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2013 pb rg58 coax cable models and measurements


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Comparative models and simulations of a RG58 coaxial cable using mathematical method, CST Cable Studio, DWS (spicy SWAN)

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2013 pb rg58 coax cable models and measurements

  1. 1. Copyright Piero Belforte Dec 24th 2013 RG58 coaxial cable: A comparison among Analytical models, DWS BTM models, TDR measures and CST 2013 Cable Studio simulations A 1m long RG58 coaxial cable, has been mathematically modeled by Spartaco Caniggia including both skin and dielectric losses in frequency domain, calculating the Inverse Fourier Transform to get the time domain step response of S-parameters S11 and S21. The method was applied for a 25ps and 5ps ramp input. Ramp stimulus rise time choice has to take into account the error introduced with respect the required ideal step stimulus theoretically required to apply the BTM (Behavioral Time Domain, Hp seminar 1993 PB -New modeling & simulation environment) method supported by DWS: Prediction of rise time errors of a cascade of behavioral cells The responses have been converted in piecewise linear (pwl) BTM models for the DWS simulator and simulated for different cable lengths using the chain utility of DWS. DWS supports file description of S-parameters behaviors but pwl approximation is mandatory to get fast simulations. Simulation time depends inversely on total number of breakpoints. Usually 10-20 breakpoints are enough for each S-parameter to get a good accuracy/speed trade off. 1
  2. 2. Copyright Piero Belforte Dec 24th 2013 A comparison between the 5ps and 25ps input BTM model is reported here: 8183274204325605as#.UrlzaMRWGSo Here a comparison between the output of a 10m cable with a 100ps ramp input obtained as a cascade of 10 cells and its analytical response The waveforms are practically coincident, confirming the validity of both the analytical method and of the BTM model. Pwl BTM models run very fast on DWS allowing the user to simulate circuits containing several basic cells in seconds. The BTM model related to 1 m long cable was then used in several Spicy SWAN circuits to compare the results with cellular (micro-behavioral) BTM models previously optimized to match the actual TDR (CSA 803) measures reported here: TDR measurement of RG58 coaxial cable S-parameters 2
  3. 3. Copyright Piero Belforte Dec 24th 2013 As example here two links to Spicy SWAN simulation reports of these configurations: 2485416218536178as#.UrlyL8RWGSo 5334337162836476as#.UrhMssRWGSo From previous comparisons on a 2m long cable, it seems that the rising edge of the S21 is faster than the actual cable response. The S11 peak is also higher (about twice) with respect the actual cable. From these results it seems that both skin effect and dielectric losses are underestimated in the mathematical model. This conclusion seems confirmed by a direct comparison with a open ended 7m long cable TDR (CSA 803) response. The simulation report of this configuration is reported here: 3485375207814476as#newwin And in the 3 following figures the direct comparison with the actual measurements is shown: 3
  4. 4. Copyright Piero Belforte Dec 24th 2013 4
  5. 5. Copyright Piero Belforte Dec 24th 2013 CST 2013 CABLE STUDIO simulations The 1m long RG58 was modeled and simulated using CST's Cable Studio version 2013. To minimize the errors due to model bandwidth, a 40Ghz bandwidth for the model was chosen. Both skin and dielectric losses were taken into account. These choices increase the simulation time: more than 1 hour was required for a 10ns window using a maximum time step of 1ps to run a single simulation. 4 CPU (I7) cores were engaged during the simulation task (50% of the full CPU processing power). The simulations were carried out for both a 25ps and a 5ps ramp input. In the 4 following figures several result comparisons are reported. 5
  6. 6. Copyright Piero Belforte Dec 24th 2013 6
  7. 7. Copyright Piero Belforte Dec 24th 2013 7
  8. 8. Copyright Piero Belforte Dec 24th 2013 Conclusions. 1) Mathematical methods can be a quick way to get fast BTM models of coaxial cables. Dielectric and skin effect losses seem underestimated unless corrective coefficient is introduced to take into account the actual physical structure of cables (tinned copper wires, stranded conductors, braided shield etc., see the 2 following figures). 8
  9. 9. Copyright Piero Belforte Dec 24th 2013 In particular tinned copper conductors can show a complex skin effect due to 1-10 um thick tin surface. Tin has a resistivity that is about 7 times greater than copper. At 1Ghz skin depth for copper is about 2um so the resistivity used as input parameter of predictive methods should be selected between copper and tin values. The optimum resistivity value should be set by fitting the S11 behavior with actual measurement. Skin depth calculator Even dielectric permittivity of the insulator should be adjusted to perfectly match the measurements with particular reference to cable delay. An adjustment of 50-100ps has been required to match the 5ns delay of the 1 m long sample. This 1m long cable requires a 5ps (or less) rise time input stimulus to get accurate results on S21 response. 9
  10. 10. Copyright Piero Belforte Dec 24th 2013 2) CST Cable Studio 2013 provides results comparable to mathematical method. Losses seems underestimated even if less than for the analytical approach for dielectric losses. Long simulation times are required (1hour with 4 I7 CPU cores).CST results are potentially utilizable to derive fast BTM models for DWS even if also in this case some correction on input parameters is required for better matching of measurements. 3) All predictive methods used so far (numerical simulation including 3D field solvers and analytical methods based on frequency domain expressions of losses) suffer of bandwidth limitations. This means that there is a lower limit of physical length of cable to be characterized and to related input ramp rise time. This limit is in the region of 1m for the RG58 under analysis corresponding to a 5ps rise time of the input ramp approximating the ideal step response. For example here a comparison between DWS and Simbeor about the prediction of S-parameters for a 5cm long RG58 is shown: 10
