IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 19, NO. 11, NOVEMBER 2000 1363 Short Papers_______________________________________________________________________________ Estimation of Power Dissipation Using a Novel Power Macromodeling Technique Zhanping Chen, Kaushik Roy, and Edwin K. Chong Abstract—In this paper, we develop a novel technique based on Markov chains to accurately estimate power sensitivities to primary inputs in CMOS sequential circuits. A key application of power sensitivities is to construct a complicated power surface in the specification-space so as to easily obtain the power dissipation under any distribution of primary inputs, thereby of- fering an effective power macromodel for high-level power estimation. We demonstrate that such a power surface can be approximated by only a lim- ited number of representative points. This benefit dramatically reduces the CPU and memory requirements. We have verified the feasibility and accu- racy of the new technique to estimate power sensitivities on a large number of sequential benchmark circuits. Results on the power dissipation under different distributions of primary inputs demonstrate the efficiency and ef- fectiveness of our power macromodeling technique. Index Terms—Estimation, modeling, power modeling and estimation, simulation, symbolic simulation, symbolic techniques, VLSI. I. INTRODUCTION The increasing use of portable computing and communication sys- tems makes power dissipation a critical parameter to be minimized during circuit and system design [5], [17]. Hence, there is a great need for tools to accurately estimate power dissipation at various levels of design abstraction. Research on power estimation has started in earnest [14], however, most of the research concentrates on the logic level. In order to shorten design time and reduce design iterations, we have to estimate power dissipation at a high level of abstraction. One of the main objectives for high-level power estimation is to develop a power macromodel for a module so that power dissipation can be easily obtained under dif- ferent distributions of primary inputs [12], [13], [15], [16], [18]. When the same module is reused, we can obtain its power by simply using a look-up table. A good macromodel must be able to determine the power under dif- ferent primary input distributions. Since power dissipation of a circuit is strongly dependent on the statistics of primary inputs, the relation- ship of power versus primary input probabilities (probability of a signal being logic ONE) and activities (probability of signal switching) is a complicated surface. Once such a surface is set up, power dissipation under different distributions of primary inputs can be easily obtained. However, to construct such a power surface, a large number of dis- crete points are required. If one chooses representative values for the probability and activity of each primary input, the number of represen- tative points in the specification-space can be ( is the number of primary inputs). Hence, to generate the power surface, a symbolic or statistical power estimation process has to be repeated times. For Manuscript received September 14, 1998; revised July 2, 2000. This work was supported in part by DARPA under Grant F33615-95-C-1625, by the Na- tional Science Foundation (NSF) under CAREER Award 9501869-MIP and 9501652-ECS, and by IBM and AT&T. This paper was recommended by Asso- ciate Editor E. Macii. Z. Chen is with Intel Corporation, Hillsboro, OR 97124 USA. K. Roy and E. Chong are with Purdue University, W. Lafayette, IN 47907 USA. Publisher Item Identifier S 0278-0070(00)10294-5. large circuits with large number of inputs, such a process is obviously impractical due to the exponential growth of complexity. Moreover, the memory or storage complexity is . In this paper, we present a novel macromodeling technique based on power sensitivity. The basic idea of our technique is to use a lim- ited number of representative points in the specification-space to ap- proximate a complicated power surface. Power dissipation under dif- ferent distributions of primary inputs is calculated by considering the representative points and power sensitivities. The power macromod- eling technique can be applied to both combinational and sequential circuits as long as efficient techniques to estimate power sensitivities are available. In [7] and [9], symbolic and statistical techniques have been proposed to estimate power sensitivities in combinational circuits. In this paper we present a novel approach based on Markov chains to ac- curately estimate power sensitivities in sequential circuits. The power sensitivities are then used to develop the power macromodel to estimate power under different distributions of primary inputs. II. PRELIMINARIES A. Power Dissipation in CMOS Logic Circuits Among the three sources of power dissipation—switching current, short-circuit current, and leakage current—switching power is by far the most dominant in current technology. Thus the average power for a CMOS circuit can be approximated by , where is the supply voltage, is the node capacitance, is the activity at node . Since is proportional to the normalized activity [ , where is the clock frequency] and is approximately proportional to the fanout at node , we can define the normalized power dissipation measure as (1) where is the fanout number at node . B. Power Sensitivity To measure the effect of the variations of primary input specifi- cations on power dissipation, we define power sensitivity to primary input activity and power sensitivity to primary input probability as where and are the activity and probability of primary input , respectively. is proportional to . Therefore, we can define normalized power sensitivity to primary input activity and normalized power sensitivity to primary input probability in terms of as follows: (2) (3) where is the activity of node . For simplicity, we can refer to and as activity sensitivities. 0278–0070/00$10.00 © 2000 IEEE