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# Power consumption of a mos inverter

### Power consumption of a MOS inverter

Question: Show that the total power consumption of an MOS inverter is P=I_{DDQ\;}V_{DD}+C_{out}V_{DD}^2\;f

Solution:

In a CMOS inverter, total power consumption is the sum of static power and dynamic power consumption. i.e

{P=P_{DC\;}+P_{dyn}.....................(i)}

Where PDC =DC (static) power consumption

Pdyn=Dynamic (signal changing) term

Again DC power is

{P_{DC\;}=I_{DD}V_{DD}}

Where IDD is DC current from the power supply. Ideally, IDD=0 in CMOS. But practically there present leakage current called quiescent leakage current IDDQ

{P_{DC\;}=I_{DDQ}V_{DD}}

Figure: A MOS Inverter

Pdyn power required to switch the state of a gate charge transferred during the transition, {Q_{e\;}=C_{out}V_{DD}}

Assume each gate must transfer this charge at {\frac1{clock\;cycle}}

Average power dissipation is

{\begin{array}{l}P_{average}\;=V_{DD}Q_ef\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;=V_{DD}V_{DD}C_{out}f\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;=C_{out}V_{DD}^2f\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=P_{dyn}\end{array}}

Where f is the frequency of signal changing.

From equation (i) we get

{\begin{array}{l}P=P_{DC}+P_{dyn}\\\;\;\;=I_{DDQ}V_{DD}+C_{out}V_{DD}^2f\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(showed)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\end{array}}

From this equation, we see that power increases with Cout and frequency and strongly with VDD (second-order).

Power consumption of a mos inverter

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