We have performed transmission experiments on sawtooth-doping superlattices of short periodicity (100\char21{}200 A\r{}). Oscillations have been observed in the transmission spectra as a function of frequency due to the size quantization effect. We present a microscopic model of the transmission which takes into account the coupling between quantum wells in the superlattices. A Kronig-Penney model for a V-shaped quantum well is presented and the dispersion is calculated. It is found that interwell tunneling is only important for high subbands. The electron impurity scattering is included within Born approximation. The random-phase-approximation density correlation function is used for the interband absorption. Excellent agreement between theory and experiment is obtained.