IR Drop

 
Derivations

Certain aspects of the chip specification are listed in the table on the right, along with typical values for a 0.13µm technology. The required power strap width is a function of these parameters.

We derive the variables Ipad, Vcore, G, L and p from these design attributes.

Ipad is the current through each core power supply pad at nominal voltage, taken by dividing the total core current by the number of core Vdd or Vss pads.

Vcore is the voltage at the edge of the core after the drop from the package pin caused by the resistances of the package leadframe, the bond wire and the core supply pad.

G is the conductance of the metal-2 plane. Half of the plane is used for Vdd power straps and half for Vss. If less than 100% of the metal-2 is used for power, say fraction p, then the conductance will be pG.

L is the parallel metal conductivity coefficient. It shows how much bigger is the total metal conductivity due to multiple metal layers, different metal layer resistivities and strap widths than the conductivity of the metal-2 power straps.

Note that normally here kw2=kc2=100%, and if kw2=ka2 and the only power straps are in metal-2, then L=1.

p is the power strap allocation percentage for metal-2. Given the design attributes in the table on the right, we calculate the metal-2 power strap allocation and from that the allocation of the other metal power straps.

kan is the relative power strap allocation, the amount of metal layer n allocated to power divided by the amount of metal-2 allocated. This is the user deciding how big the straps in each metal layer should be.

kwn is the relative power strap width, the amount of metal layer n used for power divided by the amount of metal-2 allocated to power. This is how much of the allocated space can be used for metal, the rest being needed for spacing to adjacent metal.

kcn is the ratio of the conductivity of metal layer n to metal‑2. The metal conductivities (inverse of resistivities) are a feature of the technology and we set kc2=1.

Design Attribute Typical 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 which is blocked 30%
Vdd the nominal supply voltage 1.2V
Vddmin the minimum supply voltage, typically 5% less than the nominal 1.14V
Vmin the desired voltage at the centre of the die, typically 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

Ipad = 
Pnom
Vdd × Npad
Vcore = 
Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))
  Vdd  
G = 
7
r2
kcn = 
r2
rn
mn′ = 
mn(1−ka2p)(1−ka3p))
L = 
kw1kc1(1−ps)(1−m1′)+kw2kc2(1−m2′)+ … +kwn‑1kcn‑1(1−mn‑1′)+kwnkcn(1−mn′)
p = 
{ Vddmin×Pnom ps×kc1(1−m1′) } ×  1 
(VcoreVminVdd2×G L