IR Drop

 
Derivations

The horizontal power straps have half the allocation (or twice the pitch) of vertical ones; metal resistivities are different; core power consumption is 2W with 32 core Vdd and 32 core Vss pads; 30% core is RAM blocked to metal-4; 20% is analog blocked to all layers. It is the same as a previous example but with RAM and analog blocks.

Step 1: Calculate Ipad and Vcore:

Ipad = 
Pnom
Vdd × Npad
2⁄(1.2×32) = 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 6
 kan  50% 100%  50% 100%  50% 200%
power metal allocated coefficient
 kwn  80%  80%  80%  80%  80%  80%
power metal used coefficient
 kcn  78%¹ 100% 100% 100% 100% 350%²
conductivity coefficient
 mn  50%  50%  50%  50%  20%  20%
core area blocked
¹78%=.07/.09; ²350%=.07/.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))
( 0.12 + 0.4 + 0.2 + 0.4 + 0.32 + 4.48 )
5.92

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
{ 1.14×2 −0.78×0.22×(1-0.5) } × 1
(1.125−1.08)×1.22×25 5.92
(1.403−0.086)×0.169 = 22.23%

As shown on the right, a spreadsheet can be used to iterate to the answer of p=19.69%.

If the designer sets the power strap pitch, then the supply allocation for each metal layer n is pitch×kan×p⁄2 and the supply width is pitch×kwn×p⁄2. An example is shown in the spreadsheet on the right where we have chosen a vertical power strap pitch of 250µm.

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+17.53%
  (((1−ka2p)(1−ka3p))   √(0.8031×0.9015)  

The value 17.53% is called the IR Drop Adder.

The presence of the fixed blocks has increased the percentage of metal which must be allocated to power straps from 14.92% to 19.69%, an increase of 32%.

Design Attribute Value
Pnom core power consumption 2W
ps fraction of metal-1 in the standard cells used for power supplies 22% (for vsclib)
r1 resistivity of metal layer 1 in ohms per square 0.09Ω per sq.
r2-5 resistivity of metal layers 2-5 in ohms per square 0.07Ω per sq.
r6 resistivity of metal layer 6 in ohms per square 0.02Ω per sq.
ka1,3,5
user defined   
ratio of
metal layers 1,3,5 allocated to power
metal-2 allocated to power
50%
ka4
user defined   
ratio of
metal layer 4 allocated to power
metal-2 allocated to power
100%
ka6
user defined   
ratio of
metal layer 6 allocated to power
metal-2 allocated to power
200%
m1-4 metal layers 1-4 blocked to power straps 50%
m5-6 metal layers 5-6 blocked to power straps 20%
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 32
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