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Wednesday, March 7, 2012

Delay - "Wire Load Model" : Static Timing Analysis (STA) basic (Part 4c)





Static Timing analysis is divided into several parts:



Now the question is: What is Wire Load Models (WLM).

Wire loading models
  • Used to estimate the interconnect wire delay during pre-layout in a design cycle.
  • Wire load information is based on statistics from physical layout parasitic
    • Information from the statistics is used in both conservative and aggressive tables.
    • The conservative tables are based on “mean value” plus 3-sigma; the aggressive tables on “mean value” plus 1-sigma.
  •  Different for different technology.
    • Wire load models are approximated from one technology to another based on scaling factors. Due to these approximations, the accuracy of these models diminish over multiple technology nodes
  •  Describes effect of wire length and fanout on
    •  Resistance
    •  Capacitance
    •  Area of the nets.
  •  All attributes (R, C and Area) are given per unit length wire. 
  • Slope value is used to characterize linear fanout.
  • Basically a set of tables
    • Net fanout vs load
    • Net fanout vs resistance
    • Net fanout vs area
One example of such type of table is:

Net Fanout
Resistance KΩ
Capacitance pF
1
0.00498
0.00312
2
0.01295
0.00812
3
0.02092
0.01312
4
0.02888
0.01811

As per this


In above circuit - The RC value is estimated and represented as per WLM.

The following are few snapshot of the different format of wire load model.

wire_load("WLM1")      {                                    
  resistance  :         0.0006        ;------>R per unit length
  capacitance :       0.0001        ;------> C per unit length
  area :                   0.1             ;------> Area per unit length
  slope         :         1.5             ;------> Used for linear extrapolation
  fanout_length(1,  0.002)         ; ------> at fanout “1” length of the wire is 0.002

fanout_length(2,  0.006);
fanout_length(3,  0.009);
fanout_length(4,  0.015);
fanout_length(5,  0.020);

fanout_length(7,  0.028);           ------> at fanout “7” length of the wire is 0.028
fanout_length(8,  0.030);
fanout_length(9,  0.035);
fanout_length(10, 0.040);
}

wire_load("WLM2") {
         fanout_length(  1, 1 );
         fanout_length(  2, 2 );

          fanout_capacitance( 1, 0.002 );
          fanout_capacitance( 2, 0.004 );
          fanout_capacitance( 3, 0.006 );
          fanout_capacitance( 4, 0.008 );
          fanout_capacitance( 5, 0.010 );
          fanout_capacitance( 6, 0.013 );
          fanout_capacitance( 7, 0.015 );
          fanout_capacitance( 8, 0.019 );
          fanout_capacitance( 9, 0.023 );
          fanout_capacitance( 10, 0.027);
         

          fanout_resistance( 1, 0.01 );
          fanout_resistance( 2, 0.015 );
          fanout_resistance( 3, 0.022 );
          fanout_resistance( 4, 0.026 );
          fanout_resistance( 5, 0.030 );
          fanout_resistance( 6, 0.035 );
          fanout_resistance( 7, 0.039 );
          fanout_resistance( 8, 0.048 );
          fanout_resistance( 9, 0.057 );
          fanout_resistance( 10, 0.06 );
         
         fanout_area(  1, 0.11 );
         fanout_area( 20, 2.20 );
}


Here --
Area, Resistance and Capacitance are in per unit length of the interconnect.
The slope is the extrapolation slop to be used for data points that are not specified in the fan-out length table.

In general, not all fanouts are mentioned in a given WLM lookup table. For example, in above WLM1 and WLM2  lookup table, capacitance and resistance values for fanouts 1, 2, 3, 4, 5, 7, 8, 9, 10 is given. If we want to estimate the values at fanouts in the gaps (e.g. from 6) or outside the fanout range specified in the table (e.g Fanout 20), we have to calculated those value using (linear) interpolation and extrapolation.

For WLM1
For Fanout=20

Since its more than the max value of  Fanout available in table (i.e 10) , so we have to perform extrapolation.

Net length = <length of net at fanout 10> + (20-10) x Slope
Resistance = <new calculated Net length at fanout 6> x Resistance or Capacitance value per unit length
Capacitance = <new calculated Net length at fanout 6>  x Capacitance value per unit length


Net length = 0.040 + 10 x 1.5 (slope) = 15.04 ----------> length of net with fanout of 20
Resistance = 15.04 x 0.0006 = 0.009024 units
Capacitance = 15.04 x 0.0001 = 0.001504 units

For Fanout=6

Since it’s between 5 and 7 and corresponding fanout Vs length is available, we can do the interpolation.

