Double Patterning Technique

power routing basics

Power routing basics :

• How to calculate number of core power/ground pads required?

Lets assume 1Watt power is consumed by chip and 1V is ss corner voltage

Power = Voltage*Current

P=V*I 

I = P/V

  =1/1

  = 1 ampere = 1000 milli ampere

Assume each pad can drive maximum of 100mA current.

No.of power pads required (p) = 1000/100=10  pads

No.of ground pads required (g) = p = 10 pads

Ideally 10 ground pads and 10  power pads are sufficient. In most of the cases the power distribution may not be uniform meaning the pads which are placed in the centre of chip are more effective as the sinks at centre might have less resistive paths. So we need to add more pads lets say 30% more pads.

So, no.of power/ground pads = (1+0.3)*10=13

• How to calculate the core PG ring width? Given Jmax (maximum current density of metal layer = 50mA/um)
• Core PG ring width = (Total current)/(No.of sides *Jmax)

             = 1000/(4*50)=5 u

• How to calculate pad to core trunk width?
• Pad to core trunk width = total current/(no.of sides * Jmax)

                                            = 1000/(4*50)=5 u

• How to calculate strap width and no.of straps for a block? Given width of block is W and height of block as H. Total power of block as P
• Let I = P/V
• Total current from top and bottom = (I * W)/(W+H)
• Let current is equally be supplied from top and bottom.
• Itop = Ibottom = (I * W)/(W+H)
• Similarly Ileft = Iright = (I * H)/(W+H)
• With 1% voltage drop at a node in the center
• Reffective (from Vertical) = (0.01*(VDD/2))/Itop
• Reffective (from Horizontal) = (0.01*(VDD/2))/Ileft

• Width of Straps based on EM limits :
• Total width of Vertical strap (Wvstrap-em) = Itop /Jmax
• Total width of horizontal strap (Whstrap-em) = Ileft /Jmax
• Now assume initial width of strap to be 5X of min-width
• Wvstrap = 5*0.07=0.35 (0.07 is the min width for metal6)
• Rstripe-v = (Rpsq * H)/Wvstrap
• Note :  Rpsq =  Rho/thickness
• No.of vertical straps = Nvstraps = Rstripe-v / Reffective
• Now check the total width of vertical straps = Nvstraps * Wvstrap is greater than or equal to Wvstrap-em else increase the Wvstrap accordingly.

TCL example scripts

In this post, I will upload sample scripts to refer : (Under cons)

EXAMPLE : 1

For the engineers who are familiar with static timing analysis, as a programmer I want to calculate arrival time, required time, slack at each node using the given circuit. The example script will be able to demonstrate some of the tcl functions. The following circuit 10 nodes excluding (Out node), delay of each node is represented in the brackets. The objective of this program is to write a TCL script to analyse the slack at each and every node using graph based slack analysis.

Brief introduction about the graph based STA :

We need to break the entire program into three sections :

1. Arrival time calculation (AT)

2. Required time calculation (RT)

3. Slack calculation. 

First we need to calculate AT at each node, Let's do hand calculation of arrival time at few nodes. Arrival time at node 'A' is 10 as delay of node  'A' is 10 and then it passes through node 'D' whose delay is '8',  so the arrival time at node 'D' is 18 adding the delay of traversed path. But we can reach D by traversing IN->B->D accounting the delay of 13 (5+8), so we need to choose bigger one of the two arrival times (18,13) and assign that  arrival time to node 'D' in this case it is '18'. We need to repeat the same for all the nodes.

In the second section we need to calculate the required time starting from out node 'O'. In general we might be given required time by the clock specification. But in this case we take RT as the max of all the arrival times.

The above circuit can be represented using the adjacency matrix. Please refer to following link to know more about adjacency matrix. https://en.wikipedia.org/wiki/Adjacency_matrix

physical design

Please visit this blog to learn/discuss all about physical design tips, techniques, fundamentals.

regex

Regex,regsub  :

A regular expression is simply a description of a pattern that describes a set of possible characters in an input string.

