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  • 1. Comparison of time-domain Sparameters of RG58 cable computed by: Theory, CST, SPICE, DWS S. Caniggia, P. Belforte February 04, 2014 1
  • 2. Outline • • • • • • • • • Introduction S-parameter definition in time domain Simulations of a 18.3-cm RG58 coaxial cable S11&S21 computed by analytic approach (theory) Cable Studio 2013 results as source of a BTM of a 1.83m RG58 coaxial cable used in DWS Analytical method results as source of a BTM of a 10-m RG58 coaxial cable used in DWS Conclusions Appendix: Dielectric losses (Tanδ) References 2
  • 3. Introduction • • • • • • In this report, the sixth of a series devoted to lossy lines [1,2,3,7,8], several approaches for computing time-domain step responses of a lossy line are outlined and compared. The methods used are: MWS of CST, CS of CST, RL-TL model for SPICE & DWS, Theory. The purpose is to pinpoint the advantages and drawbacks of each approach for simulating lossy lines. The feasibility of deriving BTM models to be used by DWS is analyzed. Long lossy lines can be simulated by DWS in seconds using a cascade of shorter line segment characterized as Behavior Transmission Model (BTM) by parameters S11 & S21 in time domain (7,9). These S parameters can be computed by CS or theory and can be used as models for DWS. If a piecewise linear (pwl) approximation is used for behaviors, a dramatic speedup of simulations can be obtained A typical RG58 coaxial cable is used as line sample for the study.
  • 4. Methods for time domain simulations of lossy lines [4] Three methods can be used to simulate lossy lines in transient. The choice depends on which simulator should be used for a simple or complex line structure. 1. Behavioral Transmission line Model (BTM) block, based on time-domain step responses of lossy line S-parameter to be used within the Digital Wave Simulator (DWS) [1,2,3,7,8,9] to get quick simulations. 2. Vector fitting technique (VFT) [4,6] to set, starting from analytical expression of losses, an equivalent circuit for a cascade of RLGC-TL (lossless) segments of line electrically short to be used with a SPICE-like circuit simulator such as MC10 [1,2,3,4,6] or DWS for faster (1-2 order of magnitude) simulations [1,2,3,7,8] . 3. Model Order Reduction (MOR) technique to set, starting from S parameters, an equivalent circuit of the line (complex net of RLGC-TL) for the frequency range of interest to be used by CST circuit simulator [1,2,3,7,9]. Note: • The lossy line can be both a cable or a PCB trace. • VTF and MOR should be used for the frequency range of interest. • CST is particularly suitable for complex line structures such as multi-conductor lines with shields. • DWS allows the use of hybrid BTM and circuital models [8]
  • 5. Flow chart for direct transient simulation of lossy lines by using three different methods: SPICE, CST, DWS [4]. Define the line (a,p,σ,μ,Rdc,tanθ,Kp) and compute the per-unit-line parameters: Zi, L0, C0, Gd unit cell RL TL Segmented line Full line Which model ? GC One block: measured or computed S-parameter line in time domain S11 One block complex RLGC-TL net Zi, L0,C0, Gd VFT technique Modeling Cascade of unit cells to form a block (SPICE-like Sim.) MOR technique S21 Which technique? S technique Modeling Modeling One RLGC-TL block One BTM block (DWS) (SPICE in CST) Cable block in schematic Simulated waveforms with several loadings (passive/active, linear/non-linear)
  • 6. S-parameter definition in time domain 6
  • 7. S-parameter definition for two-port network [5] I1 a1 I2 + + Z01 b1 V1 Two port network - V2 - a2 b2 Z02 With n=1,2: Normalized incident wave Vn  an  Z0n Vn  (Vn   Vn - )  Z0n (a n  b n ) 1 1 In  (Vn   Vn - )  (a n  b n ) Z0n Z0n Vn  bn  Z0n Normalized reflected wave  b1  S11 S12   a1  b   S S22  a 2   2   21   7
  • 8. S-parameter physical interpretation [5] a1 a2=0 Z01 + Source applied to Port 1 - b1  S11a1 b 2  S21a1 a1  Port 2 matched Two port network b1 Z02 b2 S11 is just the input reflection coefficient when the output is matched. S21 is the ratio of waves to the right at output and input under this condition. V1  Z01I1 2 Z01 V1  Z01I1 b1  2 Z01 When Z01=Z02=Z0 (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. 8
