IR Drop

Step 1: Calculate Ipad and Vcore:

Ipad = 
Pnom
Vdd × Npad
0.9⁄(1.2×16) = 0.047A
Vcore = 
Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))
  Vdd  
1.17×(1−2×0.047×(0.022+0.02+0.04)⁄1.2
1.163V

Step 2: Calculate the reference power supply conductance G:

G = 
7
r2
 
7 ⁄ (4 × 0.06) =  29.17 mhos

Step 3 is to set out the values of kan, kwn, kcn and mn for each metal layer, and use these to calculate the value of L.

metal layer 1 2 3 4 5 6
 kan 100% 100% 100% 100% 180% 200%
power metal allocated coefficient
 kwn  70%  80% 92.5%  80% 132.5% 135%
power metal used coefficient
 kcn  75%¹ 100% 100% 100% 100% 300%²
conductivity coefficient
 mn  50%  50%  50%  50%  50%   0%
core area blocked
¹75%=.06/.08; ²300%=.06/.02

The value of L depends on p which we don't know. We iterate to the solution and use p=0 for the first estimate.

L =  kw1kc1(1-ps)(1-m1(1-ka2p)(1-ka3p))+
  kw2kc2(1-m2(1-ka2p)(1-ka3p))+
  kw3kc3(1-m3(1-ka2p)(1-ka3p))+
  kw4kc4(1-m4(1-ka2p)(1-ka3p))+
  kw5kc5(1-m5(1-ka2p)(1-ka3p))+
  kw6kc6(1-m6(1-ka2p)(1-ka3p))
( 0.18 + 0.4 + 0.46 + 0.4 + 0.66 + 4.05 )
6.16

Step 4: Calculate the power strap allocation percentage p. The solution must be iterated, and the calculation below shows the first iteration.

m1′ =  m1×(1-ka2p)(1-ka3p)
p = 
{ Vddmin×Pnom kc1×ps(1−m1′) } ×  1 
(VcoreVminVdd2×G L
{ 1.17×0.9 −0.75×0.3×(1−0.5) } × 1
(1.161−1.1)×1.22×29.17 6.16
(0.401−0.112)×0.162 = 4.69%

As shown on the right, a spreadsheet can be used to iterate to the answer of p=4.40%.

The calculation of the die size including straps is on the next page.

Design Attribute Typical Value
Pnom core power consumption 0.9W
ps fraction of metal-1 in the standard cells used for power supplies 30% (for wsclib)
r1 resistivity of metal-1 in ohms per square 0.08Ω per sq.
r2-5 resistivity of metal-2 to metal-5 in ohms per square 0.06Ω per sq.
r6 resistivity of metal-6 in ohms per square 0.02Ω per sq.
ka1-4
user defined   
ratio of
metal layer n allocated to power
metal-2 allocated to power
100%
ka5 180%
ka6 200%
kw1
user defined   
ratio of
metal layer n used for power
metal-2 allocated to power
70%
kw2,4 80%
kw3 92.5%
kw5 132.5%
kw6 135%
m1-5 percentage of metal layers 1-5 which is blocked 50%
m6 percentage of metal layer 6 which is blocked 0%
Vdd the nominal supply voltage 1.2V
Vddmin minimum supply voltage, 2.5% less than nominal 1.17V
Vmin the desired voltage at the centre of the die 1.1V
Npad number of core Vdd or core Vss power pads 16
Rpkg the resistance of the package leadframe 22mΩ
Rbond the resistance of the bond wire 20mΩ
Rpad the resistance of the bond pad 40mΩ

spreadsheet showing initial calculation of power strap percentage from circuit characteristics