Definition of power in VLSI design

This post tells about the definition of power in VLSI design.

There is several terms of power we must consider: instantaneous power and average power. The term of power leads us to the term of energy.

Instantaneous power of the certain circuit element is the product of the current and voltage through this element and described by the formula $P (t) = I (t) V (t)$ . The instantaneous power is always time dependent, measured with Watts.

Average power through the circuit element can be found through the formula $P_{a} = \frac{1}{T} \int_{0}^{T} P (t) d t$ , measured with Watts.

Knowing instantaneous power we can find energy through the circuit element $E = \int_{0}^{T} P (t) d t$ , measured with Joules.

Let’s consider the power components of CMOS circuits. Power dissipation of CMOS circuits happens due to charging and discharging of the load capacitances when the gate switches and due to short-circuited current when all transistors of the circuits are ON at the same time. Those are the reasons of dynamic power dissipation. Dynamic power dissipation can be described by formula $P_{d y n a m i c} = P_{s w i t c h i n g} + P_{s h o r t - c i r c u i t c u r r e n t}$ .

The reasons of static power dissipation are gate leakage through the gate dielectric; junction leakage via source or drain diffusions; subthreshold leakage through the transistors in OFF state; contention current. Static power can be described by the formula $P_{s t a t i c} = V_{D D} I_{g a t e} + V_{D D} I_{d i f f u s i o n} + V_{D D} I_{c o n t e n t i o n} + V_{D D} I_{s u b t h r e s h o l d}$ .

Both dynamic and static power creates total power through the circuit element $P_{t o t a l} = P_{d y n a m i c} + P_{s t a t i c}$ .

Another classification of power is standby, active and sleep mode power. Active power is consumed during active circuit element operation. Standby power is characterising the circuit element in the standby mode. And sleep power is supplied or consumed by the circuit elements during sleep mode.

Let’s consider power characteristics of the most common circuit elements : resistor, voltage source, capacitor that can be used in future.

Instantaneous power dissipated on the resistor is $P_{R} (t) = {I_{R}}^{2} (t) R$ .

Instantaneous power supplied by the voltage source is $P_{V D D} (t) = I_{D D} (t) V_{D D}$ .

Energy stored by capacitor is $E_{C} = \int_{0}^{\infty} I (t) V (t) d t = \frac{1}{2} C {V_{C}}^{2}$ .

Let’s consider dynamic power in a detail. The biggest part of dynamic power is switching power. Considering the circuit we must consider every node of the circuit separately. Switching power depends on the capacitance of each node, and can consist of gate, diffusion and wire capacitance. The effective capacitance of the node is described by the node capacitance and activity factor. Activity factor describes possibility of the circuit to reduce power. Activity factor and dynamic power goes to zero of circuit turns off entirely. For this purpose clock gating technique is used.

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