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In this paper, the relation between small-scale fade depth and channel bandwidth in an indoor environment is investigated. The fade depth, a measure of the signal power variability over a local region in space, is evaluated for narrowband, wideband and ultrawide-band channels. The experimental analysis is based on frequency-domain measurements in the 3.1-10.6 GHz microwave band. Physical insight into the fading process is provided, and the effect of increasing bandwidth and temporal resolution is discussed. A dual-slope empirical model is developed, which accurately describes the relationship between fade depth and channel bandwidth. It is demonstrated that the fade depth, considered at the three standard deviation values, converges to about 4 dB at 1 GHz bandwidth, and a further increase in bandwidth yields only a marginal improvement in fade mitigation.