Example :

strings

Strings

• A string is a sequence of letters, it always need not be enclosed in the quotes until you use some white spaces in between the words. Tcl is a string based language it provides rich set of operations on strings.

Examples :

set str1 one

set str2 "two three"

set str3 I\ need\ not\ enclose\ this\ in\ quotes

• Following operations can be executed on strings:
• string compare
• string equal
• string length
• string match #global expression
• string toupper
• string tolower
• string totitle #it will convert the starting letter of string to uppercase
• string index
• string range
• string reverse

Example :

lists

• Lists
• Lists are equivalent to arrays in the conventional programming language like C.
• Lists can be expanded and collapsed on the fly.

• Example 1:
• set list1 "a  b c d"

File handling

File Handling :

File names could be specified in Unix format.

In order to work with a file, first one has to open a channel to the file...this is also called handle

Once the channel is opened, TCL retruns a channelId which is used to work with the files

Typical steps to be followed while working with files:

Step 1: Check whether the file specified exists or not

Step 2: Open a channel pointing to the file...TCL returns an ID

Step 3: Use the ID to work with the file

Step 4: Close the channel after use

File Open :

"open" could be used to open a channel to a file. This command returns the file-handle (channelID) which could be used to work with the files.

Syntax:

open fileName ?access mode?

where

fileName - is the name of the file to be opened for use

access mode - either r, r+, w, w+, a or a+. These are the access modes (similar to C language)

"open" opens a channel to the file specified by the fileName with the access permissions specified by the access mode. Default is "r".

A channel once opened, remains open until specifically closed.

File Close :

"close" is used to close a channel previously opened using the "open" command.

Syntax:

close fileID

where

fileID - is the channel ID of the file opened

Example :

some of the useful file operations are: (no need to open a channel for these operations)

file exists      --> checks if the specifie file exists or not

file dirname     --> returns the parent directory of the specified file

file extension   --> returns the extension (suffix) of the specified file (incl. dot)

file isfile      --> returns 1 if “name” is a normal file

file isdirectory --> returns 1 if “name” is a directory

file executable  --> returns 1 if “name” has executable permissions

file readable    --> returns 1 if “name” has read permissions

file writable    --> returns 1 if “name” has write permissions

file tail        --> returns the last pathname component of “name”

file rootname    --> returns all but the extension of the “name”

procs

procedures are supported by TCL :

Procedures return to the calling program through "return" statement

Every procedure must have a corresponding return statement. This however is not strictly required.

Once they are created, procedures could be used just as any other TCL command

Procedures are declared with the help of keyword "proc"

Each procedure may have a set of formal parameters and some variables - local and global

Syntax:

proc proc_name { formal parameters } {

  statement1

  statement2

  :

  return

}

Example:

proc plus { a b } {

  expr $a + $b

  return

}

Syntax:

proc name argList body

where,

name - is the procedure name

argList - List of arguments. If a procedure takes more than one argument, they should be specified within braces.

body - body of the procedure

Example:

% proc proc_a { a b c } { body of procedure }

% proc proc_b b { body of procedure }

Once created, a procedure could be invoked/ called just by its name

Example: proc_a { $a $b $c }, proc_b { $b } w.r.t. The above example

Every procedure has its own set of local variables.

Any two procedures may have variables with the same names. The values of the variables do not get affected since they are not visible outside the procedure block.

"global" could be used to declare the scope of some variables as global

"global" should be used inside a procedure

Syntax:

global varName ?varName ...?

where

varName - is the name of variable whose scope has to be

extended beyond a procedure. More than one variable could be 

specified.

"global" binds variable names "varName"... to global variables. References to these names will refer to global variables instead of local variables for the duration of the current procedure.

Example 1:

Example 2: Simple tree traversal iterative procedure.

