Analytical models to describe tracer transport in reservoirs commonly set conditions either on the tracer concentration or the tracer flow at the injection border. Here a different formulation based on tracer sources is presented. This approach avoids some of the physical inconsistencies that can be found when setting conditions on the tracer concentration. The case of a tracer injected as a finite-step in an infinite one-dimensional homogeneous reservoir with a uniform flow is considered. The solution is analytically obtained. The results are confronted against the two common boundary cases. The new approach predicts slightly delayed and broader pulses. The tracer breakthrough curves differences can be large for small Peclet numbers. These differences weakly reduce by increasing the injection period. The new approach contains tracer injection elements that can make it suitable to describe real conditions found in reservoir tracer tests.