 oscillator modeling methods presented in chapter 5 proceed by gradually transforming a set of circuit equa- tions into a more compact description. Even techniques for numerical simulation can be considered as model transformations. Here, the key observation is to recognize that simulation methods produce models that capture input-output behavior by means of (input signal, output signal) tuples. Hence, the models that result from numerical simulation can be described as Msim={(x1(t),y1(t));(x2(t),y2(t)) (2.1) were the Xk(t) represent vectors of input signals and the yk(t) vectors of corresponding output signals. The example at the end of this section illustrates this model transfor- mation process for a single-stage amplifier. At each stage in the process of modeling and analysis, we often have numerous possible transformations to proceed with. Which one to choose? Choice of a proper model transformation should be driven by the target we have in mind. Which part of the system's behavior is of greatest interest to us? Which kind of input signals are we dealing with? For example, if we want the resulting model to be parameterized, e.g. to be of use for trade-off analysis, the transformations should least partially- be symbolic in nature. If we are interested in the response to a limited set of input signals, numerical simulation might be the way to go. Note that in almost all cases, we want the resulting model to be as simple as possible. Example (Analysis of a single-stage amplifier): Fig. 2.4 illustrates modeling and analysis for a single-stage amplifier. The starting point is a parameterized netlist. New models are derived by transforming this netlist model. A typical transformation, for instance, involves dumping the modified nodal equations. These equations in turn serve as a starting point for further transformations. The transformations that we select should be driven by the interest in mind. This inter- est corresponds to what we want to know about the amplifier and its behavior. When 2.1.5 Modeling and ana