Behavioral models of microwave circuits with fading memory

This particular circuit is meant to be a transistor `analog' of a high-frequency microwave transistor [13]. In addition to acting as an ampli er, this circuit also tries to mimic certain (memory dependent) charge storage e ects which should be active in this example in a frequency range around 0.5 kHz. Models are also built from numerical models and data from simulations. The notion of a system having \fading memory" is that input signals far in the past should have almost no e ect on the present state. A precise mathematical de nition of this concept is usually stated in the space of input/output functional (integral) equations. Boyd and Chua hint that the notion of fading memory should also have a (di erential) state space formulation [4]. In the following example, we show that the essential ingredients of such a state space formulation is that the attracting solution should forget both its initial condition and input sequences far in the past. Both conditions are usually ful lled if the system has a unique attracting xed point. Consider a closed RC circuit driven by a voltage source vs. The voltage around a closed loop is