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A study is made of the design of broad-band (2: 1 tuning range) resonators for use with reflex klystrons of the external cavity type. The resonators considered are variations of a general type consisting of a section of waveguide with movable shorting plungers at each end and the tube located at the center. They are divided into two groups: quarter-wave or fundamental mode resonators whose high-frequency limit is set by the physical size of the tube envelope, and three-quarter-wave resonators which allow operation up to the electronic limit of the tube. Methods of treating the mode interference problem are considered for both classes of resonators.