1. 1 S-parameters of 18.3-cm RG58 from MWS S. Caniggia, P. Belforte

2. 2 Outline Introduction S-parameter definition Dielectric losses (Tanδ) Simulations of a 18.3-cm RG58 coaxial cable Behavioral transmission line (BTL) model or BTM used for a 1.83-cm RG58 coaxial cable Conclusions References

3. 3 Introduction How to compute S parameters in time domain from incident and reflected waves provided by MWS is shown. S11 and S21 in time domain as response of a step source with matched line at both ends are computed integrating the waveforms provided by MWS when using waveguide ports. Comparison with RL-TL model used by MC10 (SPICE) or DWS [1] and 2D-TL model of Cable Studio (CS) is given CS 2013 takes into account also proximity effects The accuracy of the RL-TL model has been demonstrated by comparison with measurements of a 1.83-m RG58 coaxial cable [2]. With this report, we will investigate the possibility of simulating long lossy cables by using a cascade of unit cells with S parameters in time domain (BTL model). Once S parameters are computed by 2D (CS) or 3D (MWS) as response of a short step, they can be used as input for DWS code to be implemented in CST, see slide 44 of [1].

4. 4 S-parameter definition

5. 5 Two port network + + - - I1 I2 V1 V2 a1 a2 b1 b2 S-parameter definition for two port network [3] Normalized incident wave Z 01 Z 02 Normalized reflected wave With n=1,2:

6. 6 S-parameter physical interpretation Two port network a1 a2=0 b1 b2 + - Z 01 Z 02 Source applied to Port 1 Port 2 matched S 11 is just the input reflection coefficient when the output is matched. S 21 is the ratio of waves to the right at output and input under this condition. When Z 01 =Z 02 =Z 0 (the characteristic impedance of the two port network representing a cable), and the source is a step of amplitude 2V: 1+S11 and S21 are the V1 and V2 voltages respectively.

7. 7 Port signals in MWS MWS excites the network by a gaussian pulse having a flat bandwidth up to the maximum frequency defined by the user. Port signals: (i1), (o1,1), (o2,1) of MWS have the meaning respectively of incident (a1), reflected wave at port1 (b1) and reflected wave at port2 (b2). Better results can be obtained by using waveguide ports instead of discrete ports when possible: less oscillations in reflected wave b1. To find equivalent circuit of a DUT it is better to use the option in MWS “S parameters without normalization to fixed impedance” instead of “…with…”: resonance peaks are avoided due to mismatch between port and waveguide which could be: coaxial cable, microstrip,etc. Integrating (o1,1) & (o2,1) waveforms in time domain, we get the response at port1 (1+S11) and port2 (S21) of a step pulse with rise time tr determined by the maximum frequency. The pulse for source is obtained by integrating (i1) of MWS.

8. 8 S parameters in time domain 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: V S =1+S 11 V L =S 21

9. Dielectric losses (Tanδ)

10. 10 Tandδ The dielectric loss tangents for some materials commonly used in coaxial cables are: Material tanD at 100 MHztanD at 3 GHz Air0.0 PTFE2E-415E-4 PolyEthylene, DE-34012E-43.1E-4 Polyolefin, irradiated3E-4 Polystyrene1E-43.3E-4 Polyvinal formal (Formvar)1.3E-21.1E-2 Nylon2E-21.2E-2 Quartz, fused2E-46E-5 Pyrex Glass3E-35.4E-3 Water, distilled5E-31.6E-1 For simulation we have used Tanδ=8e-4 (used in CST as default value) http://cp.literature.agilent.com/litweb/pdf/genesys200801/elements/substrate_tables/t ablelosstan.htm

11. 11 Tandδ (coax Belden) Tandelta From: H. Johnson, M. Graham, “High-Speed Signal Propagation”, Prentice Hall, 2003 For RG58, a tanδ between 1.12e-3 and 2.12e-3 are given (values higher than the previous table for polyethylene)

12. 12 Simulations of a 18.3-cm RG58 coaxial cable

13. 13 MWS structure Meshcells=545,472 Frequency range: 0-40GHz Waveguide ports Cable parameters: Dielectric=2.3, tangent delta=0 Lossy metal: 5.8e7 S/m Geometry in mm: length=183; wire radius=0.395, shield radius=1.397; shield thickness=0.127

14. 14 Exciting signal in MWS Rise time tr between 10-90% is about 23ps as used in TDR measurements Tr=23ps Gaussian (40GHz) Step source Integration of gaussian normalized to maximum value of the integral

15. 15 Port signals of RG58 in MWS i1o21 o11 ns Integrating o11 and o21 with normalizing to maximum value of the gaussian integral, we get respectively S11 and S21 as response of a step with tr=23 ps

16. 16 Cable studio (CS) structure Step source of 40GHz imported from MWS (see previuos slide)

17. 17 MC10 (SPICE) structure Cascade of 100 1.83-mm unit RL-TL cell S11=VTin S21=VTout Step source with tr=25ps

18. 18 DWS circuits RL-TL5mmx37=185mm 185-mm RG58 from CST

19. 19 Input (1+S11) and output (S21) line waveforms ps Line length= 18.3 cm 1+S11 S21 MWS waveforms MC10 and CS are similar

20. 20 S11 ps Volt MWS: solid CS: dot MC10: dash MC10 & DWS compute the same waveforms MWS & CS provide similar waveforms with less losses

