The theory is developed which describes analytically the gain and bandwidth
in frequency-multiplying gyro-traveling-wave-tubes. In this theory the inp
ut waveguide is considered in the small-signal approximation. Then, in the
drift region separating the input and output waveguides, the electron balli
stic bunching evolves which causes the appearance in the electron current d
ensity of the harmonics of the signal frequency. The excitation of the outp
ut waveguide by one of these harmonics is considered in a specified current
approximation. This makes the analytical study of a large-signal operation
possible. The theory is illustrated by using it to analyze the performance
of an existing experimental tube. (C) 2001 American Institute of Physics.