Laplace Transform Simulation Normalization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The accumulation of dynamic range in high-order Laplace transform systems leads to accuracy and convergence issues during circuit simulation, particularly in numerical methods, due to the large coefficients involved, which existing technologies have not effectively addressed.
Innovation Solution
A method and apparatus for Laplace transform system simulation that generates a high-order equation based on a transfer function, converts it into a state equation, and normalizes the coefficients by adjusting state variables with corresponding factors, resulting in a normalized state equation with a smaller dynamic range, thereby alleviating the accumulation of dynamic range issues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-order Laplace transform equations are used to model complex circuit behavior, then the system can represent more accurate component characteristics, but the dynamic range of coefficients accumulates and causes numerical accuracy and convergence problems
Solution Approach 1:
The high-order differential equation is segmented into multiple first-order differential equations by introducing state variables. This segmentation transforms the single complex equation with large coefficient dynamic range into multiple simpler equations, each with manageable coefficient ranges, thereby resolving the numerical stability issue while preserving the system's accurate behavioral representation
Solution Approach 2:
The patent applies parameter changes by normalizing the state variables through scaling factors. Each state variable is multiplied by a carefully chosen factor that adjusts its magnitude, effectively changing the parameters of the system to reduce the dynamic range of coefficients in the resulting difference equations, thus improving numerical convergence
2Adaptability or versatility
If the order of the Laplace transform system is increased to capture complex circuit behavior, then the behavioral description becomes more comprehensive, but the complexity of numerical computation increases
Solution Approach 1:
The complex high-order system is segmented into multiple first-order subsystems through state variable decomposition. This segmentation maintains the comprehensive behavioral description capability of the high-order system while reducing computational complexity by transforming difficult-to-solve high-order equations into simpler, more manageable first-order equations that are easier to simulate numerically
Solution Approach 2:
By introducing scaling factors and normalizing state variables, the patent changes the parameters of the computational system. This parameter transformation simplifies the numerical computation process by reducing the dynamic range of coefficients, making the simulation of high-order systems more computationally efficient and less prone to numerical errors
Data Source
AI summary
Disclosed are methods and apparatus for implementing system simulation. The method includes generating a high-order equation based on a transfer function that represents characteristics of at least one frequency-domain component in a circuit; converting the high-order equation into a state equation comprising a series of state variables, wherein the high-order equation and the state equation have corresponding coefficients for each order and state variable, and the coefficients of the state equation have a first dynamic range; and normalizing the coefficients for the state variables by adjusting each state variable with a corresponding factor to obtain a normalized state equation having normalized coefficients, wherein the normalized coefficients of the normalized state equation have a second dynamic range smaller than the first dynamic range. The method and apparatus improve accuracy of analyses for the system.