A novel optical fibre gyroscope, with a structure making use of the co
mbination of a Sagnac interferometer with an active fibre ring-resonat
or, is proposed and analysed. It can be regarded as a generalised stru
cture of the conventional Sagnac interferometric fibre optic gyroscope
(SIFOG). Counter-propagating optical waves in the gyroscope can circu
late many times in the sensing loop into which an optical amplifier is
incorporated to compensate partially for optical losses of each circu
lation. The optical response is effectively the sum of the optical res
ponses of a series of conventional Sagnac interferometric fibre optic
gyroscopes having effective loop length equal to the fibre loop length
multiplied by the number of circulations. We show that the sensitivit
y of the proposed gyroscope can be two orders of magnitude higher than
that for a conventional SIFOG and that the minimum detectable nonreci
procal phase shift limited by the amplifier noise is nearly one order
of magnitude smaller than that of conventional SIFOG limited by quantu
m noise. These performance enhancements cannot be obtained by incorpor
ating an optical amplifier into the conventional SIFOG structure.