Repetitive Analysis

A repetitive analysis is to be understood as calculation of the same characteristic function of the circuit, for example frequency characteristic or step response, by many changes of some parameters of the circuit. A better way to achieve a high speed of this type of calculation is to determine the characteristic function as the numerical and symbolic expression, where numerical coefficients depend on the circuit topology and the value of the fixed parameters while only variables are symbolical parameters. For example any characteristic function of linear system with 2 symbolical parameters y₁, y₂ can be expressed as:

RAN1 program - an example of the repetitive analysis:

When we use formula presented above:

• Simulation time is independent of circuit complexity.
   
• A(f): for each frequency point 8 complex numbers N₀, N₁ ... D₃  have to be determined in the preparation phase .
   
• h(t): 8 polynomial numbers N₀, N₁ ... D₃ with amount of "digits" equal to number of the time samples have to be determined in the preparation phase.

RAN5 - The repetitive analysis of circuits containing transmission line. Basic operations, as well as functions such as square roots or exp() can be calculated in polynomial number domain.