Physics Silicon Telemetry & PDN Modeling

Unlike traditional simulators that rely exclusively on static, post-simulation spreadsheet calculations, Axiom integrates real-time physical power equations directly into the simulation loop.

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Dynamic Power Dissipation

Dynamic power dissipation is governed by charging and discharging physical capacitive loads during signal transitions:

$$P_{\text{dynamic}}=\frac{1}{2}{C}_{\text{lumped}}{V}_{\text{rail}}^{2}f\alpha$$

Where:

• $C_{\text{lumped}}$: Total physical capacitance of the net (driver pin + wire routing + fanout sink pins).
• $V_{\text{rail}}$: Supply voltage rail of the driver's power domain (e.g. 1.20V Core).
• $f$: Clock frequency.
• $\alpha$: Switching activity factor (Hamming distance toggle rate).

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Energy Accumulation per Event

On every state transition of net $i$:

$$\mathrm{\Delta }{E}_i=\frac{1}{2}{C}_i{V}_{\text{rail}}^2\times \text{bit\_flips}$$

Axiom's TelemetryCollector accumulates dissipated energy per hierarchical module instance in real time, tracking instantaneous power dissipation in milliwatts ($mW$) and cumulative energy in microjoules ($\mu J$).

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Power Distribution Network (PDN) Voltage Droop

Simultaneous switching noise (SSN) occurs when multiple registers or bus lines toggle on the same clock edge, pulling high transient currents from the on-chip power rail.

Axiom models the impedance of the Power Distribution Network ($R+L\frac{di}{dt}$):

$$V_{\text{sag}}(t)=I(t)\cdot R_{\text{pdn}}+L_{\text{pdn}}\cdot \frac{di}{dt}$$$$V_{\text{effective}}(t)=V_{\text{nominal}}-V_{\text{sag}}(t)$$

When bus signals toggle simultaneously, Axiom captures:

• Instantaneous transient current spikes ($mA$).
• Supply rail voltage droop ($mV$) below nominal levels.
• Direct correlation between clock edges and power supply bounce.