Transmission surface acoustic wave (SAW) sensors are widely used in various fields of application. In order to maximize the limit of detection (LOD) of such sensor systems, it is of high importance to understand and to be able to quantify the relevant noise sources. In this paper, low noise readout systems for the application with a SAW delay line magnetic field sensor in an open-loop and closed-loop configuration are presented and analyzed with regard to their phase noise contribution. By applying oscillator phase noise theory to closed-loop sensor systems, it is shown that the phase noise of the SAW delay line oscillator can be predicted accurately. This allows the derivation of expressions for the limits of detection for both readout structures. Based on these equations, the equivalence between the LOD of open-loop and closed-loop SAW delay line readout can be shown analytically, assuming that the sensor contributes the dominant phase noise. This equality is verified by measurements. These results are applicable to all kinds of phase sensitive delay line sensors.