The Nonlinear Theory of a Class of Transistor Oscillators
D. Hester · IEEE Transactions on Circuit Theory · 1968
The nonlinear theory of a class of transistor oscillators linear differential equation of the form is developed, using the Ebers-Moll large-signal model for the transistors. Simplified versions of tuned-collector, tuned-base, and Hart ley transistor oscillators are shown to be characterized by a nonlinear differential equation of the form\ddot{x} - \mu[e^{a \dot{x}} - \kappa e^{(a+b)\dot{x}}] + \gamma \dot{x} + x = 0where\mu, \kappa, \gamma, a, andbare positive constants and\kappa\ll 1. Approximate solutions of the above equation, which are derived in a very simple manner using the phase plane approach, are compared favorably with experimental results. A push-pull version of the tunedcollector oscillator characterized by the above equation with the exponential terms replaced by hyperbolic sines is discussed.