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U. Glaeser

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Therefore, when dealing with low-activity nodes, instead of using Eq. (20.5), the following stopping<br />

criterion is used<br />

© 2002 by CRC Press LLC<br />

s⋅zα/2 N ⎛--------------⎞ ⎝ ⎠<br />

2<br />

≥<br />

η minε 1<br />

(20.8)<br />

For (1 − α) confidence level, the accuracy for the low-density nodes is given by η – n<br />

ηminε1. ≤ szα/2/ N ≤<br />

During the simulation run, after N exceeds 30, Eq. (20.5) is used as a stopping criterion as long as<br />

Otherwise, Eq. (20.8) is used instead.<br />

n ≥ η min.<br />

Power Estimation due to the Internal Nodes<br />

We included the capability of estimating internal nodes power dissipation in the Monte Carlo technique.<br />

The algorithm to compute the internal nodes power is as follows [7]:<br />

• Inputs: Functional expression of the node in terms of its inputs, and user-specified accuracy<br />

parameters<br />

• Output: Normalized power measure φ<br />

• Step 1: Factorize the functional expression<br />

• Step 2: Generate a graph to represent the expression<br />

• Step 3: Simulate the circuit with random input<br />

• Step 4: Update conducting path (event-driven process)<br />

• Step 5: Sum all charges in the discharging path<br />

• Step 6: Accumulate all the sum<br />

The given functional expression of a node is expressed in terms of its inputs. The factorization process,<br />

the same as in the probabilistic technique, is to ensure that the expression is compact and does not<br />

contain any redundant items.<br />

Graph Generation<br />

A graph to represent the factorized expression is generated to be used as the data structure in estimating<br />

power dissipation. The nodes of the graph represent all the nodes in the logic gate, such as supply rails,<br />

output node, and all the internal nodes inside the logic gate. The edges of the graph represent the inputs<br />

to the logic gate between the nodes. Information of the internal nodes capacitances and voltages are<br />

stored in nodes structure of the graph. Once the graph is generated, the circuit is simulated with randomly<br />

generated input vectors conforming to the user-specified input signal probability and activity.<br />

Note that in the case of the probabilistic method, a graph is not used, as there is no need for such<br />

data structure. In the probabilistic method, the signal probability and activity of each node are calculated<br />

as we traverse level by level from primary inputs of the circuit network to the outputs. The calculated<br />

values are then stored in the data structure within the node itself. In the statistical technique, however,<br />

the graph is needed to store the simulation run results. An example of a generated graph for a given<br />

factorized functional expression X =<br />

( AB+ C+ D)<br />

( E+ F)<br />

is shown in Fig. 20.9.<br />

Updating Conducting Paths<br />

The path in the graph needs to be updated whenever a change in the input signals occurs. The change<br />

in the input signals is defined as an event. To improve the computation speed, the updating process of<br />

the path is being done only when an event occurs. Hence, the path updating process is said to be an<br />

event-driven process.<br />

The path in the graph that needs to be updated may change from conducting to nonconducting or<br />

vice-versa, depending on the event which occurs. If the path becomes nonconducting, then the nodes at

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