Power-delay product

WHAT is the Power-Delay Product?

WHY does multiplying power by delay give energy? Power is energy-per-second ($P=E/t$). If a gate takes $t_p$ seconds to switch, then the energy for that one switch is $E = P\times t_p$. So PDP is not an arbitrary "figure of merit" — it is a real physical quantity: the energy the circuit pays each time it flips.

HOW we derive PDP from first principles (CMOS)

We derive the dynamic energy of a CMOS gate charging a load capacitor $C_L$.

Step 1 — Charge the capacitor from 0 to $V_{DD}$. Why this step? A CMOS output rising to logic-1 means the PMOS network pulls $C_L$ up to $V_{DD}$. The energy drawn from the supply is what we must account for.

Charge delivered: $Q = C_L V_{DD}$. Energy drawn from supply during a full charge: $E_{supply} = \int_0^\infty V_{DD}\, i(t)\,dt = V_{DD}\int_0^\infty i\,dt = V_{DD}\,Q = C_L V_{DD}^2$

Step 2 — Where does that energy go? Why this step? Energy must be conserved; half is stored, half is burned.

Energy stored on the capacitor: $E_{cap}=\tfrac12 C_L V_{DD}^2$. Energy dissipated in the PMOS resistance while charging: $E_{supply}-E_{cap}=\tfrac12 C_L V_{DD}^2$.

Step 3 — Discharge (output falls to 0). Why this step? When output goes 1→0, the stored $\tfrac12 C_L V_{DD}^2$ is dumped through the NMOS and burned as heat.

Step 4 — Energy per full cycle (one up + one down): $E_{cycle}= \tfrac12 C_L V_{DD}^2 + \tfrac12 C_L V_{DD}^2 = C_L V_{DD}^2$

Step 5 — Average dynamic power at switching frequency $f$ (activity factor $\alpha$): $P_{avg}=\alpha\, C_L V_{DD}^2 f$

WHY is the frequency term gone? Because PDP measures per-event energy, not power-over-time. We deliberately removed the "how often" so that speed-cheating doesn't help you.

Why PDP alone isn't enough → EDP

Worked Examples

Common Mistakes (Steel-manned)

Active Recall

Connections

• Dynamic power dissipation
• CMOS Inverter
• Propagation delay
• Energy-delay product (EDP)
• Voltage scaling / DVFS
• Switching activity factor
• RC charging energy

Concept Map

Hinglish (regional understanding)