  • 9. Port signals in MWS • • • • MWS stimulates the network by means of 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. These resonances are 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 source pulse is obtained by integrating (i1) of MWS. 9
  • 10. 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) [6, Fig.7.3] Definitions of S parameters in time domain: •VS=1+S11 •VL=S21 When TL has characteristic impedance different from the loads, distortions occur 10
  • 11. Simulations of a 18.3-cm RG58 coaxial cable 11
  • 12. S-parameters calculations • • • • • • Time-domain S-parameters computation from incident and reflected waves provided by MWS is shown. S11 and S21 time-domain step responses 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 [1,2,3] and 2D-TL model of Cable Studio (CS) [3] is given. CS 2013 takes into account also proximity effects [3]. The accuracy of models has been evaluated by comparison with actual TDR measurements of a 1.83-m RG58 coaxial cable [2,3,7,8]. The lack of dielectric losses in the RL-TL model is somewhat compensated by the overestimation of skin effect [3]. 12
  • 13. MWS structure •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 Meshcells=545,472 13
  • 14. Input signal in MWS Gaussian (40GHz) Step source Integration of gaussian normalized to maximum value of the integral Tr=23ps 14 Rise time tr between 10-90% is about 23ps as used in TDR measurements
  • 15. Port signals of RG58 in MWS i1 o21 ns o11 ns Integrating o11 and o21 and normalizing the results to the maximum value of the gaussian integral, we get respectively S11 and S21 as response of a step with tr=23 ps 15
  • 16. Cable studio (CS) structure Step source with 40GHz bandwidth imported from MWS (see previuos slide) Ohmic losses only 16
  • 17. MC10 (SPICE) structure The equivalent RL circuit was obtained by VFT applied to compact expressions for coaxial cable without factor ½, see Eq.7.57 of [6] Step source with tr=25ps S11=VTin S21=VTout Cascade of 100 1.83-mm unit RL-TL cell 17
  • 18. DWS (Spicy SWAN [12 ]) circuits RL-TL5mmx37=185mm 185-mm RG58 from CST 18
  • 19. Input (1+S11) and output (S21) line waveforms Line length= 18.3 cm 1+S11 S21 MWS waveforms ps Remark: MC10 and CS provide similar waveforms 19
  • 20. S11 Volt MC10&DWS MWS: solid CS: dot MWS&CS MC10: dash ps • MC10 & DWS with RL-TL cells compute the same waveforms [10] • MWS & CS provide about similar waveforms with less losses (lower values than DWS & MC10) 20
  • 21. 1+S11 and S21 Volt 1+S11 MC10 MWS: solid MWS&CS CS: dot MC10: dash MWS&CS MC10 S21 DWS 1+S11 ps • MC10 & DWS compute the same waveforms [10] • MWS & CS compute similar waveforms with about half losses S21 • S11 of CS & DWS show some slight segmentation due to 37cell discretization 21
  • 22. 1+S11 and S21 with and without dielectric losses MC10 CS CS MC10 •Solid MC10 RLTL without dielectric losses •Dash CS 2013 without dielectric losses •Dot CS 2013 with dielectric losses (Tanδ=0.8m) Dielectric losses introduce just a slight difference in this portion of the waveform 22
  • 23. CS 2012: Adding dielectric losses (tanδ=0.8m) Volt Ohmic losses 1+S11 S21 sec Volt Ohmic + dielectric losses 1+S11 S21 sec •There are slight differences in this portion of the waveform •The segmentation effect is eliminated 23
  • 24. CS 2013: Adding dielectric losses (tanδ=0.8m) Volt Ohmic losses 1+S11 S21 sec Volt Ohmic + dielectric losses 1+S11 •The segmentation effect is eliminated also for ohmic losses • There is a slight increase of losses due to proximity effect in CST 2013 vs 2012 S21 sec 24
  • 25. Input and output line voltages VS VL MC10 VS VL MWS 2013 VS VL CS 2013 •For MC10 a ramp has been used •For MWS and CS the time integral of a gaussian (40GHz BW) has been used. • S11 (=Vin-1) and S21 (=Vout) should be computed with an input step of about 1ps rise time to approximate the ideal step response. • A non zero rise time input could give some inaccuracy when using these responses to get a BTM model [11]. • In the following slides this error 25 will be estimated.