Example 3 :

continue and break

• Continue and Break statements

• Continue statement will terminate the current execution of the loop and start the next iteration.
• Break statement will terminate the execution of the loop and comes out of the loop.
• Continue and Break statements are very important in real life implementation.

•  For example, you might run placer or some extraction which is running for like a very long time (say 48 hours) and you do not want to lose your database with all the fixes you can use break and come out of the loop. Another example is if you do not want to execute the timer update on every iteration, but want to execute in every other iteration.

 Example 1:

Control Structures

Control Structures : (Under construction)

In general execution of the program would be sequential, if the programmer needs to change the flow of execution, he can very well do using certain tcl constructs. We will discuss about them in this section. Following are the different constructs which are available in TCL:

• if - else & if - elseif - else structure
• while structure
• foreach  structure
• for structure
• switch

• if - else & if - elseif - else structure

     If the condition is evaluated true, command1 and command2 will be executed.

     Syntax :

       if { condition } {

       command1

       command2

       }

     You can use if-else structure as well. i.e. if the condition is true do this and if it is false do that.

    Syntax :

     if { condition } {

       command1

       command2

      } else {

        command3

        command4

     }

You can use if-elseif-else and even nested if within each group.

If condition1 is evaluated to true, command_m would be executed, else if condition2 is evaluated to true command_n. If neither the condition evaluates to true, command_p would be executed

   if { condition1 } {

  command_m  

 } elseif { condition2 } { 

  command_n    

} else {  

command_p  

  }

Example 1:

While loop :

• While the condition evaluates to true iterate over the loop again and again till it evaluates to false. Once it evaluates to false come out of the loop.

while { condition } {

statement1;statement2;updation; }

Example 2:


For loop :

It is similar to the while loop except that you can have a flexibility to  initialize the loop iterator and also update the iterator in the same line.

for { initiliaze } { condition } { updation } {

command1;command2;..}

Example 3:


foreach control structure:
It loops over a set of variables in the list and executes operations on each variable. It is the most commonly used control structure in the TCL.

foreach var <list> {

execute operation on var;
statement1;
statement2;
.
.
}

Example 4:

TCL arrays

TCL array: (Under construction)

• Array is a collection of variables.
• Associative  -> abstract data type composed of a collection of key value pairs. 
• Key value pairs are not ordered.
• Each variable can hold any value or an array.

How to create an array in tcl?

• We can create an array using set or "array set"

Array operations :

Different operations associated with array

array exists
array get
array names
array set
array size
array unset
array startsearch
array nextelement
array anymore
array donesearch
array statistics

Output: 

sat and Saturday are same

wed and Wednesday are same

fri and Friday are same

thu and Thursday are same

sun and Sunday are same

tue and Tuesday are same

mon and Monday are same

Note: Observe that key and value pairs are not ordered.

Example:2

Output:
4 is associated to  Thu

5 is associated to  Fri 

1 is associated to  Mon 

6 is associated to  Sat 

2 is associated to  Tue 

7 is associated to  Sun 

3 is associated to  Wed

All array operations are listed in this example
Example:3


Example:4

TCL upvar command usage

upvar, a built-in Tcl command, links a variable to some other variable at the specified level of evaluation.

i.e If you want to change the value of variable from with in the procedure we can use upvar to do that.

Example:

proc upvar_demo {var1 var2} {

upvar $var1 procvar1

upvar $var2 procvar2

set procvar1 TCL

set procvar2 Script

}

set outvar1 Hello

set outvar2 World

puts "Values of variables before executing the procedure"

puts "outvar1 : $outvar1"

puts "outvar2 : $outvar2"

upvar_demo outvar1 outvar2

puts "Values of variables after executing the upvar procedure"

puts "outvar1 : $outvar1"

puts "outvar2 : $outvar2"

#Output :

Values of variables before executing the procedure

outvar1 : Hello

outvar2 : World

Values of variables after executing the upvar procedure

outvar1 : TCL

outvar2 : Script