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The generation of microwave radiation at gigahertz frequencies in high-voltage, high-current, pulsed-power diodes has been investigated both with electromagnetic particle-in-cell simulations and laboratory experiments. Pulsed power in the form of a 1.2-4.5-MV 60-ns TEM wave is fed to the diode by a coaxial line consisting of a 3-cm-diameter anode and a 2-cm-diameter cylindrical stalk terminated by a hollow cathode. A thin aluminized plastic foil, serving as a grid, is placed in front of the cathode. The high-voltage pulse is magnetically insulated by a 75-95-kA current flow within the cathode stalk, producing a field-emitted electron flux from the cathode tip. As the electrons pass through the grid into a 6-cm-diameter cylindrical waveguide, the space-charge limiting current within the guide is exceeded, and a virtual cathode is formed. A large percentage of all subsequently emitted electrons reflex between cathode and virtual cathode, in accordance with the Barkhausen-Kurz description. By varying the distance between the cathode and grid, a tunable and discrete set of subgigawatt modes is produced in the X, Ku, K, and Ka microwave bands.