Statistical analysis for practical circuit design

Statistical analysis using the Monte Carlo method is shown to have significant value in the design of practical circuits. Three integrated circuit examples are described; a logic circuit with critical dc properties, a gate with stringent transient requirements, and a hybrid circuit which combines precise linear high-frequency and transient performance. Characterization and modeling problems are described in detail. A particular device family is described by deriving statistics for the parameters of a single nonlinear model, which is then used directly for dc and transient cases and can be linearized for ac applications. Parasitic elements are included for fast high-frequency applications. Complex performance criteria are derived in a post-processor in order that the results be expressed by figures of merit which are practically meaningful, such as noise immunity of a logic gate and operating margin of a digital repeater.