21. 21 1+S11 and S21 ps 1+S11 S21 Volt MWS: solid CS: dot MC10: dash DWS 1+S11 S21 MC10 & DWS compute the same waveforms MWS & CS compute similar waveforms with about half losses S11 of CS & DWS presents some slight segmentation

22. 22 1+S11 and S21 with and without dielectric losses MC10 Solid MC10 Dash CS 2013 Dot CS 2013 with dielectric losses (Tanδ=0.8m)

23. 23 CS 2012: Dielectric losses (tanδ=0.8m) Ohmic losses 1+S11 S21 sec Volt Ohmic + dielectric losses 1+S11 S21sec Volt There are slight differences The segmentation effect is eliminated

24. 24 CS 2013: Dielectric losses (tanδ=0.8m) Ohmic losses 1+S11 S21 sec Volt Ohmic + dielectric losses 1+S11 S21 sec Volt The segmentation effect is eliminated also for ohmic losses There is a slight increase of losses due to proximity effect in CST 2013

25. 25 Input and output line voltages VS VL MC10 MWS 2013 CS 2013 For MC10 a ramp has been used For MWS and CS the time integration of a gaussian (0-40GHz) has been used. S11 (Vin-1) and S21 (Vout) should be computed with a step of about 1ps has response of a quasi-ideal pulse This could give some inaccuracy when using these parameters as BTL model. In the following slides this error will be estimated

26. 26 Comments on simulations MC10 & DWS by using RL-TL model compute the same waveforms and are used as reference being validated experimentally [1], [2] MWS & CS provide similar waveforms with less losses respect to RL-TL model, as verified in [1], [2]. MWS waveforms evolves more rapidly than CS towards dc values for high values of time. S11 of DWS presents some slight segmentations that can be eliminated by using more unit cells (example 100 as done with MC10). No segmentations of S11 with CS 2013

27. 27 Behavioral transmission line (BTL) model or BTM used for a 1.83-cm RG58 coaxial cable

28. BTL model The S11 and S21 computed by cable studio (CS) 2013 on a 18.3-cm of RG58 (0-40GHz) are the input for the BTM. The waveforms obtained by a ramp of 1ps are inserted into the BTM by PWL technique and not as ASCII files. DWS computes VS&VL voltages by a cascade of 10 BTM with a ramp of 25 ps and the waveforms are compared with those computed by CS 2013 using a model valid in the range 0- 10GHz.

29. 29 VS&VL (cable length=18.3cm, model:0- 40GHz,tandelta=0.0) S-parameter waveforms do not seem influenced by the tr, apart the oscillations in S11 A fixed time step of 0.1ps has been used 1+S11 S21 1+S11 tr=25ps tr=1ps

30. 30 VS&VL (cable length=18.3cm, model:0- 40GHz,tandelta=0.8m) 1+S11 tr=25ps tr=1ps S11 waveforms does not seem influenced by the tr, apart the oscillations in S11 A fixed time step of 0.1ps has been used S21 1+S11 S21

31. 31 VS&VL (cable length=18.3cm, model:0- 40GHz,tandelta=0.8m): more time tr=25ps Time step=1ps Samples=4001 1+S11 S21 Zoom

32. 32 VL zoom (cable length=18.3cm, model:0- 40GHz,tandelta=0.8m) tr=25ps tr=1ps S21 waveforms is influenced by tr To be used for BTM Time step=0.02ps Samples= 8001 Time step=0.1ps Samples= 4001 S21

33. PWL technique

34. 34 VS&VL (cable legth=1.83m, model:0-10GHz, tandelta=0.8m) step time=1ps, points=4001 tr=25ps 10 BTM with DWS CS 2013 1+S11 S21 1+S11 S21 S11 & S21 waveforms are in good agreement

35. step time=1ps, points=4001 35 Zoom VL (cable length=1.83m, model:0- 10GHz, tandelta=0.8m) S21 CS 2013 tr=25ps S21 10 BTM with DWS S21 computed by 10 BTN seems to be a little faster

36. Comments on BTM The S11 waveform obtained by a cascade of BTM (CS+DWS) is in good agreement with the one the one obtained by a BTM for the total length of the cable (CS only) The S21 front obtained by a cascade of BTM (CS+DWS) seems to be a little faster than the one obtained by a BTM for the total length of the cable (CS only) There are some critical points in using the cascade of BTM: 1.The S parameters are inserted into BTM by PWL technique and not by ASCII files, the consequence is a lack of accuracy at starting and ultimate S21 front. 2.The cable model used in CS has limited bandwidth (0-40 GHz) for a source of 1 ps used as S-parameter computation for BTM. The limited bandwidth is imposed by the calculation time. The correct ramp should be 25ps but this would introduce a significant error in computing the S21 front.

37. 37 Conclusions BTM obtained by a 3D model (MWS) is not feasible because the mesh cells required by a source of 1 ps should be too large for the computation. BTM obtained by a 2D model (CS) could be feasible but with some critical points due to the PWL technique used for DWS and the limited bandwidth of the cable model to be used in CS to obtain S parameters for unit cell.

38. 38 Reference [1] Piero Belforte, Spartaco Caniggia, “CST coaxial cable models for SI simulations: a comparative study”, March 24th 2013 [2] P. Belforte, S. Caniggia,, “Measurements and Simulations with1.83-m RG58 cable”, April 5th 2013 [3] Ramo, Whinnery, Van Duzer, “Fields and wave in communication electronics”, John Wiley, 3rd Edition [4] CST, “CST Cable Studio 2013: Coax cable analysis”, 2013