Example Calculation of Power Strap Width with 5LM, 30% Fixed Blocks, Same Resistivities and Widths, 1W Core Power

Step 1: Calculate Ipad and Vcore:

Ipad =	Pnom Vdd × Npad
=	1⁄(1.2×16) = 0.052A

Vcore =	Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))   Vdd
=	1.164×(1−2×0.052×(0.025+0.0125+0.05)⁄1.2
=	1.155V

Step 2: Calculate the reference power supply conductance G:

G =	7 4×r2
=	7 ⁄ (4 × 0.07) =	25 mhos

Step 3 is to 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.

metal layer 1 2 3 4 5 6  kan 100% 100% 100% 100% 200%   0% power metal allocated coefficient  kwn  80%  80%  80%  80%  80%   0% power metal used coefficient  kcn 100% 100% 100% 100% 100%   0%¹ conductivity coefficient  mn  30%  30%  30%  30%  30%   0% core area blocked

¹no M6 layer

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))
=	( 0.44 + 0.56 + 0.56 + 0.56 + 1.12 )
=	3.24

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  (Vcore−Vmin)×Vdd2×G L
=	{ 1.164×1 −1×0.22×(1-0.3) } × 1 (1.155−1.08)×1.22×25 3.24
=	(0.430−0.156)×0.309 = 8.49%

As shown on the right, a spreadsheet can be used to iterate to the answer of p=7.70%.

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	= x+8.34%
	√(((1-ka2p)(1-ka3p))		√0.92302		0.9230

The value 8.34% is called the IR Drop Adder.

The width of the power straps is set by the pitch, strap allocation or width chosen by the user and the value of p just calculated. An example is shown in the table below, where we set the supply strap allocation to 5.5µm and compare it to the old solution.

	p	allocation		pitch	core side
		met‑1‑4	met‑5
old	17.27%	5.5µm	5.5µm	64µm	9.671mm
new	7.70%	5.5µm	11µm	143µm	8.667mm