  • 26. Comments on simulations • • • • • • MC10 & DWS by using RL-TL model compute the same waveforms and are used as reference being validated experimentally [1,2,3]. 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 shows a small ringing due to finite number of cell segmentation. This effect can be eliminated by using more unit cells (example 100 as done with MC10). DWS simulations are very fast (50+ times faster than MC 10) at equal cell number. 26
  • 27. S11&S21 computed by analytic approach (Theory)
  • 28. Analytic method • • • • • • The method used for computing S11 & S21 in time domain is outlined in [4] and with more details in chapter 7, subparagraph of [6]. A linear ramp of tr=25ps for a cable length of 18.3cm and tr=100ps for 1.83m are used as input . Tangent delta (θo) is set to 0.8m, see Appendix. Skin effect is computed by Eq.7.57 of [6] by using a factor ½ for comparison with CS and without the factor ½ for comparison with RL-TL model. MathCad code professional 2001i is used for analytic computations. The comparisons are performed among: RL-TL model (RL-TL), Cable Studio ohmic losses (cs), Cable Studio ohmic+dielectric losses (cs_d), analytic results with all losses (Theory).
  • 29. Line structure & input signal Source signal: tr=25ps Zocoax Vsin (1+S11) Len Vl (S21) Vs=2V Zocoax tr (10%-90%) Coaxial cable rw: wire radius rsh : internal shield radius dcoax: shield thickness
  • 30. Skin effect (compact expressions) ½ factor • In [5], Ziwcoaxb and Zishcoaxb expressions for a coaxial cable, are reported without the factor ½, while for a round wire the factor ½ should be used. •It will be shown that cs waveforms are in agreement with theory using factor ½ (round wire) while RL-TL waveforms are in agreement with theory without factor ½ because vector fitting technique (VFT) was applied starting from these expressions.
  • 31. Skin effect impedances (Ohm/m) •ZiSkinw Internal wire impedance computed as round wire, see chapter 7 of [6] for the expressions. •Ziwcoaxb Internal wire impedance computed by compact expression with ½ factor. •Zishcoaxb Shield impedance computed by compact expression with ½ factor. • ZiSkin= Ziwcoaxb+ Zishcoaxb Total impedance of the cable ZiSkinw and Ziwcoaxb provide the same values See also the results reported in [3] for the 18.3cm RG58 cable
  • 32. Dielectric losses and line parameters Dielectric losses Line parametrs For more details, see chapter 7 of [6]
  • 33. Output rise time comparison (Len=18.3cm) MC, CS, CS_d ps Theory ns • Good agreement nevertheless a ramp and not a gaussian shape has been used • A delay of 22ps has been introduced into theorical result for comparison reasons
  • 34. S11&S21 computed with factor ½ (Len=18.3cm) cs_d cs_d Theory • Good agreement between cs_d and theory • S11 of theory is slightly lower
  • 35. S11&S21 computed without factor ½ (Len=18.3cm) •Very good agreement between RL-TL model and theory RL-TL RL-TL ps Theory ns •The reason is that the RL-TL model was obtained by VFT using compact skin effect expressions for coaxial cable without factor ½.
