Example Calculation of Power Strap Width with 6LM, 30% RAM, 20% Analog, Different Resistivities and Widths, 2W Core Power

The horizontal power straps are half the width (or twice the pitch) of vertical ones; metal resistivities are different; core power consumption is 2W with 32 core Vdd and 32 core Vss pads; 30% core is RAM blocked to metal-4; 20% is analog blocked to all layers.

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  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  50%  50%  50%  50%  20%  20% core area blocked

¹78%=.07/.09; ²350%=.07/.02

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))+
	kw6kc6(1-m6(1-ka2p)(1-ka3p))
=	( 0.12 + 0.4 + 0.2 + 0.4 + 0.64 + 4.48 )
=	6.24

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
=	{ 1.164×2 −0.78×0.22×(1-0.5) } × 1 (1.155−1.08)×1.22×25 6.24
=	(0.860−0.086)×0.160 = 12.40%

As shown on the right, a spreadsheet can be used to iterate to the answer of p=11.45%.

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+9.44%
	√(((1−ka2p)(1−ka3p))		√(0.8855×0.9428)

The value 9.44% is called the IR Drop Adder.

The power strap widths are set by the user defined pitch, strap allocation or width 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	width metal			pitch		core
		1-4	5	6	hor	ver	side
old	19.69%	5.5µm	5.5µm	11µm	112µm	56µm	9.402mm
new	11.45%	5.5µm	11µm	11µm	192µm	96µm	8.756mm