amb98a], it is more common to say that the system behaves in a weakly nonlinear manner. 2.2.2.2 Widely spaced time constants Many wireless applications transmit their information by upconverting it to the GHz frequency range or beyond. For example, GSM operates in the 900 MHz frequency 2.2.2 Properties of frontend building block behavior T slow 1/finfo carrier Figure 2.7: Many wireless applications transmit information by upconvert- ing it to the GHz range. This results in signals containing widely spaced time constants. The carrier introduce a fast time constant fast while the upcon- verted information induces a slow time constant Tslow. band, DCS1800 in the 1.8 GHz band while wireless LAN (WLAN) applications op- erate near 2.4 GHz (ISM band) or 5 GHz (military applications). Signal bandwidths, however, are often orders of magnitude smaller. GSM bands are, for instance, 200 kHz wide while WLAN bands occupy a few MHz. Hence, the rate at which information is transmitted is well below the carrier frequency, or finfo < fcarrier (2.2) The resulting signals, illustrated in fig. 2.7, can be described as rapid oscillations with a slowly modulated amplitude and phase. This kind of behavior can also be generated by a building block's internal transient dynamics. For example, both high-Q harmonic oscillators and PLLs settle at a rate that is much slower than that of their steady-state output oscillation. Traditional SPICE-like simulators [Nag75] experience a great deal of trouble in eval- uating this kind of behavior. As illustrated in Fig. 2.8, the time step Tsim with which simulations proceed is inversely proportional to the highest signal frequency, or (2.3) The total time interval Tsim over which simulations are performed is typically a multiple of the length of a single information symbol, or Tsim~Thro N (2.4) 2.2 GOOD MODELS FOR TELECOMMUNICATION FRONTENDS: ARCHITECTURES AND THEIR BEHAVIORAL PROPERTIES Tsim~N/finfo Tsim~ 1/fcarrier Figure 2.8: The time step Tsim with which Spice-like simulations proceed is inversely 