Systematic effects important to separated-oscillatory-field measurements of the $n$$=$$2$ Lamb shift in atomic hydrogen

We evaluate a number of systematic effects that are important for an experimental microwave measurement of the $n$$=$$2$ S-to-P intervals in atomic hydrogen. The analysis is important for both re-evaluating the best existing measurement [Lundeen and Pipkin, PRL 46, 232 (1981)] of the 2S$_{1/2}$-to-2P$_{1/2}$ Lamb shift, and for a new measurement that is ongoing in our laboratory. This work is part of a larger program to understand the several-standard-deviation discrepancies between various methods for determining the proton charge radius.