CMOS dynamic power — why frequency matters for dissipation Why is the operating frequency a critical factor in determining power dissipation for CMOS logic?

Introduction / Context:
CMOS logic exhibits very low static power, but dynamic (switching) power dominates as frequency rises. Understanding the C * V^2 * f relationship is essential for low-power design and for sizing decoupling networks and regulators in fast digital systems.

Given Data / Assumptions:

• CMOS gates have parasitic input and interconnect capacitances.
• Each logic transition charges or discharges these capacitances.
• Supply current spikes occur on transitions, not during static states.

Concept / Approach:
Each transition moves charge Q = C * V between the rails. The energy drawn per transition is approximately E = C * V^2. With f transitions per second (scaled by toggle probability and activity factor), average dynamic power is P ≈ C * V^2 * f * alpha. Therefore, higher f linearly increases dynamic power for a given voltage and capacitance budget.

Step-by-Step Solution:

Verification / Alternative check:
Measure supply current vs. clock rate on a CMOS device; current rises roughly linearly with frequency for a fixed activity factor.

Why Other Options Are Wrong:

• A: At low frequency, dynamic component decreases, not increases.
• B and D: “70.7 % of rated power” is unrelated to CMOS switching power.

Common Pitfalls:
Ignoring activity factor (alpha) and short-circuit current during transitions, which also contribute but still increase with f.

Final Answer:
At high frequencies, charging and discharging the gate capacitance will draw a heavy current from the power supply and thus increase power dissipation.