A novel approach to determine the start-up conditions in microwave negative impedance oscillator design

In the design of sinusoidal oscillators, it is possible to exploit linear CAD techniques to determine the start-up conditions. In microwave negative impedance oscillators, the start-up can be tested through the application of the Nyquist criteria at the open loop gain, that in this context can be represented by the product of both reflection coefficients in a section. This work presents a novel approach to determine the whole set of values of the reflection coefficients product for which the oscillation start-up and build-up, for a given frequency, are guaranteed under the small signal hypothesis. Therefore the well known start-up condition normally expressed in terms of impedances, has been translated in terms of reflection coefficients product. In this way for a specific reflection coefficient of resonant passive network, it is possible to draw the set of reflection coefficients values of active device, for which the presence of negative real part poles is achieved. Moreover it is going to be established a sufficient condition to determine the start-up for a given frequency. This condition define an area on the Smith chart (the Eye) which bind the choice of resonant circuit reflection coefficient. Finally we succeeded to define a criterion to choose the characteristic impedance value which guarantee the effectiveness of the common oscillation tests, used in CAD systems.