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 in a table like the one on the right.

Then the calculation proceeds in 5 steps.

Step 1: Calculate the voltage on the supply pad Vpad:

Vpad =

Vddmin-2×Ipad×(Rlead+Rbond+Rpad)

Step 2: Calculate the supply conductance G. Normally this is the conductance of the metal‑2 layer.

G =	7
	4×r(2)

Step 3: Set out the values of j(n), k(n) 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. j(n) says how much more conductive a metal layer is than the value 1/r from the table at the top right. k(n) sets out the relative widths we want for each metal layer as a power supply.)

metal layer	1	2	3	4	5	6	7	8
j(n)
metal conductivity coefficient
k(n)
power strap coefficient
m(n)
core area blocked

The expression for L is:

L =	j(1)×k(1)×(1-ps)×(1-(1-p)×m(1)) +
	j(2)×k(2)×(1‑(1‑p)×m(2))+…+j(8)×k(8)×(1‑(1‑p)×m(8))

The value of L is a function of p, the amount of metal used for 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 3 uses the estimate for p to calculate L. Step 4 uses this value of L to calculate P(S), the power supplied by the standard cell supply lines.

P(S) =	(Vpad‑Vmin)×Vdd2×ps×(1‑(1‑p)×m(1))×j(1)×G
	Vpad

Step 5 uses this value of P(S) to calculate a new value for p, since the rest of the power is supplied by the power straps.

p =	Vpad	×	Ptot-P(S)
	(Vpad-Vmin)×Vdd2		G×L

This new value of p is then used for the next calculation of L and the iteration continues until an acceptable level of accuracy has been reached.

A spreadsheet can be set up to provide the answer as shown on the right. The yellow boxes are user input like core power consumption Ptot or the initial estimate for p. The pink boxes are calculated values.

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

horizontal pitch	M1 =	2×w / (k(1)×p)
vertical pitch	M2 =	2×w / (k(2)×p)
horizontal pitch	M3 =	2×w / (k(3)×p)
vertical pitch	M4 =	2×w / (k(4)×p)
horizontal pitch	M5 =	2×w / (k(5)×p)
vertical pitch	M6 =	2×w / (k(6)×p)

 
If the core side before power strap insertion had a length x, then afterwards it has a length

x

√((1-k(2)×p)×(1-k(3)×p))

j(n) 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 j(1)=70/90=78%.

k(n) is the ratio of the width of the power strap in metal layer n to the width of the reference (metal-2) straps. If for example we do not want metal-1 power straps (except those already inside the standard cells), then k(1)=0%.