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Additional resources for Power Distribution Networks with On-Chip Decoupling Capacitors

Example text

10) where A is the magnetic vector potential of the system, determined as A(r) = µ 4π J (r ′ ) dr ′ . 10) yields the expression of the magnetic energy in terms of the current distribution in a system, Wm = µ 8π J (r) · J (r ′ ) dr dr ′ . 12) can be rewritten as Wm = µ 8π i j V V i j J (r) · J (r ′ ) dr dr ′ . 13) Assuming that the relative distribution of the current in each volume Vi is independent of the current magnitude, the current density distribution J can be expressed in terms of the overall current magnitude 30 2 Inductive Properties of Electric Circuits I and current distribution function u(r), so that J (r) = Iu(r).

2. 3. 4. 5. 1 Definitions of inductance There are several ways to represent the magnetic characteristics of a circuit. Understanding the advantages and limitations of these approaches presents the opportunity to choose the approach most suitable for a particular task. Several representations of the inductive properties of a circuit are presented in this section. 1. 2. 3. 4. 1 Field energy definition Inductance represents the capability of a circuit to store energy in the form of a magnetic field.

Provided the disturbance persists, the phase difference between the system and the on-chip clocks can accumulate for tens or hundreds of clock periods, until the PLL feedback adjustment becomes effective. , between an integrated circuit and other system components controlled by different clock signals). Synchronizing the clock domains is critical for reliable communication across these domains. The maximum phase difference between two clock domains is characterized by the peak-to-peak jitter. Fig. 14.

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