Dear Piero,

my Spice program gives up much earlier of a 1 us, as you can see from the attached files. After 100 ns the signal is almost sinusoidal.

In an ideal transmission line, the desired result would be a square wave.

It is interesting to see, in attached Draft2.pdf, the AC transfer function of the 10 cell circuit.

As we can see, every LC cell adds a peak in the transfer function of the circuit,  and a corresponding sinusoid in its step response. Since in the proposed circuit, there aren't passive element, the 10 sinusoids approximation of the square wave should remain at output node forever; but not in our simulation.

From the simulations I performed, I can say that the effect Gmin that SPICE add to all nodes, is negligible. So the low pass effect is mainly due to the ode solver algorithm.

regards

Simone

P.S. Like you, I am also the coauthor of a simulator based on wave exchange. I regret to be aware of your work only now.

One of the below works is in public domain. I can send you the other, if you are interest. In the meanwhile I'll read the big user manual of DWS.

Article SystemC-WMS: Wave mixed signal simulator for non-linear hete...

Article System level modelling of RF IC in SystemC-WMS

Hi Simone,

                  yes, i agree with you, the dumped waveform of your simulator can be due to "losses" due to ODE solver. DWS simulation doesn't use a solver but a wave processor. The reported waveform is the "exact" solution because I verified it running the DWS  sim at a time step lower than 1ps (eg 500ps) getting practically the same result of the 1ps response. There is no problem with the simulation time because DWS is typically 100X faster than Spice at comparable  accuracy level.

If you like you can try the circuit directly on a Chrome or Safari Web browser running the online version of Spicy SWAN: https://www.ischematics.com/webspicy/portal.py

or using the Ipad app (about 100,000 users of web and mobile versions so far).

More info about DWS TL models and related LC approximations are available here:

https://www.researchgate.net/publication/272818374_VI_TRAJECTORY_PLOTS_FOR_TRASMISSION_LINE_MODELS_EVALUATION

and here:

https://www.researchgate.net/publication/272885636_TRANSMISSION_LINE_APPROXIMATIONS_USING_LC_CELLS

I also ignored your WMS simulator, so I'm very glad to find someone using similar algorithms. DWS story is 40 years long...

If you like we can exchange more info about our tools.

Technical Report VI TRAJECTORY PLOTS FOR TRASMISSION LINE MODELS EVALUATION

Technical Report TRANSMISSION LINE APPROXIMATIONS USING LC CELLS

Here the S-parameters of the 10 LC CELL cascade calculated by DWS:

https://www.researchgate.net/publication/273138156_10_LC_CASCADE_.1-5Ghz_S-PARAMETERS_BY_DWS_VVNA

And here you will find the related interactive plot of the same responses:

https://plot.ly/~piero.belforte/1380/_10-lc-5nh-2pf-cell-cascade-dws-s-parameters-vvna-by-piero-belforte/

Technical Report 10 LC CASCADE .1-5Ghz S-PARAMETERS BY DWS VVNA

And here what happens for the S-parameters in the case of a cascade of 100 LC CELLS (L=5NH C=2PF)

https://www.researchgate.net/publication/273141388_100_LC_CASCADE_.1-5Ghz_S-PARAMETERS_BY_DWS_VVNA

The related 5K samples interactive plot Is available here:

https://plot.ly/~piero.belforte/1398/_100-lc-5nh-2pf-cell-cascade-s-parameters-from-dws-vvna-by-piero-belforte/

Technical Report 100 LC CASCADE .1-5Ghz S-PARAMETERS BY DWS VVNA

And here what happens for the S-parameters in the case of a cascade of 100 LC CELLS with 1/10 L and C values. The bandwidth is enlarged to about 32.5 Ghz with the 10 CELL situation as expected

https://www.researchgate.net/publication/273142799_100-LC_%28.5NH_.2PF%29_CELL_CASCADE.1-40Ghz_S-PARAMETERS_BY_DWS_VVNA

The related 10K samples interactive plot Is available here:

https://plot.ly/~piero.belforte/1414/_100-lc-5nh-2pf-cell-cascade-s-parameters-from-dws-vvna-by-piero-belforte/

Technical Report 100-LC (.5NH .2PF) CELL CASCADE:.1-40Ghz S-PARAMETERS BY DWS VVNA