  • 36. S11 computed with factor ½ (Len=1.83m) Theory Cable studio (Bandwith=10GHz) CST provides slightly lower values
  • 37. S21 computed with factor ½ (Len=1.83m) Theory Both methods provide the same values Cable studio (Bandwith=10GHz)
  • 38. 1+S11 computed without factor ½ (Len=1.83m) Theory Cable studio (Bandwith=10GHz) Theory provides more than doubled values for S11
  • 39. S21 computed without factor ½ (Len=1.83m) Theory Theory computes slight lower rising edge values Cable studio after the 80% of its DC level (Bandwith=10GHz)
  • 40. Comments on analytic approach • • • • Good agreement between CS and theory waveforms considering all losses. RL-TL model overestimates the losses due to the lack of .5 factor in skin effect compact expressions used to get the equivalent RL circuit by Vector Fitting Technique. This difference compensates the lack of dielectric losses in the model RL-TL and justifies the good agreement with the measured waveform tails as shown in [2,3]. The S21 rising edge coming from the RL-TL model is too fast due to lack of dielectric losses and can be compensated using a DWS RL_LTL hybrid model as shown in [8]
  • 41. Cable Studio results as source of a BTM of a 1.83-m RG58 coaxial cable used in DWS 41
  • 42. Used BTM procedure • • • • The S11 and S21 computed by cable studio (CS) 2013 for a 18.3cm of RG58 (0-40GHz) have been used as sources to get the Behavioral Transmission Model (BTM) in DWS. The waveforms obtained from a 1ps ramp input are used in the BTM model as PWL approximations and not directly as ASCII file (both ways provided by DWS) to speed up the simulations . For comparisons, a ramp of 25ps is also considered. DWS has been used to compute VS&VL voltages obtained from a cascade of 10 BTM with a ramp input. The waveforms are compared with those computed by CS 2013 using a model valid in the range 010GHz.
  • 43. CS VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.0) tr=25ps 1+S11 A fixed time step of 0.1ps has been used for CS simulation tasks tr=1ps 1+S11 S21 S-parameter waveforms do not seem influenced by the tr, apart the oscillations in S11 43
  • 44. CS VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.8m) tr=25ps 1+S11 A fixed time step of 0.1ps has been used S21 tr=1ps 1+S11 S21 S11 waveform does not seem influenced by the tr, apart the oscillations in S11 44
  • 45. VS&VL (cable length=18.3cm, model:040GHz,tandelta=0.8m): extended time scale 1+S11 tr=25ps S21 Time step=1ps Samples=4001 Zoom 45
  • 46. VL edge detail (cable length=18.3cm, model:040GHz,tandelta=0.8m) tr=25ps S21 Time step=0.1ps Samples= 4001 tr=1ps S21 Time step=0.02ps Samples= 8001 •S21 rising edge is strongly influenced by input tr • Waveform from 1ps stimulus can be used to extract BTM models using 46 the PWL technique
  • 47. PWL generation PWL generation: The CS output waveform is digitized by extracting the time and amplitude values at user chosen points (see small circles along the waveform). The manual choice is performed with the aim of minimizing the number of points but still achieving a good accuracy .This can been accomplished by a graphic digitizer program due to the availability of the image files. In case of ASCII files compatible with the .g format of DWS, a DWV viewer feature is provided to quickly accomplish this task in a semi-automatic way.
  • 48. VS&VL (cable length=1.83m, model:0-10GHz, tandelta=0.8m, tr=25ps) V 1+S11 CS 2013 Cascade of 10 BTM cells with DWS S21 ns V 1+S11 S11 & S21 waveforms are in good agreement ns 48
  • 49. VL (S21) edge detail (cable length=1.83m, model:010GHz, tandelta=0.8m, tr=25ps) V CS 2013 S21 Cascade of 10 BTM cells with DWS ns • S21 waveforms are in good agreement • S21 rising edge computed by 10 BTM seems to be a little lower 49
  • 50. Comments on BTM results • The S11 waveform obtained by DWS from a chain of 10 BTM cells derived from CS is in good agreement with the one obtained by CS for the total length of the cable The S21 edge obtained by a cascade of 10 BTM cells seems to be slightly faster than the one obtained by a CS for the total length of cable There are some key points to be taken into account in using the cascade of BTM cells : • • 1. 2. 3 4 A fast (1ps) edge has to be used as input stimulus to extract the BTM model of the unit cell. A slower rise time stimulus as 25ps would introduce a significant error in computing the S21 edge [11]. A suitable bandwidth (e.g. 40Ghz) has to be set in CS to get an accurate response to the 1ps input required for the BTM model. This bandwidth determines the number of cascaded RLCTL cells of the CS circuital model (100-cell for a 183mm long cable) and the simulation time of CS. BTM model accuracy depends on the number and placement of the breakpoints chosen for the pwl behavior. Normally 20-30 breakpoints are enough to get a good speed/accuracy trade off. An impressive DWS vs speedup factor (3 to 4 orders of magnitude) is obtained for “long” cables using chain of BTM cells
  • 51. Analytical methods used to extract a 1-m unit cell BTM to simulate a 10-m RG58 coaxial cable with DWS
  • 52. Procedure adopted for BTM cell extraction • • • The theoretical expressions previously shown in this report are used to get approximated S11 and S21 step responses for a 1-m RG58 cable. Two different ramps of tr=5ps and tr=25ps respectively are used as input stimuli. The computed waveforms are digitized to get the breakpoints for build up the pwl BTM cell model A chain of 10 equal cells is simulated by DWS to get the response of a 10-meter cable.
