[SI-LIST] Re: step response simulators

  • From: Paul Levin <levinpa@xxxxxxxxxxxxx>
  • To: si-list@xxxxxxxxxxx
  • Date: Sun, 24 Jun 2007 21:18:40 -0700

Dear Cliff,

I have a hard time believing your "appropriate answer" below. The final 
number of the four numbers multiplied together is 2.08, just three 
significant digits. If the possible error in this number is 0.005-, then 
the fractional error is +/-0.25%. Your 207.78 suggests a much more 
accurate result. I would hesitate to report much more than "208.", where 
the decimal point is significant.

Your least accurate number rule is the correct one for addition and 
subtraction.

Regards,

Paul Levin
Senior Principal Engineer
Xyratex
___________________

Cliff Clark wrote:
> I have a dilemma.  I hope you can help me resolve it.
>  
> If we were to multiply the following numbers together:
>  
> 6.7894323  x
> 3.4965 x
> 4.208 x
> 2.08 
>  
> A spreadsheet or calculator might yield the result:
>  
> 207.7811094
>  
> However, the spreadsheet or calculator does not distinguish between
>  
> 2.08, and the value 2.0800000
>  
> The appropriate answer is:
>  
> 207.78
>  
> Any result past two decimal points is uncertain since the least accurate 
> number of our series contains only two decimal places.*
>  
> *Reference:
>  
> http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
>  
> An important consequent to correctly determining the number of decimal points 
> of accuracy is “errors per part”.  One digit of inaccuracy in the reported 
> value of 207.7811094 is
>  
> 0.0000001 errors / 207.7811094 parts = 4.81E-10 errors / part
>  
> This expression appears to have greater accuracy than the more appropriate 
> determination:
>  
> 0.01 errors / 207.78 parts = 4.81E-05 errors / part
>  
> Likewise with respect to division, each number of the following series is 
> divided by the next:
>  
> 6.7894323  /
> 3.4965 /
> 4.208 /
> 2.08 
>  
> A spreadsheet or calculator might yield the result:
>  
> 0.2218507
>  
> However, the spreadsheet or calculator may not distinguish between
>  
> 2.08, and 2.0800000
>  
> The appropriate answer is:
>  
> 0.22
>  
> Any result past two decimal points is uncertain since the least accurate 
> number of our series contains only two decimal places.
>  
> Consult reference:
>  
> http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
>  
> for similar rules for other mathematical calculations.
>  
> ************
>  
> Ok, let’s apply the described principle to simulation and simulators.
>  
> Suppose that we work hard to reduce our error of a simulation down to just 50 
> ps.  If the simulation runs 1000 ns, the result will be:
>  
> 50e-12 errors / 1000 e-9 parts  = 5e-5 errors / part
>  
> The result for a 100 ns second simulation is:
>  
> 50e-12 errors / 100 e-9 parts  = 5e-4 errors / part}
>  
> Let’s suppose that we were particularly diligent and we reduced our error in 
> half to just 25 ps.  If the simulation runs 1000 ns, the result will be:
>  
> 25e-12 errors / 1000 e-9 parts  = 2.5e-5 errors / part
>  
> The result for a 100 ns second simulation is:
>  
> 25e-12 errors / 100 e-9 parts  = 2.50E-04 errors / part}
>  
> For emphasis let’s consider what happens if we had some way of reducing our 
> error to just 10 ps:
>  
> If the simulation runs 1000 ns, the result will be:
>  
> 10e-12 errors / 1000 e-9 parts  = 1e-5 errors / part
>  
> The result for a 100 ns second simulation is:
>  
> 10e-12 errors / 100 e-9 parts  = 1E-04 errors / part
>  
> One more time:  Let’s suppose there existed someway for us to reduce our 
> error of simulation to just 1 ps.
>  
> 1e-12 errors / 1000 e-9 parts  = 1e-6 errors / part
>  
> The result for a 100 ns second simulation is:
>  
> 1e-12 parts of error / 100 e-9 total parts  = 1E-05 errors / part
>  
> *****
>  
> Step Response Simulators take a given simulation deck, along with its 
> associated models and projects error rates of 1e-12.  I’d be grateful if you 
> can help me to understand how it is possible to use a simulation that is no 
> more accurate than 1e-6 errors per part and yield valid results of 1e-12 
> errors per part using a Step Response Simulator.  Note that errors / part is 
> not associated with any particular physical quantity such as length, time, 
> bits, etc ..
>  
> - As an aside, in many circumstances simulation error is worse than 1e-3.
> Much appreciation,
>  
> Cliff Clark
> _________________________________________________________________
> Live Earth is coming.  Learn more about the hottest summer event - only on 
> MSN.
> http://liveearth.msn.com?source=msntaglineliveearthwlm
> ------------------------------------------------------------------
> To unsubscribe from si-list:
> si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
> 
> or to administer your membership from a web page, go to:
> //www.freelists.org/webpage/si-list
> 
> For help:
> si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
> 
> 
> List technical documents are available at:
>                 http://www.si-list.net
> 
> List archives are viewable at:     
>               //www.freelists.org/archives/si-list
> or at our remote archives:
>               http://groups.yahoo.com/group/si-list/messages
> Old (prior to June 6, 2001) list archives are viewable at:
>               http://www.qsl.net/wb6tpu
>   
> 
> 
> 
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field


List technical documents are available at:
                http://www.si-list.net

List archives are viewable at:     
                //www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu
  

Other related posts: