Steady-state analysis of parametric frequency changers

The operation of a parametric frequency changer of the two C-Core type is analyzed in both the frequency doubling and frequency halfing modes. The analysis begins with the formulation of two expressions which relate the flux in each core to the MMF's of the input and output circuits. A fifth-order polynomial is used to represent the nonlinear magnetization curve of the built-up magnetic structure due to the MMF of one side acting alone. An approximate solution to the nonlinear differential equation governing the output side leads to some interesting expressions for the required tuning capacitor, parametric power transfer, input and output currents, and the relationship between input and output voltages.