  • 53. Signals & line voltages for 1-m of RG58 Tr=25p s S21 Data used as input for BTM S11 Tp Data used as input for BTM Time period Tp should be large enough to reach with approximation the dc values of S11
  • 54. Signals & line voltages for 10-m of RG58 Source signal: tr=100ps Line voltages: input (vsin) & output (vl) Tp Time period Tp should be large enough to reach with approximation the dc values of S11
  • 55. S21 (vl) rising edge (10-m cable) Edge computed by Theory Edge computed by DWS using 10 BTM cells with tr=5ps Edge computed by DWS using 10 BTM cells with tr=25ps
  • 56. S21 (vl) rising edge of a 10-m cable: detailed view with equalized delays for edge comparison Edge computed by Theory Edge computed by DWS using 10 BTM cells with tr=5ps Edge computed by DWS using 10 BTM cells with tr=25ps As expected [11], better agreement is obtained by using tr=5ps as input for the 1m basic cell
  • 57. S11 reflections computed by Theory reflections computed by DWS by using 10 BTM with tr=5ps The difference after t=40ns is due to S11 behavior truncation after the first 40ns window. Beyond 40ns the analytical S11 response was not available due to FFT issues. At least a 400ns window should be required.
  • 58. BTM model from theoretical responses: key points 1. 2. 3. As for the BTM model extracted from Cable Studio simulations, some key points have to be pointed out: The S21 rising edge should be computed by IFFT using an enough short rise-time ramp as input (e.g. 5ps for 1-m cable) to limit the rise time error of the BTM cells cascade [11]. The reflection coefficient (S11) should be computed using an input stimulus period enough large to allow a good approximation of steady state (dc ) values. A tradeoff between this period and IFFT computation time is required. Therefore, a global tradeoff is needed to take into account accuracy requirement for simulations, fast tr, and large period Tp for IFFT computation. The BTM model extracted taking into account previous points is very fast and achieves a good accuracy level.
  • 59. Using Cable Studio: user considerations • • • • • • • • • • The results of CS are strongly influenced by several options set by the user. The effect of options on final results is not always clear to the user. TLM (modal) option is required to get accurate results. TLM produces circuital models including thousands of RLC and TL elements. The unit cell TL delay can be a number like TD=9.54361271247e-012 sec. This kind of values requires to set short fixed time step (e.g. 100fs) to get reliable results from CS simulations . Otherwise overall delay and behavior of a 100-cell cascade can be strongly affected. The Bandwidth to be set to get the modal TLM directly affects the number of cascaded cells in the cable model . For example a 40Ghz BW generates a 100-cell model for a 18.3 cm cable. CS 2013/14 simulations at fixed step can require several minute on a multicore CPU. DWS can achieve a 10-50X speed up over CS to simulate complex TLM models generated by CS [13 ]. To extract accurate BTM models for DWS, a rise time of about 1ps for a 20-cm unit cell and 5ps for a 1-m unit cell is suggested as stimulus signal of the cable. The same rule of thumb should be utilized to extract BTM models from analytical methods. 59
