shows good agreement between model andmeaure19
20measuremodelSplice 1discontinuityDistributed impedancediscontinuitiesThe waveforms are not matched in time for better comparison.Distributed impedance discontinuities on the actual cable are wellvisible.
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 aslower 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,23S21:measureS21:model
S21 edge comparison (model2)24In this slide the splice markers are NOT exactly matched to superimpose thewaveforms.The measured risetime is identical to that of the model (80ps), but the shapedifferences of model 1 are confirmed: slower measured waveform foot andfaster upper portion of measured edgesMeasureModel
25measureRL-TL model5 Gbit/sec10 Gbit/secWCED: Worst Case Eye Diagrams (from DWV: Digital Wave Viewer) :YELLOW : 5Gbit/sec, RED: 10Gbit/secEYE CLOSURE and ISI JITTER are slightly higher in the measure due todielectric losses not taken into account in the modelEYE shapes are more symmetrical in the measure: this can be also due todielectric losses not taken into account in the model
26Removing Splices from the simulative model, the simulated eye diagramgets more open and less similar to the eye calculated from actual measure(including splice effects). The dielectric loss effect (not considered in themodel) symmetrizes the eye diagram.
27S11PWL-BTM modelRL-TLS21BTMRL-TLAs can be pointed out from the plots the BTM is far more realistic than theRL-TL model. It is also 10-50 times FASTER (sim time under 1sec).
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 waveformresolution (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 (edgefoot 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 todielectric losses not taken into account in the model DWS is very effective in terms of accuracy and sim times (at least 50X faster thanMC10) BTM S-parameters modeling, supported by DWS, can take into account effects likedistributed 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 28
MC10 simulation featuresMC10 uses the model RL-TL of [1, section 7.2.1]The RL network is the result of vector fittingtechnique applied to Eq. 7.59 of  that are the sameof Eq. V.18 of .
Z0coax=49.95TDcoax=25.293ps (nodelay adaptation withmeasurements)This circuit was obtained from Eq. 7.57 of  byvector fitting technique adopting 10 poles.The model is valid up to 10 GHz, see Fig. 7.21 of 
Comments on Measure & MC10 simulationsIn this situation MC10 simulations are in goodagreement with DWS simulations nevertheless thedelay of the unit cell were not optimized tomeasurements and despite MC10 issues with RL-TLcircuits .To achieve good accuracy, it is very important to useat least a maximum step time of 1ps or a fixed timestep of 2.53ps=1/10 of unit cell delay.
CS simulation featuresCable Studio 2013 takes into account both skin and proximityeffect 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 MHzas should be required by the input risetime) is used for savingsimulation time.A fixed time step=2.5ps is used.Dielectric losses has tanδ=0.8m (8e-4) at 100MHz, default valuein CST.Setup impedance discontinuities are considered.
Permittivity εr=2.3Tanδ = 0.8x10-3at 100MHzFixed time step=2.5ps1+S11S21SourcewithTDRinput file
nsMeasured CS with (dadot) and without(dash) dielectric lossesVolt•Loss effect is under estimated•There is an offset of about 0.005
•Loss effect is under estimated•There is an offset of about 0.005MeasuredCS with (dadot) and without(dash) dielectric lossesnsVolt
•Measure (solid)•CS with (dadot) andwithout (dash) dielectriclossesMC10 delaymodified forcomparison withDWS waveformLosses are slightlyunder estimated alsowith tanδ=0.8mDielectric losses introduce adelay of 0.4nsnsVoltnsVolt
•Measure (solid)•CS with (dadot) andwithout (dash) dielectriclossesCS delay is modified forcomparison with DWSwaveform (see slide 23)S21 is in goodagreement with themeasurement whentanδ=0.8m is usedDielectric losses introduce adelay of 10ps (anticipation)nsVoltnsVolt
Comments on Measure & cs simulationsCS provides the expected wave shapes of the S parameters in timedomain.It is very important to use the option: “allow modal models” in“2D (TL) modeling settings” to avoid fast oscillations on the frontof 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 40,000MHz 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 accountproximity effect also, than cs2012
MC10 models This section is divided into two parts:1. The model RL-TL as described previously for MC10& DWS sims is compared with CS2. The analytic model as described in [1, 126.96.36.199] with acorrection factor of ½ and using the exacttransmission line model for computing s parametersas reported in[1, 11.2.3] is compared with CS andMWS.
