IR Drop

 
Derivations

An alternative to calculating the supply strap width given the core power consumption is to calculate the core power given the width of the supply straps. We will use a power strap allocation percentage p=15% with the power strap ratios and metal resistivities of the previous example to find the maximum core power.

Step 1: Estimate Vcore using Ipad=50mA:

Vcore = 
Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))
  Vdd  
1.14×(1−2×0.050×(0.025+0.025+0.1)⁄1.2
1.126V

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   0%   0%   0%   0%   0%   0%
core area blocked
¹78%=.07/.09; ²350%=.07/.02

From which

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))
( 0.24 + 0.8 + 0.4 + 0.8 + 0.4 + 5.6 )
8.24

Step 4: Calculate Pnom. Pnom depends on the value of Ipad which we don't know, so we start with Ipad=50mA which gives us Vcore, then Pnom and a new value of Ipad. We use a spreadsheet to iterate to the solution. The yellow squares mark user input and the pink squares are calculated values. The first estimate for Pnom is shown below.

Pnom = 
{ (VcoreVminVdd2 } ×G×(kc1×ps+p×L)
Vddmin
{ (1.126−1.08)×1.22 } ×25×(0.78×0.22+0.12×8.24)
1.14
1.445×(0.173+1.236) = 2.036W

The iteration leads to the solution of Pnom=2.007W. This is slightly higher than the 2W of the previous example, which we expect because the power strap allocation percentage is slightly higher at 15% instead of 14.92%.

Design Attribute Typical Value
p metal power supply allocation percentage 15%¹
ps the fraction of metal-1 in the standard cells dedicated to 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%
mn percentage of metal layer n blocked to power straps 0%
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 = 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
¹ the width (which is probably what is measured) is p×kw, or 80% of this value

spreadsheet example