Example Calculation of Core Power with 6LM, Different Resistivities and Widths and 15% of Metal‑2 allocated to Power

An alternative to calculating the supply strap width given the core power consumption is to calculate the core power given the width of the supply straps. We will use a power strap allocation percentage p=15% with the power strap ratios and metal resistivities of the previous example to find the maximum core power.

Step 1: Estimate Vcore using Ipad=50mA:

Vcore =	Vddmin(1−2× Ipad ×(Rpkg+Rbond+Rpad))   Vdd
=	1.14×(1−2×0.050×(0.025+0.025+0.1)⁄1.2
=	1.126V

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   0%   0%   0%   0%   0%   0% core area blocked

¹78%=.07/.09; ²350%=.07/.02

From which

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))
=	( 0.24 + 0.8 + 0.4 + 0.8 + 0.4 + 5.6 )
=	8.24

Step 4: Calculate Pnom. Pnom depends on the value of Ipad which we don't know, so we start with Ipad=50mA which gives us Vcore, then Pnom and a new value of Ipad. We use a spreadsheet to iterate to the solution. The yellow squares mark user input and the pink squares are calculated values. The first estimate for Pnom is shown below.

Pnom =	{ (Vcore−Vmin)×Vdd2 } ×G×(kc1×ps+p×L) Vddmin
=	{ (1.126−1.08)×1.22 } ×25×(0.78×0.22+0.12×8.24) 1.14
=	1.445×(0.173+1.236) = 2.036W

The iteration leads to the solution of Pnom=2.007W. This is slightly higher than the 2W of the previous example, which we expect because the power strap allocation percentage is slightly higher at 15% instead of 14.92%.