Summary of Supply Power Strap Width Calculation

In order to calculate the width of power straps in a design, firstly the design attributes need to be set out in a table like the one on the right.

Then the calculation proceeds in 5 steps.

Step 1: Calculate Ipad and Vcore:

Ipad =

Pnom Vdd × Npad

Vcore =

Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))   Vdd

Step 2: Calculate the reference power supply conductance G:

G =

7 4×r2

Step 3: Set out the values of k_an, k_wn, k_cn and m_n for each metal layer, and use these to calculate the value of L.
(L is the parallel metal conductivity coefficient. That is, how much bigger the total metal conductivity will be than the reference metal conductivity due to multiple metal layers with different conductivities and widths. k_an and k_wn set out the relative allocations and widths we want for the power supply on each metal layer. k_cn says how much more conductive a metal layer is than the value 1⁄r₂ for metal-2.)

metal layer	1	2	3	4	5	6	7	8
kan
power metal allocated coefficient
kwn
power metal used coefficient
kcn
metal conductivity coefficient
mn
core area blocked

The expression for L is:

L =	kw1kc1(1-ps)(1-m1(1-ka2p)(1-ka3p))+
	kw2kc2(1-m2(1-ka2p)(1-ka3p))+
	… +
	kw8kc8(1-m8(1-ka2p)(1-ka3p))

The value of L is a function of p, the amount of metal allocated to the power supplies and whose value we do not know. Since we don't know it, we estimate it. Our first estimate for p will be p=0%.

Step 4: Calculate the power strap allocation percentage p.

m1′ =

m1×(1-ka2p)(1-ka3p)

p =	{ Vddmin×Pnom −kc1×ps(1-m1′) } ×  1  (Vcore−Vmin)×Vdd2×G L

The first value of p uses the value of L calculated with p=0. This allows a better estimate of L and the iteration leads to the solution, as shown in the spreadsheet example on the right. The yellow boxes are user input like core power consumption Pnom or the initial estimate for p. The pink boxes are calculated values.

Step 5: Calculate the new core size x′.

x′ =	x
	√(((1−ka2p)(1−ka3p))

The value of p sets the new core size and the power strap allocation and pitch.
If we want to set the power straps to a width of W_sn, then their pitch is:

horizontal pitch	M1 =	2×Ws1 ⁄ (kw1×p)
vertical pitch	M2 =	2×Ws2 ⁄ (kw2×p)
	…
vertical pitch	M8 =	2×Ws8 ⁄ (kw8×p)

kwn is the ratio of the width of the power straps in metal layer n to the width of the reference (metal-2) straps. kan is the ratio of the allocated space for the power straps. If for example we do not want metal-1 power straps (except those already inside the standard cells), then ka1=0%.
kcn is the ratio of the conductivity of metal layer n to the reference metal layer, normally metal‑2. For example, if metal-1 has a resistivity of 90Ω per sq. and metal-2 70Ω per sq., then kc1=70⁄90=78%.	kcn =  r2 rn