The dynamic power formula

Switching power follows P = alpha x C x V^2 x f. Alpha is the mean toggles per cycle, C the switched capacitance, V the supply, and f the clock rate.

Every number here is a stated EXAMPLE parameter. Real values vary with the library, the workload, and the operating point.

Worked comparison

Substitute the EXAMPLE parameters for the ungated clock first. Then scale by the gated activity factors.

EXAMPLE parameters (not silicon data): C = 100 pF, V = 0.8 V, f = 500 MHz
ungated clock, alpha = 1.00:
P = 1.00 x 100e-12 F x (0.8 V)^2 x 500e6 Hz
  = 100e-12 x 0.64 x 500e6 = 64e-12 x 500e6 = 32000e-6 W = 32.0 mW
gated, enable active 1 cycle in 4, alpha = 0.25:
P = 0.25 x 32.0 mW = 8.0 mW
saving = 32.0 - 8.0 = 24.0 mW = 75.0%
gated harder, enable active 1 cycle in 10, alpha = 0.10:
P = 0.10 x 32.0 mW = 3.2 mW
saving = 32.0 - 3.2 = 28.8 mW = 90.0%

A runnable model

The program below replays the hand arithmetic and checks all five results. It proves the code agrees with the worked comparison.

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import sys

C = 100e-12
V = 0.8
F = 500e6

def dyn_power(alpha):
    return alpha * C * V * V * F

p_ungated = dyn_power(1.0)
p_gate25 = dyn_power(0.25)
p_gate10 = dyn_power(0.10)

def close(got, want):
    return abs(got - want) < 1e-12

checks = [
    (p_ungated, 0.032),
    (p_gate25, 0.008),
    (p_gate10, 0.0032),
    ((p_ungated - p_gate25) / p_ungated, 0.75),
    ((p_ungated - p_gate10) / p_ungated, 0.90),
]

for i in range(len(checks)):
    got, want = checks[i]
    if not close(got, want):
        print("FAIL: check " + str(i + 1) + " got " + str(got) + " want " + str(want))
        sys.exit(1)

print("PASS: gated model gives 8.0 mW at 25 percent enable and 3.2 mW at 10 percent")

Common mistakes

The arithmetic is exact for the stated alpha, but the formula is only the switching term: real power adds short-circuit, glitch and leakage terms, so alpha is not the only uncertainty. Measure or bound the enable rate before quoting the saving.

Related topics

• Enable flops and the gating opportunity

• Operand isolation

• Area, Power and Timing Trade-offs