  • 60. Conclusions • • • • • • • • Cable Studio computes the step responses of the cable in good agreement with MWS and the analytic approach based on theory. RL-TL circuital model provides overestimation of losses because the VFT used for getting the equivalent RL circuit was applied by using compact analytic expression for coaxial cable without the factor ½ [6]. This factor compensates the lack of dielectric losses in the RL-TL model with the exception of S21 rising edge. A closer result with the measurement is shown in [2] and [3]. An improved RL-TL hybrid circuital-BTM model is shown in [8]. A BTM cell model cannot be practically obtained by a 3D model (MWS) because the number of mesh cells required by a source with rise time in the order of 1 ps is too large for the computation. A BTM cell can be obtained by a 2D model (CS) feasible with a good tradeoff between the CS input bandwidth and the stimulus rise time. The analytical approach is feasible to get the BTM model. A tradeoff is needed between the required fast input rise time and large period value used for the IFFT computation. A two-step modeling using two different theoretical responses (fast edge & short period, slower edge & larger period) should give the best results DWS can be used with major speed benefits both for TLM (10 to 50X) and BTM (up to 10000X) cable models DWS can also utilize both hybrid ( BTM and TLM) and full BTM models directly extracted or optimized to actual TDR measures [8]. 60
  • 61. Appendix: Dielectric losses (Tanδ)
  • 62. Typical Tanδ values • The following tables are extracted from the literature. • They should be compared with the value of Tanδ=0.8m used in this report.
  • 63. Tandδ ablelosstan.htm The dielectric loss tangents for some materials commonly used in coaxial cables are: tanD at 100 MHz tanD at 3 GHz Air 0.0 0.0 PTFE 2E-4 15E-4 PolyEthylene, DE-3401 2E-4 3.1E-4 Polyolefin, irradiated 3E-4 3E-4 Polystyrene 1E-4 3.3E-4 Polyvinal formal (Formvar) 1.3E-2 1.1E-2 Nylon 2E-2 1.2E-2 Quartz, fused 2E-4 6E-5 Pyrex Glass 3E-3 5.4E-3 Water, distilled 5E-3 1.6E-1 Material For simulation we have used Tanδ=8e-4 (used in CST as default value) 63
  • 64. Tandδ (coax Belden) For RG58, a tanδ between 1.12e-3 and 2.12e-3 are given (values higher than the previous table for polyethylene) Tandelta From: H. Johnson, M. Graham, “High-Speed Signal Propagation”, Prentice Hall, 2003 64
  • 65. References [1] Piero Belforte, Spartaco Caniggia, “CST coaxial cable models for SI simulations: a comparative study”, March 24th 2013CST models for theRG58 coax cable [2] Piero Belforte, Spartaco Caniggia,, “Measurements and Simulations with1.83-m RG58 cable”, April 5th 2013 [3] Piero Belforte, Spartaco Caniggia, “TDR measurements and simulations of RGU 58 coaxial cable S-parameters”, June 04, 2013 TDR measures and simulations of RG58 cable [4] Spartaco Caniggia, “Modeling interconnects and power distribution network in PCBs, CST workshops, Milano, 26-11-2013 [5] Ramo, Whinnery, Van Duzer, “Fields and wave in communication electronics”, John Wiley, 3rd Edition [6] S. Caniggia, F. Maradei, “Signal Integrity and Radiated Emission of High-Speed Digital Systems”, John Wiley & Sons, 2008 65
  • 66. References (2) [7] Piero Belforte “ TDR mesurements of RG58 coaxial cable Sparameters”, April11th 2013 TDR measurements of RG58 coax cable [8] Piero Belforte “ RG58 coaxial cable: A comparison among Analytical models, DWS BTM models, TDR measures and CST 2013 Cable Studio simulations”, Dec. 24th 2013 Models and measurements for a RG58 coax [9] Piero Belforte “A new modeling and simulation environment for highperformance digital systems” HP Digital Symposium (1993) [10] Piero Belforte “DWS vs MC10: a comparative benchmark” April 15th 2013 DWS vs MC10 [11] Piero Belforte “ Prediction of rise time errors of a cascade of equal behavioral cells” May 2nd 2013 Rise time error prediction [12] [13] SWAN sim of a CST2014 TLM cable model 66