CMOS Dynamic Power

P = C × V² × f

Quick answer

This calculator solves P = C × V² × f for Power. With Load Capacitance 100 pF, Supply Voltage 12 V, Switching Frequency 10 MHz, the result is 144 mW. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Power (mW)
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Formula

P = C × V² × f

Description

CMOS dynamic power dissipation occurs when gates switch states, charging and discharging their load capacitances. The quadratic voltage dependence is why modern processors aggressively reduce supply voltage to save power. The capacitance term includes gate input capacitance, interconnect capacitance, and any external load. Reducing clock frequency linearly reduces dynamic power, which is the basis for dynamic frequency scaling in modern processors. This is the dominant power component in active CMOS circuits.

Variables

  • P — Dynamic power dissipation (W)
  • C — Total switched capacitance (F)
  • V — Supply voltage (V)
  • f — Switching frequency (Hz)

Practical Notes

Total CMOS power also includes static (leakage) power and short-circuit power. At advanced process nodes (below 28nm), leakage power becomes comparable to dynamic power. Activity factor (α) is often included: P = α × C × V² × f, where α is the fraction of gates switching per cycle (typically 0.1-0.3).

Symbols and units

Symbol Meaning Default unit Accepted units
P Power mW µW, mW, W, kW
C Load Capacitance pF pF, nF, µF, mF, F
V Supply Voltage V pV, nV, µV, mV, V, kV
f Switching Frequency MHz Hz, kHz, MHz, GHz

Step by step

  1. 1. What you know: Load Capacitance 100 pF, Supply Voltage 12 V, Switching Frequency 10 MHz
  2. 2. The relation: P = C × V² × f
  3. 3. Substitute: C = 100 pF, V = 12 V, f = 10 MHz
  4. 4. Result: Power = 144 mW

Worked examples

Minimum range

Given: Load Capacitance 1 pF, Supply Voltage 0.33 V, Switching Frequency 100 kHz

Result: Power = 0.01089 µW

Low range

Given: Load Capacitance 10 pF, Supply Voltage 3.3 V, Switching Frequency 1 MHz

Result: Power = 108.9 µW

Typical

Given: Load Capacitance 100 pF, Supply Voltage 12 V, Switching Frequency 10 MHz

Result: Power = 144 mW

High range

Given: Load Capacitance 1 nF, Supply Voltage 0.23 kV, Switching Frequency 100 MHz

Result: Power = 5.29 kW

Maximum range

Given: Load Capacitance 10 nF, Supply Voltage 2.3 kV, Switching Frequency 1 GHz

Result: Power = 52900 kW

Solving for each variable

Solve for Power

Load Capacitance 1 pF, Supply Voltage 0.33 V, Switching Frequency 100 kHz → 0.01089 µW

Solve for Load Capacitance

Power 100 µW, Supply Voltage 0.33 V, Switching Frequency 100 kHz → 9.183 nF

Solve for Supply Voltage

Power 100 µW, Load Capacitance 1 pF, Switching Frequency 100 kHz → 31.62 V

Solve for Switching Frequency

Power 100 µW, Load Capacitance 1 pF, Supply Voltage 0.33 V → 0.9183 GHz

How Power changes with Load Capacitance

Load Capacitance (input) Power (result)
10 pF 14.4 mW
25 pF 36 mW
50 pF 72 mW
75 pF 108 mW
100 pF 144 mW
150 pF 0.216 W
0.2 nF 0.288 W
0.4 nF 0.576 W
0.7 nF 1.008 W
1 nF 1.44 W

The same result in other units

Unit Value
µW 144000
mW 144
W 0.144
kW 0.000144

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Frequently asked questions

How do you calculate CMOS Dynamic Power?

Use P = C × V² × f. With Load Capacitance 100 pF, Supply Voltage 12 V, Switching Frequency 10 MHz, Power works out to 144 mW.

What is the formula for CMOS Dynamic Power?

The formula is P = C × V² × f. CMOS dynamic power dissipation occurs when gates switch states, charging and discharging their load capacitances.

How do you find Load Capacitance when you know the other values?

Rearrange for Load Capacitance: with Power 100 µW, Supply Voltage 0.33 V, Switching Frequency 100 kHz, Load Capacitance is 9.183 nF.

How do you find Supply Voltage when you know the other values?

Rearrange for Supply Voltage: with Power 100 µW, Load Capacitance 1 pF, Switching Frequency 100 kHz, Supply Voltage is 31.62 V.

What units does CMOS Dynamic Power use?

Power is shown in µW, mW, W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Digital Logic formulas →
CMOS Dynamic Power Rise Time to Bandwidth Setup Time Margin Static Power Dissipation Clock Skew Timing Margin Logic Noise Margin Digital Fanout Pull-Up Resistor for Logic

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