  11. 11. Copyright Piero Belforte Dec 24th 2013 A direct time-domain mathematical expression of S-parameters could overcome the bandwidth (rise time) limitation issue. 4) BTM models extracted from actual TDR measurements are the most realistic because they take into account all actual cable behaviors including impedance micro discontinuities. In this case the TDR measurement setup has to be de-embedded to get accurate results. With TDR rise times in the order of 20ps (CSA803) the minimum cable length to be characterized is in the order of 1-2 m or more . BTM pwl models run very fast (seconds) on DWS (Spicy SWAN) using picosecond range simulation time steps even for long cables. Only one CPU core is engaged on multi-core CPUs for each DWS task, minimizing the power consumption. Pwl S-parameters models are numerically very stable, so that even a not perfect matching between S11 and S21 is allowable to get numerically stable results. Obviously this modeling method can be applied to all types of cable and interconnnections. Here a Spicy SWAN simulation report related to a trifilar cable: 1030073586323447as#.UrxsasRWGSo 5) Accurate micro-behavioral BTM models for DWS can be derived from previous methods (Analytical and CST) and/or from circuital cellular models (Spice, DWS) applying corrections to 11
  12. 12. Copyright Piero Belforte Dec 24th 2013 match the actual measurements. Here an example of this procedure applied to optimize some breakpoint of a 18.3cm BTM cell derived from a vector-fitting RL-TL model. The optimization process automatically de-embeds cell parameters (breakpoints) from TDR setup effects because the optimized configuration includes the measurement setup. Optimization of coax cable BTM cell breakpoints This procedure could be performed automatically by a suitable optimization program. 6) Hybrid micro-behavioral models can be also developed mixing in the same basic cell S-parameter behavioral blocks and circuital elements. This Hybrid technique has been utilized to match the S21 rising edge of a 1.83m long cable within the 5 cm RL-TL cell by replacing the lossless Transmission Line of the elementary cell with a lossy TL (LTL). The RL-TL using an ideal TL is not able to take into account dielectric loss effect on S21 rise time. Only one parameter ( S21 ramp rise time, 3ps) is required to match the actual measurement by taking dielectric losses into account. 0115134168853871a#.UrqxucRWGSo In this way a fast mixed circuital/behavioral model is obtained with a "short" spatial definition step (5cm). 12
  13. 13. Copyright Piero Belforte Dec 24th 2013 Micro-behavioral technique has been also successfully utilized in the past (Piero Belforte 1993-2009) to get fast and accurate DWS models of p.c.b. power distribution metal planes: 1993-P.C.B. power/ground distribution plane models 2009 Micro-behavioral models of FR4 laminates and to lossy coupled traces of p.c. boards: 2009-micro-behavioral models of lossy coupled lines (set 480p for best viewing) Micro-behavioral techniques have the advantage of "scaling down" the length of the elementary cell with respect the original measure. In this way even sub-multiple lengths of the original measured cable can be simulated mitigating the bandwidth limitation of both analytical and simulative methods. A simple TDR measurement at one-port only with other ports left open is required to optimize the micro-behavioral model (pwl breakpoints). 7) A Hybrid cell structure can be also utilized to model the long waveform tail of both S11 and S21. A single RC cell with negative parameters values added to the BTM 2-port block is enough to create the long tail in the truncated behavior of BTM cells. The following figure shows an example of the correction effect of the 13
  14. 14. Copyright Piero Belforte Dec 24th 2013 added RC cell (-0.1 ohm in parallel to -10uF) for a 10 m long cable modeled as cascade of 10 BTM cells (100ps ramp input stimulus). 8) Complex structures including metal planes and coaxial cables can be simulated in seconds using measure-derived BTM models leading to high-reality results: 7017134125327611as#.UrxeTMRWGSo 14
  15. 15. Copyright Piero Belforte Dec 24th 2013 8) Actual cables are affected by impedance discontinuities that are not included in predictive models. Only measure-derived BTM models can take into account in a simple way these additional effects still holding fast simulation speed(seconds) even for long cables. The distributed micro-reflections of reflected wave (S11) cause and additive random noise that affects bidirectional transmission configurations. In the following example this effect is clearly visible: 5623343426046486a#.UrxpOsRWGSo 15
  16. 16. Copyright Piero Belforte Dec 24th 2013 This kind of simulations is out of reach of conventional models and simulators. 9) DWS is the most accurate and fast simulation engine for circuital (RLC-TL), behavioral and hybrid s-parameters models. Several order of magnitude simulation time speedup factors can be obtained over conventional NA simulators: DWS vs Microcap10 comparative benchmarks 16
  17. 17. Copyright Piero Belforte Dec 24th 2013 2012 - DWS vs Microcap 10 time trial (set HD option for best viewing) 10 ) Actual measurements are always needed to validate the models even for "simple" geometries like coaxial cables. 17
  18. 18. Copyright Piero Belforte Dec 24th 2013 Useful WEB links Hp seminar 1993 PB -New modeling & simulation environment DWS concepts 2007- J. SCHRADER- WIRELINE EQUALIZATION BOOK 2013_PB_TDR MEASUREMENTS ON RG58 COAXIAL CABLE CST 2013-S.Caniggia-Modeling interconnects and pdn of pcb Skin effect depth calculator 18
  19. 19. Copyright Piero Belforte Dec 24th 2013 2013-Linkedin discussion on PDNs 19