2012 trasmission line approximation using lc cells pb_dws

Piero Belforte April 18th 2012

Copyright Piero Belforte 2012

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Trasmission Line approximation using LC cells

This Application Note analyzes the effect of approximating with lumped LC

cells an ideal TL (Z0=50 ohm, TD=1ns) terminated at the ends to 50 ohm and

connected 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 doesn't need this approximation

because TLs are the most efficient circuit element of DWS set. In this AN

DWS has been also utilized to model the fully LC lumped circuits used in

Spice 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 the

cascade of 10 cells.



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2) Transmission Line modeled as a cascade of 100 equal LC cells

The 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 the

cascade of 100 cells.

The values of parameters L and C of each cell are set 1/10 of the previous

case because the number of cells is higher of a factor of 10.



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3) Transmission Line modeled as an ideal TL

The following is the DWS netlist of case 3. The circuit is described directly

using element T of DWS related to an ideal TL.



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This can be also the reference case because TLs are modeled in DWS

without approximations (except delay quantization depending on the choice of

simulation TSTEP ). In all previous cases TSTEP is 1PS allowing an exact

modeling 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 CPU

utilized at 12.5% of full load. Setting up a lower TSTEP (in the femtosecond

region, an inversely proportional increase of sim times is obtained,but there is

no significant variations of the result).



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Results

In the following the simulation output plots are shown:

Case 1

Case 2

Case 3 (reference)



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Comparative plots (1,2 and 3):

Detailed plots:



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Worst Case Eye diagrams at 1Gbps



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The followings are Worst Case Eye Diagram (WCED) contours derived from

the previous simulations , showing the distortion effects due to the

approximation of lumped LC model of TL. The exact model of TL (DWS)

generates the best contour without no distortion. These WCEDs are created

using the companion viewer of DWS (DWV) used to display the waveforms of

this AN.

1Gbps WCEDs

4 Gbps WCEDs

From the previous WCED plots it is evident that the 10-cell model has serious

distortion problems at 1Gbps and at 4Gbps the eye is practically closed.



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The 100-cell model is good up to 4Gbps if the generator rise time is in the

order of hundred of picoseconds as in this case. The problem arise from the

complexity because 200 circuital elements are required to model a single TL.

To investigate the distortion due to 100-cell approximation, the following

situation has been simulated:

Here the pulse generator has a rise time of 10ps and the simulation time step

is set to 10femtoseconds on a window of 10ns (1 Million calculated points ).

In the following the results compared to the ideal case. With respect the

previous simulations, the ringing due to lumped circuit approximation is more

evident at both ends, as espected.



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Generator rise time:10ps , ideal TL vs 100 LC cells

Comparison to Circuit Lab results



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The following is a comparison of the plots from Circuit Lab and DWS with

similar 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 rise

edge of DWS to get the same ISI (Inter Symbol Interference) amount due to

previous transitions.

In this case the simulation time of CL was about 2 minutes compared to 30

milliseconds of DWS.

Obviously DWS is far more efficient when dealing with ideal TL.

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2012 trasmission line approximation using lc cells pb_dws