Pound circuit-induced frequency sensitivities in ultra-stable cryogenic oscillators

The Pound technique is widely used in ultra-stable cryogenic oscillators to prevent frequency drift due to variations in the path delay between room-temperature electronics and the cryogenic resonator. We calculate frequency sensitivities to several other microwave signal corruptions that are not rejected by the Pound technique. Considering only linear circuit elements, we identify a quadratic variation of phase with frequency and a linear variation of amplitude with frequency as the lowest order processes that can induce frequency offsets. As an example, we evaluate the consequence of this frequency sensitivity for thermally induced frequency variation in an image-rejection filter.