Net length = ( (net length at fanout 5) + (net length at fanout 7) ) / 2
Resistance = <new calculated Net length at fanout 20> x Resistance value per unit length
Capacitance = <new calculated Net length at fanout 20> x Capacitance value per unit length


Net length = (0.0020 + 0.0028)/2=0.0048/2=0.0024   ----------> length of net with fanout of 6
Resistance = 0.0024 x 0.0006 = 0.00000144 units

Capacitance = 0.0024 x 0.0001 = 0.00000024 units
In the similar way we can calculate the WLM for any no of fanout value.

WLMs are often used in pre-placement optimization to drive speedups of critical paths. Since timing-driven placement plausibly makes nets on critical paths shorter than average, some optimism may be incorporated into the WLM. Thus, a WLM may actually consist of more than one lookup table, with each table corresponding to a different optimism level. There are several ways to incorporate the optimism level. If we use the WLMs that come from the (ASIC vendor’s) design library, usually there are several tables from which we can select. We can also increase the optimism level of a WLM by multiplying all values in the WLM by some factor less than 1.2 For example, we can use 0.25, 0.5, or 0.75.

WLM Types
For flows that run timing-based logic optimization before placement, there are three basic types of WLMs that can be used:
  1. Statistical WLMs 
    • Are based on averages over many similar designs using the same or similar physical libraries.
  2. Structural WLMs 
    • Use information about neighboring nets, rather than just fanout and module size information.
  3. Custom WLMs 
    • Are based on the current design after placement and routing, but before the current iteration of preplacement synthesis.

Now the Question is: Where do the wire load models come from?

Normally the semiconductor vendors will develop the models.
ASIC vendors typically develop wireload models based on statistical information taken from a variety of example designs. For all the nets with a particular fanout, the number of nets with a given capacitance is plotted as a histogram. A single capacitance value is picked to represent this fanout value in the wireload model. If a very conservative wireload model is desired, the 90% decile might be picked (i.e. 90% of the nets in the sample have a capacitance smaller than that value).



In this example  90% of nets have a capacitance smaller then 0.198pf. So in the WLM table, you will notice that fanout_capacitance( 3, 0.198 ).
Similar statistics are gathered for resistance and net area.
Usually the vendor supplies a family of wireload models, each to be used for a different size design. This is called area-based wireload selection

Few Advance concepts:

Till now we have discussed that for a particular Net you can estimate the RC value as per the WLM. Let me ask you one question. What if your design is hierarchical? Do you think even in that case you can use the same WLM for a particular net which is crossing the hierarchical boundaries?   Short ANS is: you can use it but you will lose the accuracy.  
Just to solve this problem, Vendors usually supplies multiple WLMs. There are different Modes for WLM analysis- few important are:

WLM analysis has three modes:
  1. Top:
    • Consider the design as it has no hierocracy and use the WLM for the top module to calculate delays for all modules. 
    • Any low level WLM is ignored.
  2. Enclosed: 
    • Use the WLM of the module which completely encloses the net to compute delay for that net. 
  3. Segmented:
    • If a net goes across several WLM, use the WLM that corresponds to that portion of the net which it encloses only.




13 comments:

  1. Excellent explanation so far. very effective.

    Thanks a lot...

    Waiting for the next one.

    ReplyDelete
  2. How does one calculate RC delay between two cells given only placement information without routing?

    ReplyDelete
    Replies
    1. HI, Simple ans of this question is ...
      Wire load models are approximated from one technology to another based on scaling factors. Means if you are in the cycle of 28nm, then you can use your experience of 32nm and scale it for 28nm.
      So one thing important here-- these are not accurate value -- these are always approximate. its like you never traveled from London to Newyork... but still you have idea about the time you will take ... if you fly/drive/walk. :)

      Delete
  3. 1) Why Area information is enclosed in WLM? When does it become useful?
    2) As for the transition delay over the cell, could it calculated using WLM? How?

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
  4. excellent work
    but i had a question:

    what do you mean by the fan-out here?? .... you didn't mean the fan-out of the driver or am i wrong??

    ReplyDelete
  5. This comment has been removed by the author.

    ReplyDelete
  6. Is that a mistake in WLM calculation?
    The formula for capacitance and resistance of fanout = 20 should be
    resistance = (new calculated net length for fanout 20) x resistance value of unit length
    capacitance = (new calculated net length for fanout 20) x capacitance value of unit length

    And for fanout = 6, they should be
    resistance = (new calculated net length for fanout 6) x resistance value of unit length
    capacitance = (new calculated net length for fanout 6) x capacitance value of unit length

    Their order should be reversed.

    ReplyDelete
  7. good one. thanks

    ReplyDelete
  8. suppose length of the routing is L and if we insert a buffer in the middle, what happens to the total delay?

    ReplyDelete

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