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

9. Spicy Swan (DWS) simulations

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 DWS netlist related to setup model 2 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. Measure/simulation comparisons The following slides show the differences between measured and simulated waveforms including setup effects. 18

19. S11/S22 measure vs model (DWS) 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. S11 measure vs model: detail on a 5ns window 20 measure model 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. S21 comparison on a 50ns window 21 model measure

22. S21 comparison on a 5ns window 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. S21 WCED comparison (including setup) 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. 5Gbit/sec WCEDs: SPLICE EFFECTS 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. Comparison of BTM model of the cable with the RL-TL model 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

29. MC10 (SPICE) simulations

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. MC10 setup model …. 1+S11 S21 366 RL-TL unit cells

32. 5-mm RL-TL unit cell 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. Source waveform (v(1S)) Imported from TDR measurement

34. S11 (MC10&measure) Good agreement with DWS results Measured MC10 Volt ns

35. S21 (MC10&measure) Good agreement with DWS results Measured MC10 Measured MC10 MC10 delay is modified for comparison with DWS waveform (see slide 23) ns 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.

37. Cable studio (CST 2012&2013) simulations

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

40. S11 (cs 2012&measure) 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. S11 (cs2013&measure) 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. S21 (cs2012&measure) 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. S21 (cs2013&measure) 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

45. Frequency-domain S parameters of 5- cm RG58

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. S11 parameters for 5-cm rg58 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. S21 parameters for 5-cm rg58 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 dB CS 2013

50. S21 parameters for 5-cm rg58: zoom -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 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. 1-m round wire and coaxial cable wire Zi(f) Exact eq. for a round wire [1, Eq.7.8a] r DC 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. S11 parameters for 5-cm rg58 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. S21 parameters for 5-cm rg58 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.comwww.ischematics.com [5] MC10: www.spectrum-soft.comwww.spectrum-soft.com [6] Cable and Micro Wave Studio: www.cst.comwww.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- microcap-10-rlhttp://www.slideshare.net/PieroBelforte1/2013-pb-dws-vs- microcap-10-rl