General procedure for two integrator loops fractional order oscillators with controlled phase difference

This paper studies the fractional order two integrator loop based sinusoidal oscillators with two fractional order elements of different orders. Two general cases have been discussed and closed forms for the oscillation frequency and oscillation condition are driven. In addition, the effect of the fractional orders on the phase difference between the two oscillatory outputs is also presented. Design procedure for the two general cases is illustrated with numerical examples and validated through circuit simulations for three examples of oscillators based on two integrator loops.