Linear passage pulses provide a simple approach to ultra-wideband electron paramagnetic resonance (EPR) spectroscopy. We show by numerical simulations that the efficiency of inversion of polarization or coherence order on a single transition by idealized passage pulses is an exponential function of critical adiabaticity during passage, which allows for defining an effective flip angle for fast passage. This result is confirmed by experiments on E' centers in Herasil glass. Deviations from the exponential law arise due to relaxation and a distribution of the adiabaticity parameter that comes from inhomogeneity of the irradiation field. Such inhomogeneity effects as well as edge effects in finite sweep bands cause a distribution of dynamic phase shifts, which can be partially refocused in echo experiments. In multilevel systems, passage of several transitions leads to generation of coherence on formally forbidden transitions that can also be described by the concept of an effective flip angle. On the one hand, such transfer to coherence on forbidden transitions is a significant magnetization loss mechanism for dipole dipole coupled electron spin pairs at distances below about 2 nm. On the other hand, it can potentially be harnessed for electron spin echo envelope modulation (ESEEM) experiments, where matching of the irradiation field strength to the nuclear Zeeman frequency leads to efficient generation of nuclear coherence and efficient back transfer to electron coherence on allowed transitions at high adiabaticity.