The rapid bifurcation of the Wien bridge oscillator

The Wien bridge oscillator is analyzed for a piecewise linear saturation model of an operational amplifier. This model predicts a discontinuous or jump transition to an oscillatory state as the amplifier's gain
K
is increased past a critical level
K_c
. This vertical bifurcation yields a large oscillation which possesses intervals of saturation during a period. Moreover, the concomitant distortion grows rapidly as
K
is increased past
K_c