A gridded microwave tube contains a cold cathode, an anode, and a grid located between the anode and cathode. In one embodiment, the cold cathode has a refractory metal substrate (30,50,60,70,80,90) and carbon nanotube emitters (32,42,53,62,73), the emitters (32,42,53,62,73) having a diameter of 1 to 300nm and a length of 0.05 to 100µm. The grid-cathode spacing is 1 to 100µm, the grid (34,43,54,63,74) contains apertures having a maximum dimension of 0.5 to 100µm, and the grid thickness is 0.1 to 50µm. Emission from the cathode directly onto the grid material itself, which undesirably heats the grid, is reduced by either (a) the presence of a shadow mask (33) between the grid (34) and the emitters (32) or (b) selective formation of the emitters (42,53,62,73) on the surface of the substrate (50,60,70,80,90). The microwave tube operates at a frequency of greater than 0.5GHz, advantageously greater than 2GHz.
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