Maximum instability curves of a microwave series-feedback oscillator

An analytical approach to acquire the maximum instability curves of a two-port microwave series-feedback oscillator for the design of its feedback network is presented. This approach is given by utilizing inequality expressions of the input reflection coefficients Γ_in and Γ_out of a two-port series-feedback network defined at port 1 and port 2 with a feedback termination Γ_SF. Then the explicit expressions are derived for the maximum instability curves in the Γ_SF-plane to lead one to properly design the feedback network based on the instability consideration. For the selected Γ_SF value, the conditional instability regions of Γ₁ and Γ₂ can also be calculated for the design of the loads 1 and 2. The resulting instability expressions are implemented in the Agilent ADS software to enhance its computer-aided capability on the design of microwave oscillators.