A linear theory of 3-pole oscillators

Modified `y¿ parameters are defined, which are applicable to 3-terminal networks. The use of these parameters simplifies the calculations, by preserving the algebraic symmetry throughout. The three values of loop gain of any active 3-pole network are evaluated, and a simple relationship between their real maxima is shown. It is established that, for a maximum real loop gain, the optimum passive 3-pole network to be connected to any active 3-pole network is purely reactive. The admittance matrix of the reactive 3-pole network is evaluated and the maximum permissible loading on any pair of terminals is determined. Equivalent results have been obtained by Page and Boothroyd. A simple relationship between the three values of maximum real loop gain and the three maximum permissible loadings is established. The condition that a given active 3-pole network shall be capable of oscillating at a given frequency is derived. An equivalent condition has been produced by Mason, using a different approach.