Both DoE and RSM modules work best if all system responses behave more or less linearly with respect to the control variables. Unfortunately, this behavior is very rarely encountered in real applications, To accurately model the system behavior, transformations of the parameter space are used to to linearize the dependence of the output variables on the transformed input parameters. Subdivision of the parameter space as well as fitting of the response surfaces takes place in transformed space.
For each input parameter, a transformation function can be selected from a set of predefined transformations. If the transformation function needs parameters ( transformation parameters), these parameters may either be specified explicitly, e.g., in the case when a physical formula has been established, or they may be determined automatically from a set of sample points. Additionally, it is also possible to select the best one of a given set of transformation functions for a given set of sample points. Thus, the user does not need to specify the transformation to use.
It is important to note that all transformation functions have to be defined by specifying code for both the forward and reverse directions and assigning a reference name to the transformation before they can be used. All information on transformations is stored centrally and accessed exclusively by the reference name. E.g., for a given technology, a transformation called vth-lg can be defined, which analytically reflects the short-channel effect and is used to linearize the dependence of the threshold voltage on the gate length for DoE and RSM.