In our first electrical engineering class, we learn that the voltage across an inductor is L di/dt. We are ingrained with the idea that the voltage across an inductor is generated by the changing current through it. Not so, says Larry Smith, industry Power Integrity expert from Qualcomm and member of the SIJ EAB.
At DesignCon 2018, Smith presented a PDN tutorial to a packed room. He emphasized that when charge is consumed by the circuits on a die when core logic switches, there is a voltage droop on the power rails of the die. This voltage droop is inevitable. It is related to the amount of charge consumed by the on-die switching circuits and the on-die capacitance.
Figure 1. Smith presented a tutorial on PDN design to a packaged room at DesignCon 2018.
It’s this voltage droop on the die that appears across the package lead inductor. The board side of the package lead is at a fixed voltage, while the die side of the package lead inductor drops. It’s this voltage drop, Smith argues, that drives the di/dt through the inductor.
Figure 2. The measured rail voltage on a die when a single clock edge triggers many gates to switch, consuming charge showing the initial voltage droop.
“The forcing function that drives the di/dt through the inductor is the voltage droop on the die from the charge consumed from the on-die capacitance,” Smith says. This is illustrated by the relationship,
Many designers think they want a low inductance in the package leads to keep the voltage drop across the package lead low. The voltage drop on the power rail is inevitable, Smith says, and independent of the package lead inductance. It is about the initial voltage droop from charge consumption.
Low lead inductance is required to enable a higher di/dt which will replenish the charge on the die and more quickly reduce the voltage droop on the die.
Figure 3. The step change in voltage across the inductance drives the di/dt which will replenish the on-die charge.
Is the glass half full or half empty? It depends on whether you are filling it or emptying it. Likewise, does a di/dt cause the voltage across the inductor, or does the voltage drop cause the di/dt? It depends on what is the cause and effect.
Smith points out that the rail noise on the die is caused by the charge consumed by switching gates. This causes the voltage drop on the die, which also appears across the package lead inductor. The voltage noise on the die has nothing to do with the package lead inductance. What the package lead inductance controls is how long it takes the rail collapse to recover, also an important term.
Smith says that getting the cause and effect right is key to understanding the root cause of on-die PDN noise which is the first step to engineering acceptable noise.