Piero Belforte April 18th 2012Copyright Piero Belforte 20121Trasmission Line approximation using LC cellsThis Application ...
Piero Belforte April 18th 2012Copyright Piero Belforte 201222) Transmission Line modeled as a cascade of 100 equal LC cell...
Piero Belforte April 18th 2012Copyright Piero Belforte 201233) Transmission Line modeled as an ideal TLThe following is th...
Piero Belforte April 18th 2012Copyright Piero Belforte 20124This can be also the reference case because TLs are modeled in...
Piero Belforte April 18th 2012Copyright Piero Belforte 20125ResultsIn the following the simulation output plots are shown:...
Piero Belforte April 18th 2012Copyright Piero Belforte 20126Comparative plots (1,2 and 3):Detailed plots:
Piero Belforte April 18th 2012Copyright Piero Belforte 20127Worst Case Eye diagrams at 1Gbps
Piero Belforte April 18th 2012Copyright Piero Belforte 20128The followings are Worst Case Eye Diagram (WCED) contours deri...
Piero Belforte April 18th 2012Copyright Piero Belforte 20129The 100-cell model is good up to 4Gbps if the generator rise t...
Piero Belforte April 18th 2012Copyright Piero Belforte 201210Generator rise time:10ps , ideal TL vs 100 LC cellsComparison...
Piero Belforte April 18th 2012Copyright Piero Belforte 201211The following is a comparison of the plots from Circuit Lab a...
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2012 trasmission line approximation using lc cells pb_dws

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The limits of the lumped LC-cell model for transmission lines are shown in this document.

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2012 trasmission line approximation using lc cells pb_dws

  1. 1. Piero Belforte April 18th 2012Copyright Piero Belforte 20121Trasmission Line approximation using LC cellsThis Application Note analyzes the effect of approximating with lumped LCcells an ideal TL (Z0=50 ohm, TD=1ns) terminated at the ends to 50 ohm andconnected to a pulse generator of amplitude 2Volts and rise time 200ps(linear rise). This kind of approximation is often used by traditional (Spice)simulators to model an ideal TL. DWS doesnt need this approximationbecause TLs are the most efficient circuit element of DWS set. In this ANDWS has been also utilized to model the fully LC lumped circuits used inSpice models.Three different situations are analyzed using DWS:1) Transmission Line modeled as a cascade of 10 equal LC cells :The following is the DWS netlist of case 1. The circuit is described using the.CELL and the .CHAIN statements of DWS for automatic generation of thecascade of 10 cells.
  2. 2. Piero Belforte April 18th 2012Copyright Piero Belforte 201222) Transmission Line modeled as a cascade of 100 equal LC cellsThe following is the DWS netlist of case 2. The circuit is described using the.CELL and the .CHAIN statements of DWS for automatic generation of thecascade of 100 cells.The values of parameters L and C of each cell are set 1/10 of the previouscase because the number of cells is higher of a factor of 10.
  3. 3. Piero Belforte April 18th 2012Copyright Piero Belforte 201233) Transmission Line modeled as an ideal TLThe following is the DWS netlist of case 3. The circuit is described directlyusing element T of DWS related to an ideal TL.
  4. 4. Piero Belforte April 18th 2012Copyright Piero Belforte 20124This can be also the reference case because TLs are modeled in DWSwithout approximations (except delay quantization depending on the choice ofsimulation TSTEP ). In all previous cases TSTEP is 1PS allowing an exactmodeling of the TL delay of 1ns. In all netlists a maximum number of points(LIMPTS) is set to 10,000.All sims run in few microseconds on a Pavilion PC with I7 quad core CPUutilized at 12.5% of full load. Setting up a lower TSTEP (in the femtosecondregion, an inversely proportional increase of sim times is obtained,but there isno significant variations of the result).
  5. 5. Piero Belforte April 18th 2012Copyright Piero Belforte 20125ResultsIn the following the simulation output plots are shown:Case 1Case 2Case 3 (reference)
  6. 6. Piero Belforte April 18th 2012Copyright Piero Belforte 20126Comparative plots (1,2 and 3):Detailed plots:
  7. 7. Piero Belforte April 18th 2012Copyright Piero Belforte 20127Worst Case Eye diagrams at 1Gbps
  8. 8. Piero Belforte April 18th 2012Copyright Piero Belforte 20128The followings are Worst Case Eye Diagram (WCED) contours derived fromthe previous simulations , showing the distortion effects due to theapproximation of lumped LC model of TL. The exact model of TL (DWS)generates the best contour without no distortion. These WCEDs are createdusing the companion viewer of DWS (DWV) used to display the waveforms ofthis AN.1Gbps WCEDs4 Gbps WCEDsFrom the previous WCED plots it is evident that the 10-cell model has seriousdistortion problems at 1Gbps and at 4Gbps the eye is practically closed.
  9. 9. Piero Belforte April 18th 2012Copyright Piero Belforte 20129The 100-cell model is good up to 4Gbps if the generator rise time is in theorder of hundred of picoseconds as in this case. The problem arise from thecomplexity because 200 circuital elements are required to model a single TL.To investigate the distortion due to 100-cell approximation, the followingsituation has been simulated:Here the pulse generator has a rise time of 10ps and the simulation time stepis set to 10femtoseconds on a window of 10ns (1 Million calculated points ).In the following the results compared to the ideal case. With respect theprevious simulations, the ringing due to lumped circuit approximation is moreevident at both ends, as espected.
  10. 10. Piero Belforte April 18th 2012Copyright Piero Belforte 201210Generator rise time:10ps , ideal TL vs 100 LC cellsComparison to Circuit Lab results
  11. 11. Piero Belforte April 18th 2012Copyright Piero Belforte 201211The following is a comparison of the plots from Circuit Lab and DWS withsimilar settings of the input generator and for the 10 LC cells situation.The comparison has to be made between the falling edge of CL and the riseedge of DWS to get the same ISI (Inter Symbol Interference) amount due toprevious transitions.In this case the simulation time of CL was about 2 minutes compared to 30milliseconds of DWS.Obviously DWS is far more efficient when dealing with ideal TL.

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