IR Drop

 
Derivations

This example is the previous one with 30% of the core area blocked to all metal routing because of fixed blocks. This 30% is the core area before adding power straps.

Step 1: Calculate Ipad and Vcore:

Ipad = 
Pnom
Vdd × Npad
1⁄(1.2×16) = 0.052A
Vcore = 
Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))
  Vdd  
1.14×(1−2×0.052×(0.025+0.025+0.1)⁄1.2
1.125V

Step 2: Calculate the reference power supply conductance G:

G = 
7
r2
 
7 ⁄ (4 × 0.07) =  25 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
 kan 100% 100% 100% 100% 100%
power metal allocated coefficient
 kwn  80%  80%  80%  80%  80%
power metal used coefficient
 kcn 100% 100% 100% 100% 100%
conductivity coefficient
 mn  30%  30%  30%  30%  30%
core area blocked
kan and kcn are 100% because all power straps have the same space allocated and the metal resistivities are the same. kwn is 80% for all metal layers because the power strap widths and spacings are also all the same.

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))
( 0.44 + 0.56 + 0.56 + 0.56 + 0.56 )
2.68

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
{ 1.14×1 −1×0.22×(1-0.3) } × 1
(1.125−1.08)×1.22×25 2.68
(0.701−0.156)×0.374 = 20.40%

As shown on the right, a spreadsheet can be used to iterate to the answer of p=17.27%.

The presence of the fixed blocks has increased the percentage of metal which must be allocated to power straps from 12.53% to 17.27%, an increase of 38%.

Step 5: Calculate the new core size. If the initial core size estimate without power straps is x, then with power straps the core size becomes x

x′ =   x  =   x  =   x  = x+20.88%
  (((1-ka2p)(1-ka3p))   √0.82732   0.8273  

The value 20.88% is called the IR Drop Adder.

Let us look at a more complex example.

Design Attribute Value
Pnom core power consumption 1W
ps fraction of metal-1 in the standard cells used for power supplies 22% (for vsclib)
rn resistivity of metal layer n in ohms per square 0.07Ω per sq.
kan
user defined   
ratio of
metal layer n allocated to power
metal-2 allocated to power
100%
kwn
user defined   
ratio of
metal layer n used for power
metal-2 allocated to power
80%
mn percentage of metal layer n blocked to power straps 30%
Vdd the nominal supply voltage 1.2V
Vddmin the minimum supply voltage, 5% less than nominal 1.14V
Vmin the desired voltage at the centre of the die, 10% less than the nominal 1.08V
Npad number of core Vdd or core Vss power pads 16
Rpkg the resistance of the package leadframe 25mΩ
Rbond the resistance of the bond wire 25mΩ
Rpad the resistance of the bond pad 100mΩ

kcn = 
r2
rn

spreadsheet example