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A fully printed fractal-perturbed resonant-type composite right/left-handed transmission line (CRLH TL) is proposed with electrically smaller dimensions. The CRLH structure consists of Koch-curve-shaped complementary split ring resonators etched on the ground plane and capacitive gaps embedded in the Koch-curve-shaped conductor line. A generic modelling technique for a set of resonant-type circuits, demonstrated to be extremely useful in the accurate extraction of the circuit elements, has been developed for the first time based on the effective medium concept. With the help of this modelling method, a quarter-wavelength impedance transformer (QIT) made of the CRLH TL is readily synthesised. The full fractal perturbation gives rise to the large lumped circuit elements which predict a significantly lower resonance. To demonstrate possible applications of the CRLH QIT, a Wilkinson power divider is designed, fabricated and measured. A good agreement of S-parameters between simulation and measurement has confirmed not only the design, but also the modelling technique that is of a reference value for characterisation. The engineered divider obtains a 58.9% size reduction and exhibits moderate in-band and out-of-band (isolation) performances in comparison with its conventional counterparts, advancing a step in miniaturisation strategy.