U. Glaeser

FIGURE 20.10 Charge-sharing.
Charge-Sharing among the Internal Nodes
Charge-sharing among the internal nodes occurs when the conducting path that connects the nodes is
not connected to either Vsupply or GND. The nodes along the path are then isolated from the supply rails,
and will not be charged or discharged. These isolated nodes will come to a new equilibrium state, a val ue
between Vsupply and GND. In the isolated state, the capacitances of the internal nodes are connected in
parallel, and share the charges among themselves, thus the term charge-sharing. The new equilibrium
voltage among the internal nodes is
© 2002 by CRC Press LLC
t1 t0 A 0 1
B 1 0
C 0 0
(20.9)
where n is the number of isolated nodes, and V j is the initial voltage across the internal node capacitance
C j. An example of the charge-sharing process is il lustrated in Fig. 20.10. The event occurs when inputs
A and B switch at time t 1. The internal nodes are then isolated from V supply and GND. The new equilibrium
voltage between the two isolated internal capacitances is calculat ed to be
20.5 Experimental Results
A
3-input NAND
B
A
B
C
V dd
V = (Cint1 V1 + Cint2 V2) / (Cint1 + Cint2)
V
n
∑
∑
Both the probabilistic and the statistical techniques have been implemented in C within University of
California at Berkeley’s SIS [17] environment. SIS is an int eractive tool for synthesis and optimization
of logic circuits. The test circuits used in obtaining the results are the benchmarks presented at ISCAS
in 1985 [11]. These circuits are combinational circuits and Table 20.1 shows the number of primary
inputs, outputs, nodes, and circuit level of each benchmark circuit.
C
t 1
t 0
V1
Cint1
V2
n
Cj j=1
Cint2
( CjV j)
j=1
= ---------------------------
Cint 1 ⋅ V1 + Cint 2 ⋅ V2 V =
------------------------------------------------
+
C int 1
C int 2
C L