lysis: model creation, transformation and interpretation Input signal Output signal Dump nodal equations Numerical simulation Vin - VG Model transformation dud dt C.duG dt = (VG, UD) + VDD - UD Extract transfer function VD(s) Figure 2.4: Analyzing the behavior of a single-stage amplifier involves trans- forming one model for the amplifier into another one. The idea is to select those transformations that yield the most simple results and/or that empha- size that part of the amplifier's behavior in which we are interested. interested in the response to a particular input signal, a transformation involving nu- merical simulation is the way to go. When interested in the impact of the load capaci- tance CL on the gain-bandwidth product, symbolic transformations present themselves as suitable candidates. Of course, when the symbolic expressions become too compli- cated, results are useless and we need to try a different transformation. In short, the art of system and circuit analysis comes down to selecting the proper sequence of model transformations. As a final note, we address automated modeling and analysis. Creating the initial model is often hard to automate. Coming up with a suitable circuit topology or an adequate elementary building block (transistor) model will always require some inge- nuity. Transforming the models, however, can be automated if the transformations are formalized to the point that they can be written down as computer algorithms. This requires clear specification of the structure of the models that serve as an input. Fur- thermore, we must also state the conditions for the transformation to yield reliable results. Algorithms for symbolic analysis [Fern98], model-order reduction [Odab97] and numerical simulation [Kund97, Nag75] represent some well-known examples of automated model transformations. 2.2 GOOD MODELS FOR TELECOMMUNICATION FRONTENDS: ARCHITECTURES AND THEIR BEHAVIORAL PROPERTIES RF in RF in Figure 2.5: Frontend architectures of (a) a heterodyne receiver and (b) a low- IF receiver.