e resonant tanks is small. Note that the template in Fig. 5.28 does not cover all possible oscillator topologies. For example, the oscillator circuit in Fig. 5.9 cannot be mapped onto it. However, it is straightforward to adapt the method to handle more general templates. In what follows, we briefly step through the theory of the sections 5.3 to 5.6 as it applies to a system of coupled harmonic oscillators. 5.8.1.1 Normalizing and partitioning the circuit equations The equations that model a system of K coupled resonant tanks are given by dik Vk (5.142) 5.8 HARMONIC OSCILLATOR BEHAVIORAL MODELING (5.143) for k = 1,..., K. Here Ck and Lk respectively represent the effective capacitance and inductance of the k-th resonant tank. The currents ..,t) model the contributions of the transistor feedback together with the inductor and capacitor losses. In a first step, we normalize the system of equations (5.142). To do so, we change variables: (5.144) (5.145) (5.146) (5.147) (5.148) (5.149) Here, W0,k = 1/VLkCk is the resonant frequency of the k-th tank, Vk is an estimate for the magnitude of the voltage swing over the capacitor Ck and 1k,max is a measure for the maximum feedback current delivered by the controlled current sources. The variable E equals the ratio between the maximum feedback current 1k,max and the current Itank,k = W0,kCkVk = Vk/ (W0,kLk) circulating in the resonant tank. The Vk should be chosen such that E is the same for all tanks. Furthermore, it is assumed that all resonant frequencies W0,k cluster around the mean frequency W0, i.e. (5.150) were ESk is the (small) relative deviation of W0,k from W0. With (5.144)-(5.149), the system (5.142)-(5.143) becomes (5.151) (5.152) The right-hand sides of (5.151)-(5.152) clearly fall into two components. The first two terms correspond to the behavior of the lossless resonant tanks. The terms preceded by an E model the transistors currents, the tank losses and the resonant frequency mis- matches. Since all latter terms are small, at least for well-matched resonan