hspice book hspice ch10 1 Thu Jul 23 19 10 43 1998 Chapter 10 Analyzing Electrical Yields An electrical circuit must be designed to the tolerances associated with the specific manufacturing process The electrical yield refers to the number of parts that meet the electrical test specifications Maximizing the yield is important for the overall process efficiency Star Hspice analyzes the yield by using statistical techniques and observing the effects of element and model parameter variation Specifying Analytical Model Types Using Algebraic Expressions Using Built In Functions Using Parameters in Simulation Varying Parameters and Libraries Performing Worst Case Analysis Performing Monte Carlo Analysis Worst Case and Monte Carlo Sweep Example Simulating Circuit and Model Temperatures Star Hspice Manual Release 1998 2 10 1 hspice book hspice ch10 2 Thu Jul 23 19 10 43 1998 Specifying Analytical Model Types Analyzing Electrical Yields Specifying Analytical Model Types You can model parametric and statistical variation in circuit behavior in StarHspice by using The PARAM statement Use to investigate the performance of a circuit as specified changes in circuit parameters are made Monte Carlo Analysis The statistical standard deviations of component values are known Use for centering a design for maximum process yield or for determining component tolerances Worst Case Corners Analysis The component value limits are known Automates quality assurance for basic circuit function for process extremes quick estimation of speed and power trade offs and best case and worst case model selection through parameter corners library files Data Driven Analysis Use for cell characterization response surface or Taguchi analysis See Chapter 19 Performing Cell Characterization Automates cell characterization including timing simulator polynomial delay coefficient calculation There is no limit on the number of parameters simultaneously varied or number of analyses to be performed Convenient ASCII file format for automated parameter value generation Can replace hundreds or thousands of Star Hspice runs Yield analyses are used to modify DC operating points DC sweeps AC sweeps and transient analysis They can generate scatter plots for operating point analysis and family of curves plots for DC AC and transient analysis The MEASURE statement in Star Hspice is used with yield analyses allowing you to see distributions of delay times power or any other characteristic described with a MEASURE statement Often this is more useful than viewing a family of curves generated by a Monte Carlo analysis When the MEASURE statement is used a table of results is generated as an mt file which is in readable ASCII format and can be displayed in AvanWaves Also when MEASURE statements are used in a Monte Carlo or data driven analysis the 10 2 Star Hspice Manual Release 1998 2 hspice book hspice ch10 3 Thu Jul 23 19 10 43 1998 Analyzing Electrical Yields Specifying Analytical Model Types Star Hspice output file includes calculations for standard statistical descriptors Mean x1 x2 xn N Variance x 1 Mean 2 x n Mean N 1 Sigma Average Deviation Variance x 1 Mean x n Mean N 1 Star Hspice Manual Release 1998 2 10 3 hspice book hspice ch10 4 Thu Jul 23 19 10 43 1998 Using Algebraic Expressions Analyzing Electrical Yields Using Algebraic Expressions You can replace any parameter defined in the netlist by an algebraic expression with quoted strings Then use these expressions as output variables in the PLOT PRINT and GRAPH statements Using algebraic expressions can expand your options in the input netlist file Use algebraic expressions in the following ways Scaling or changing of element and model parameters Parameterization PARAM x 5 Algebra PARAM x y 3 Functions PARAM rho leff weff 2 leff weff 2u Hierarchical subcircuit algebraic parameter passing subckt inv in out wp 10u wn 5u qbar ic vdd ic qbar qbar ic ends Algebra in elements R1 1 0 r ABS v 1 i m1 10 Algebra in MEASURE statements MEAS vmax MAX V 1 MEAS imax MAX I q2 MEAS ivmax PARAM vmax imax Algebra in output statements PRINT conductance PAR i m1 v 22 Star Hspice uses double precision numbers 15 digits for expressions userdefined parameters and sweep variables For better precision use parameters instead of constants in algebraic expressions since constants are only singleprecision numbers 7 digits 10 4 Star Hspice Manual Release 1998 2 hspice book hspice ch10 5 Thu Jul 23 19 10 43 1998 Analyzing Electrical Yields Using Algebraic Expressions Algebraic Expressions for Output The syntax is PAR algebraic expression In addition to using quotations the expression must be defined inside the PAR statement for output The continuation character for quoted parameter strings is a double backslash Outside of quoted strings the single backslash is the continuation character Star Hspice Manual Release 1998 2 10 5 hspice book hspice ch10 6 Thu Jul 23 19 10 43 1998 Using Built In Functions Analyzing Electrical Yields Using Built In Functions In addition to simple arithmetic operations Star Hspice provides a number of built in functions that you can use in expressions for example The Star Hspice built in functions are listed in Table 10 1 Table 10 1 Star Hspice Built in Functions HSPICE Form Function Class Description sin x sine trig Returns the sine of x radians cos x cosine trig Returns the cosine of x radians tan x tangent trig Returns the tangent of x radians asin x arc sine trig Returns the inverse sine of x radians acos x arc cosine trig Returns the inverse cosine of x radians atan x arc tangent trig Returns the inverse tangent of x radians sinh x hyperbolic sine trig Returns the hyperbolic sine of x radians cosh x hyperbolic cosine trig Returns the hyperbolic sine of x radians tanh x hyperbolic tangent trig Returns the hyperbolic sine of x radians abs x absolute value math Returns the absolute value of x x sqrt x square root math Returns the square root of the absolute value of x sqrt x sqrt x pow x y absolute power math Returns the value of x raised to the integer part of y x integer part of y pwr x y signed power math Returns the absolute value of x raised to the y power with the sign of x sign of x x y log x natural logarithm math Returns the natural logarithm of the absolute value of x with the sign of x sign of x log x log10 x base 10 logarithm math Returns the base 10 logarithm of the absolute value of x with the sign of x sign of x log10 x 10 6 Star Hspice Manual Release 1998 2 hspice