Conventional emission-gated amplifiers use a gridded, thermionic cathode to density modulate the beam before it is accelerated to anode potential, the advantages of such beams being well established. At higher frequencies (2-18 GHz), field-emitter arrays (FEAs) are being developed for emission gating. Future FEA-driven amplifiers promise great efficiency and compactness-advantages which are critical in applications such as the vacuum power booster in the Microwave Power Module (MPM). A need presently exists for a methodology to analyze system performance and to evaluate research alternatives. This paper offers such a methodology. Specifically, it predicts the performance of FEA-driven klystrode and twystrode amplifiers. Power, efficiency, gain, bandwidth, and size are analyzed in terms of fundamental parameters, such as the FEA tip radius. Geometries and performance ranges of currently available FEAs are emphasized. Thin-annulus beam optics and other relevant constraints are developed as required. The fundamental relationships are described mathematically to simplify understanding. For example, the RF-convoluted Fowler-Nordheim equation is integrated analytically to obtain the current ratio, a critical parameter connecting input (FEA) and output circuits. Whereas simulation codes are used extensively (e.g. MAGIC is used to predict output circuit efficiency), all parametric results are reduced to simple expressions. As a consequence, it is possible to express the gain-efficiency-bandwidth product in terms of FEA excitation voltages, capacitance, and Fowler-Nordheim constants. Other examples will be presented. The entire end-to-end analysis has been reduced to a single nomogram, and it is also available in spreadsheet form.