Summary form only given. Inductive output amplifiers (IOAs) such as twystrodes and klystrodes use an emission-gated beam in which the emission current density is modulated. Although emission gating offers clear advantages in efficiency and compactness, it makes stringent demands on the cathode structures where the gating occurs. Recent improvements in gated field-emitter array (FEA) technology provide a new alternative to thermionic electron sources for emission gating at frequencies above UHF; this new opportunity, however, is subject to the integration of FEA technology into the vacuum-tube environment. The gain, efficiency, and power output of an inductive output amplifier are contingent upon the current-voltage characteristic and high-frequency impedance of the gated cathode. A model, called the "end-to-end analysis", has been developed to examine quantitatively the design specifications for such cathodes. We will present a specific set of design curves for an IOA (a twystrode) having field-emission cathode, to recommendations for mutual optimization of the FEA and the output leading circuit of the IOA. Progress in the realization of an experimental twystrode based on these guidelines will be described, including perveance, focusing, and beam quality considerations. The cathodes being fabricated for this tube are gated, low-voltage FEA cathodes having record densities of Mo field-emission tips. These cathodes will be discussed, with specific emphasis on how requirements for emission-current density, current/tip, transconductance, capacitance, and cathode layout are being satisfied. Scaling and optimization of key parameters such as cathode transconductance and device reliability will be described. An important issue for the twystrode is the realization of a broadband (/spl sim/one octave) cathode input matching circuit. S-parameter measurements of the input impedance of the cathodes will be presented, together with the design of a cathode input circuit having an octave bandwidth.