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A distributed amp is a clever way to provide enormous bandwidths, as much as 100 GHz. Some distributed amplifiers can operate down to DC as well, so they are used as opto-electronic amps. The theory behind the distributed amplifier is that a number of FETs (at least two but more typically four, five or six) are fed by a periodic structure at the input that resembles a terminated transmission line. The combination of FET capacitance with the high-impedance connection lines resembles a lumped-element version of a fifty-ohm line. This trick is used to impedance match the input and output.
One limitation of distributed amplifiers is they don't make efficient power amplifiers. The load that each FET sees is not even close to optimum, and the signal distribution is such that some FETs get far greater voltage stress than others. They make mediocre LNAs for the same reasons.
Here are some pictures of distributed amplifiers. The first one is from Agilent.
Here's a cascode distributed amp, made by Bookham: