 Dem00b], V1 (T) is called the oscillator's perturbation projection vector (PPV). Furthermore, the function (5.106) has been termed the impulse sensitivity function (ISF) [Haji98] associated with the input source u(t). This ISF is periodic with respect to T. Using the ISF, (5.105) is written as (5.107) The averaged phase behavior, i.e. the dominant slow-varying component that often grows unbounded, is then determined by (5.108) Here, we applied the ideal averaging operator (5.90) which, in this case, is often the most convenient one to proceed with. In many cases, the equations (5.107) and (5.108) capture the oscillator behavior that is of main interest. 5.7.2 Practical application: oscillator injection locking We illustrate the practical application of (5.107) and (5.108) by means of the study of an oscillator's injection locking behavior. To make the example more concrete, results are elaborated for the harmonic oscillator in Fig. 5.22(a). It is, however, straightforward to generalize them to other oscillator circuits. Moreover, all results that follow are described by means of symbolic expressions. This illustrates a powerful feature of the framework here presented: the ability to derive (approximate) symbolic expressions to describe the often complex nonlinear phenomena. In what follows, we study what happens when the harmonic oscillator in Fig. 5.22(a) is injected with a weak sinusoidal current (5.109) Here, wo is the oscillator's free-running frequency while, as usual, T = Wot is the nor- malized time variable. Iu is the amplitude of the injected current. Furthermore, the frequency wo + Aw of the injected signal u(t) is assumed to deviate only slightly from wo, i.e. Aw/wol << 1. The SPICE simulation result in Fig. 5.23 illustrates the kind of behavior that occurs: the oscillator's output signal phase-locks onto the injected signal. In literature, this phenomenon is known as injection locking [Adl46, Jez74]: an oscil- lator locks, both in phase and frequency, onto an externally injected signal. Injection loc