Part1: CST simulation featuresThe frequency range considered is: 0-10 GHzMWS and Cable Studio (CS) S parameters are computedby CST 2013 if not specifiedNormal accuracy is used for 2D modeling of CSMeshcells=71,944 computed by adaptive mesh refinementare used for MWS
Part 1: Comments on S parametersMaking reference to , , we have:DWS, MC10, CS models consider a solid shield while the actual RG58cable has a braided shield.S11 with ohmic losses only: CS 2010 & 2013 no modal show coincidentwaveforms; CS modal provides lower valued waveform; MC10 andMWS are lower also and are very similar with slight higher resonancesfor MWS when the frequency increases.S11 computed by CS with different types of losses are practically thesame.S21 with ohmic losses only: MWS, CS (no modal), CS (modal) computethe same attenuation; Higher attenuation is computed by CS 2010 (nomodal) and close to MC10 as previously verified.S21 computed by CS with dielectric losses (tanδ=0.8m) provides anattenuation of 0.023 dB close to the nominal 0.026 dB at 1 GHzreported in the data sheet of the RG58.S21 computed by CS (ohmic+diel) is slight lower than MC10 up to 7GHz.
Part2: MC10,CST, MWS simulation featuresThe 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 usedfor 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 +jωCoMWS considers both ohmic and dielectric lossesIt is used a tanδ=0.8m for all frequencies
Zi(f) Exact eq. for around wire [1, Eq.7.8a]rDC dc value fpr for around wire [1, Eq.7.6]Zif(f) approximate eq.for a round wire [1,Eq.7.15], type 1Ziwcoax(f) approximateeq. for a round wire [7,Eq.V.13], type 2Ziwcoaxt(f)approximate eq. for acoaxial wire [7,Eq.V.18] and [1, 7.59]•Exact and approximate equations (Types 1&2)for a round wire are in good agreement over0.3MHz.•Approximate equation for a coaxial wire used forRL-TL model overestimates the losses over0.03MHz.ΩMHz
•Cable studio: solid line with ohmic, dielectric (do), ohmic+dielectric (d)•MC10: dashed line with ohmic, dielectric (do), ohmic+dielectric (d)•MWS: dash-dot lineCS provideshigher S11parameters
•Cable studio: solid line•MC10: dashed line•MWS: dash-dot lineDielectricOhmicOhmic+dielectricMHzVery good agreement among thedifferent methods can be noted
Part 2: Comments on S parametersWhen using expression for a coaxial wire cable thatdiffers from round wire by a factor ½, the ohmiclosses are overestimated.S11: Cable Sudio computes parameters for every typeof losses about 20 dB higher than those given by MC10using the analytic expressions for a round wire.S21: Cable Sudio computes parameters for every typeof losses in good agreement with those given by MC10using the analytic expressions for a round wire.S11&S21: MWS computes parameters in goodagreement with MC10 using the analytic expressionsfor a round wire.
ConclusionsFor 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 inpart takes into account the dielectric loss effect. To be verifiedconsidering the actual dielectric losses of the coaxial cable.RL-TL model: it is valid up to 10 GHz in Spicy Swan (DWS) or MC10and provides waveforms close to the measurements if a constant timestep equal at least 1/10 of the unit cell delay is used.RL-TL model: S11 is under estimated in the time interval equal twicethe cable delay because the model does not take into accountdiscontinuity and dissymmetry along the cable.RL-TL model: S21 front is slight faster than measurement up to 0.4 ofits maximum value because the model does not take into account thedielectric losses. Cable studio (frequency domain): S11 is overestimated (about 20dB)while S21 is in good agreement with those computed by MC10 by usingexact analytic expressions for lossy round wire for all types of losses.Cable studio (time domain): S11 is underestimated for all the timeinterval while S21 is estimated well with ohmic and dielectric losses(tanδ=0.8m), and fixed time step=2.5ps.
References S. Caniggia, Francesca Maradei, “Signal Integrity andRadiated Emission”, John Wiley & Sons, 2008 P. Belforte, S. Caniggia, “CST coaxial cable models for SIsimulations: a comparative study”, March 24th 2013 P. Belforte, S. Caniggia,, “Measurements and Simulationswith 1.83-m RG58 cable”, April 5th 2013 Spicy SWAN : www.ischematics.com MC10: www.spectrum-soft.com Cable and Micro Wave Studio: www.cst.com M. D’Amore, “Compatibiltà Elettromagnetica”, Siderea,2003 (in Italian) P. Belforte DWS versus Microcap 10: 10 RL-TL cell cascadecomparative benchmarkhttp://www.slideshare.net/PieroBelforte1/2013-pb-dws-vs-micro