Patent Publication Number: US-2005117510-A1

Title: Cell Current ReConstruction Based on Cell Delay and Node Slew Rate

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
      R. Marchulescu, D. Marculescu and M. Pedram, “Switching Activity Analysis Considering Spatiotemporal Correlations”, Proc. of ICCAD, 1994. Ghosh, S. Devades, K. Keutzer, and J. White, “Estimation of Average Switching Activity in Combinational and Sequential Circuits”, Proc. of the 29 DAC, pp. 253-259, June 1992.  
     BACKGROUND OF THE INVENTION  
      A lot of recent VLSI applications are getting larger and faster. Among them, the mobile systems require lower power as more functions are integrated into the system. Generally, the methods to build the low power system are controlling the threshold voltage, or reducing the supply voltage. However, the low power system results in lowering of speed and decreasing the noise immunity, which debases the reliability of the systems.  
      IR-drop analysis and power (or current) estimation of the design are the major activities for the low power system. Conventionally, the current and IR drop estimation can be obtained with the circuit simulators, such as spice simulator, time-mill or rail-mill by Synopsys. But the problems of estimation lie in the capacity and performance of circuit-level simulators. The circuit level simulators cannot perform the VLSI design if it has more than tens of thousands of transistors. Even though they can provide accurate analysis, these can hardly do full-chip simulation. It takes so much time to simulate SoC full-chip that it cannot be applied to analyzing the recent SoC designs. This is why gate-level power estimation is more acceptable than transistor-level for analyzing SoC design.  
      In gate-level power estimation, probabilistic methods seemed efficient if we did not consider correlation among signals in the design. Since these techniques treated only density of the transition, we could get only the average value of the power consumption, not any peak one. Instead of the probabilistic method, the switching information of gate-level simulator is-applied to the power analysis. Since the switching period of each component consumes over 90% of total power consumption of each component, the transition activity of each component is an essential factor to analyze the power estimation.  
      The development of power estimation technique at gate level gives great help to predict the average power consumption of system, because it provides useful accurate information, which is less than 10% error compared with silicon measurement. Although the average value is very meaningful to know about the thermal effect, EM (Electo-Migration) phenomenon, and the required PAD counts, but the peak current of system and IR-drop at the net of component are dominant factors to determine the exact timing violation at the VDSM.  
      There is a simple technique to get the peak value of the power; dividing the simulation periods into pieces and performing power estimation. However, these values are merely the average current of pieces of simulation periods, and we might miss the peak current value caused by consecutive events. There are few researches to predict the peak system power until now. Our method is to find the active window period and re-construct the current of a cell to find peak power consumption and peak IR-drop value. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       FIG. 1 . The starting time and the ending time of an event of Z  
       FIG. 2 : (a) extension from event point by slew rate  
       FIG. 2 : (b) result of extension of (a)  
       FIG. 2 : (c) Current window of a cell in case of non-zero interconnect delay  
       FIG. 3 . Adjustment of the current based on the real Vdd and Idd 
    
    
     DETAILED DESCRIPTION  
      The Method to Find Current Window from the Events and Delay Calculation of a Cell  
      It is obvious that switching current of a cell flows only when the cell activates. The power of a cell is the average current in the simulation period. During the simulation period, the peak current value is much larger than the average one because the dormant period of a cell is normally much longer than the active period. To detect the peak current value, we should know the current window period and the total charge quantity. Our basic idea on current window is to employ the event time and slew rates of signals and extends twice to get the accurate starting and ending event time.  
      From the result of logic simulator like VCD(Value Change Dump) file, we can get logical starting and ending time point. In  FIG. 1 , the event of B occurs at t 2 , which causes the event at Z at t 3 . It looks like that the t 2  and t 3  are starting time point and end time point, respectively. However, the signals of B and Z have the transition time, which is called by slew rate computed by delay calculation. To consider the effect of signal transition time, we extend the starting time by the slew rate of B to get t 2   −1  and the ending time by that of Z to get t 3   +‘ in  FIG. 2 .  
      In addition to extension for slew rate of Z, one more extension is performed as shown in  FIG. 2 -( c ) to consider the interconnect delay, which is becoming dominant delay in VLSI designs. After two extensions, we can obtain the whole window (t 2   −1  and t 3   +2 ) for an event to arrange the current of a cell. In our approach, there is no current outside current window while the existing method always takes the average current derived by power consumption.  
      The Method to Construct Current Waveform  
      In  FIG. 1 , considering the (vdd) supply node and the current (idd), the idd is divided into intrinsic-current (I intrinsic ) and load-current (I load ), as shown at  FIG. 1 . I intinsic  can be obtained by the energy value of the event from the power library. The energy value is essential to get the peak-to-peak value of the current. After finding current window, the proposed method finds the I intrinsic  is as follows, 
          1 .Find the power value from the library with slew rate and output load using interpolation     2.Compute the current I intrinsic  (t) between events or locate user-defined PWL waveform        

