AM-to-PM Transfer as Reflection of Phase Concavity

Modern communications systems that involve nonlinear, high-power amplifiers, and linearizers typically have many specifications on linearity, including nonlinear phase shift, amplitude modulation-to-phase modulation (AM-to-PM) conversion, carrier-to-third-order-intermodulation (C/3IM) separation, noise power ratio (NPR), and AM-to-PM transfer. For large(ges10 db) carrier separations and high gain linearity, we demonstrate that AM-to-PM transfer in traveling-wave tube amplifiers is approximately proportional to the second derivative of the RF phase versus input drive curve (phase concavity), with a negligible contribution from phase slope. The validity of this approximation improves as the amplifier transfer characteristic approaches that of an ideal limiter. This result allows insight into the AM-to-PM transfer behavior and prediction of the metric with minimal computation. This also allows one to more easily understand the trades involved when optimizing between AM-to-PM transfer and other linearity figures of merit (such as C/3IM).