CMOS dynamic power — why frequency matters for dissipation Why is the operating frequency a critical factor in determining power dissipation for CMOS logic?
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AAt low frequencies, power dissipation increases.
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BAt high frequencies, the gate will only be able to deliver 70.7 % of rated power.
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CAt high frequencies, charging and discharging the gate capacitance will draw a heavy current from the power supply and thus increase power dissipation.
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DAt high frequencies, the gate will only be able to deliver 70.7 % of rated power and charging and discharging the gate capacitance will draw a heavy current from the power supply and thus increase power dissipation.
Answer
Correct Answer: At high frequencies, charging and discharging the gate capacitance will draw a heavy current from the power supply and thus increase power dissipation.
Explanation
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:
Recognize charging/discharging of gate capacitance on each edge.Compute energy per transition proportional to C * V^2.Multiply by transitions per second (frequency * activity) → power scales with f.Conclude that higher frequency increases dissipation due to repeated capacitance charging.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.