      In case of knowing the current waveform and calibrating it already, we just lay the current waveform on the activation window. Otherwise, we have to re-construct the current shape keeping the total energy value. The shape is user-defined variable. For simple explanation, we use rectangle shape in this patent. The value E from library is an average energy value when the event occurs at every I ns. So the current value is 
 
 E=∫i ( t )* v ( t ) dt=I   intrinsic   *V   DD   *T   window /1( ns ) 
 
 where v(t) is constant V DD . Thus the final current value is  
         I   intrinsic     =         V   DD   *     ⁢     T   window   *     ⁢   1.09     E         
 
 at  
               t   2     -   1       ≤   t   ≤     t   3     +   2               (   1   )             
 
      Note that I intrinsic  reflects internal current only. We should re-construct current waveform for load capacitance independently. The load current is computed based on the slew rates, effective start and end rate of the current wave, which is represented by x %-y %. The begin and end charging time pair is computed by the (x, y) pair, the segment is obtained by extending each of the pair to the level 0 and level 1 value, respectively. For example, if the slewrate is 35-65%, (35, 65) the segment of the slope and offset are obtained from the pair (the time of 65%, the time at 35%). And the charging time begins at the cross point of the segment at 0V, and ends at the cross point of the segment at 5V. The charge Q of the cell during the period is as follows,  
       Q   =         C   eff     ⁢   V     =         ∫     t   ⁢           ⁢   1       t   ⁢           ⁢   2       ⁢       i   ⁡     (   t   )       ⁢     ⅆ   t         =       ∫     t   ⁢           ⁢   1       t   ⁢           ⁢   2       ⁢         i   m     ⁡     (   t   )       ⁢     ⅆ   t                 
 
 while t 1  is the time when voltage level 0, and t 2  is the time when voltage level 1. The i(t) is modeled by i m (t) which is one of the average value, trigonometry, and diamond shape. For example, if we use average value, the I load  is  
       Q   =         C   eff     ⁢   V     =         ∫     t   ⁢           ⁢   1       t   ⁢           ⁢   2       ⁢       i   ⁡     (   t   )       ⁢     ⅆ   t         =       l   load   *     ⁢   Λ   ⁢           ⁢   T             
         I   load     =             C   eff     ⁢   V               T   load               
 
 at  
               t   3     -   1       ≤   t   ≤     t   3     +   1               (   2   )             
 
      In the post-layout stage, C eff  is not equal to C total  any more because there are resistive properties in interconnect line, which prevent the driver cell from driving all capacitances simultaneously. Thus, there are delay called interconnect delays, T interconnect . In this patent, we think the interconnect capacitance is C interconnect =(C total C eff ) simply. Then, the interconnect current is,  
         I   interconnect     =         C   interconnect     ⁢   V       T   interconnect           
 
 at  
         t   3     +   1       ≤   t   ≤     t   3     +   2           
 
      The total current of a cell is, 
 
 I   total   =I   cell ( t )+ I   load ( t )+ I   interconnect ( t ) 
 
      The Simple Current Adjustment Considering the Variation of Non-Ideal Voltage Source  
      Since the computed current values are obtained from the ideal voltage source, present invention includes the adjustment procedure to have realistic value. The V dd  and I dd  from the source are sometimes pulled down to the marginal level, due to the long distance or overload, so the analysis should concern the dirty V dd  and I dd  to get the correct and realistic result. The adjustment procedure is based on the following mathematical background. By using the voltage value of previous time step, we compute a new current value, 
 
 i   dd ( t )= I   Ideal   ={V   dd ( t−uts )/ V   Ideal }   2  
 
 where uts is unit time step. 
 
      Present invention emphasizes on not only the power value of a cell (or a gate), but also the activation time to figure out the current waveform of a cell(or gate). The accurate analysis of cell current is fundamental to examine peak system current and peak IR-drop. By constructing the cell current of a design, we can get the peak system power by just summation of cell current at each time point