Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation

After recalling the major disadvantages of integer order sinusoidal oscillators, we use noninteger order filters to make oscillators of fractional order greater than 2. These oscillators are unusual not only in their order but also in their properties, due to an uncommon form of the oscillator frequency as regards the direct production of low frequency sine waves. An algebraic performance criterion for the quality of systems just above the threshold of oscillation gives the optimum fractional order ensuring the sharpest tuning and the greatest frequency stability. The fact that the special form of the oscillation frequency in such systems satisfies the requirements of linearization of frequency modulation characteristics, is used in low frequency FM at large deviation and high linearity.