Question

The Pentium 4 Prescott processor, released in 2004, has a clock rate of 3.6 GHz and voltage of 1.25 V. Assume that, on average, it consumed 10 W of static power and 90 W of dynamic power.
The Core i5 Ivy Bridge, released in 2012, had a clock rate of 3.4 GHz and voltage of 0.9 V. Assume that, on average, it consumed 30 W of static power and 40 W of dynamic power.
a) For each processor find the average capacitive loads.
b) Find the percentage of the total dissipated power comprised by the static power and the ratio of static power to dynamic power for each technology.
c) If the total dissipated power is to be reduced by 10%, how much should the voltage be reduced to maintain the same leakage current? Note: power is defined as the product of voltage and current.

Answer 1

Answer:

a) C = 3.2 x 10^-8 F, C = 2.9 x 10^-8 F

b) 10%, 42.86%, 0.11, 0.75

c) 0.849 volts to maintain the same leakage current in the Pentium 4 Prescott Processor. 0.783 Volts to maintain the same leakage current in the Core i5 Ivy Bridge Processor.

Explanation:

For the Pentium 4 Prescott processor:

Clock rate (f) = 3.6 GHz

Voltage (V) = 1.25 V

Static Power Consumption = 10 W

Dynamic Power Consumption = 90 W

For the Core i5 Ivy Bridge processor:

Clock rate (f) = 3.4 GHz

Voltage (V) = 0.9 V

Static Power Consumption (SP) = 30 W

Dynamic Power Consumption (DP) = 40 W

(a) To find the average capacitive loads, use the formula:

DP = (1/2) x C x V² x f

Rearranging:

C = (2 x DP)/(V² x f)

For the Pentium 4 Prescott processor:

C = (2 x 90) / [(1.25)² x 3.6 x 10^9]

C = 3.2 x 10^-8 F

For the Core i5 Ivy Bridge processor:

C = (2 x 40) / [(0.9)² x 3.4 x 10^9]

C = 2.9 x 10^-8 F

(b) Percentage of the total dissipated power comprised by the static power can  be found by the formula:

[Static Power/(Static Power + Dynamic Power)] x 100

For the Pentium 4 Prescott Processor:

[10/(90+10)] x 100  = 10%

For the Core i5 Ivy Bridge Processor:

[30/30+40] x 100 = 42.86 %

Ratio of static power to dynamic power for each technology can be computed as:

Pentium 4 Prescott: 10/90 = 0.11

Core i5 Ivy Bridge: 30/40 = 0.75

(c) The total dissipated power can be calculated by:

P = DP + SP

For Static Power we have the formula:

SP = VI where I is the leakage current.

I = SP/V

For Pentium 4 Prescott: I = 10/1.25 = 8A

For Core i5 Ivy Bridge: I = 30/0.9 = 3.33 A

The total disspited power is reduced by 10%, meaning the ratio of new power to old power must be 90% = 0.9. So,

New Power/Old Power = 0.9

For Pentium 4 Prescott:

DP + SP / 100 = 0.9

VI + CV²F = 0.9 x 100

V(8) + (3.2 x 10^-8)V²(3.6 x 10^9) = 90

8V + 115.2V² - 90 = 0

By solving the quadratic equation, we get the positive answer as 0.849. This means that the voltage should be reduced to 0.849 volts to maintain the same leakage current in the Pentium 4 Prescott Processor.

For Core i5 Ivy Bridge:

DP + SP / 70 = 0.9

V(3.33) + (2.9 x 10^-8)V²(3.4 x 10^9) = 70 x 0.9

3.33V +98.6V² -63 = 0

By solving the quadratic equation we get the positive answer as 0.783. This means that the voltage should be reduced to 0.783 Volts to maintain the same leakage current in the Core i5 Ivy Bridge Processor.