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Unformatted text preview: 11.2 Optimal sizing of power and ground trees. We consider a system or VLSI device with many subsystems or subcircuits, each of which needs one or more power supply voltages. In this problem we
consider the case where the power supply network has a tree topology with the power supply (or
external pin connection) at the root. Each node of the tree is connected to some subcircuit that
draws power.
87 We model the power supply as a constant voltage source with value V . The m subcircuits are
modeled as current sources that draw currents i1 (t), . . . , im (t) from the node (to ground) (see the
ﬁgure below).
R2
R1 R3
i 3 ( t) i 2 ( t)
R5
R4 V i 5 ( t) R6
i 1 ( t)
i 6 ( t) i 4 ( t) The subcircuit current draws have two components:
ik (t) = idc + iac (t)
k
k
where idc is the DC current draw (which is a positive constant), and iac (t) is the AC draw (which
k
k
has zero average value). We characterize the AC current draw by its RMS value, deﬁned as
RMS(iac ) =
k 1
T →∞ T T lim 0 1/2 iac (t)2 dt
k ....
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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