Forced oscillations and waves in active non-self-oscillatory systems. Turbulence. Burst instability. Excitation of waves with negative energy

Abstract

An amplifier is a system transforming and intensifying a signal arriving at its input (Fig 14.1). It is evident that, to perform these functions, the amplifier must include Figure 14.1: Block design of an amplifier an energy source, i.e., it must be an active system. First of all we consider a linear amplifier, viz., the amplifier with gain factor independent of the input signal magnitude. In this case the superposition principle is valid, i.e., different components of the input signal x(t) are amplified independently of one another. Internal fluctuations inevitably present in each amplifier can be taken into account by means of adding a certain effective noise ξ(t) to the input signal x(t). If x(t) = 0 and (t) is white noise with intensity N then the noise power spectrum at the output of the amplifier is determined by the dependence of the gain factor k on the frequency of the input signal ω. Let this dependence be described by a complex function k(ω). Then the noise power spectrum at the output of the amplifier is S(ω) = N | k(ω) Even with small intensity of the input noise N the output noise can be quite large, if the gain factor k is large. It follows from this that for the correct description of the operation of such an amplifier we cannot ignore fluctuations, both external and internal. As mentioned above, the power spectrum at the output of a linear amplifier with a white noise at its input is determined by the frequency response of the amplifier. In the case that a gain factor has a clearly defined resonance character, the signal at the output of the amplifier can be not dissimilar in aspect to the output signal of a self-oscillatory system. Open image in new window Fig. 14.1 Block design of an amplifier.