Matrix Analysis of Oscillators and Transistor Applications

The use of matrix techniques leads to the classification of feedback, harmonic oscillators into four basic types. The oscillator is considered to be made up of two two-port networks: one contains the active element; the other, the feedback network. The equations for oscillation are expressed in terms of the two-port parameters. The method is applied specifically to the Hartley and Colpitts oscillators and their duals. The use of matrices in the analysis brings out the similarities between the oscillators. The Colpitts and Hartley circuits are of one class and require a small L/C ratio to reduce the effect of the active element upon frequencies, whereas their duals require a small C/L ratio. While the equations are derived for the low frequency case, two methods of high-frequency analysis are presented. The application of the equations to transistors is considered and several practical circuits for the dual oscillators are given. A short discussion of the bias elements and their effect on frequency and starting conditions is also included.