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The performance of giant magneto-impedance (GMI)-based magnetometers is currently limited by the noise due to the electronic conditioning circuitry. We propose a simple model of this noise for a GMI sensor using a synchronous detection scheme. The GMI sensing element consists of a thin pick-up coil wound around a Co-rich amorphous micro-wire. It is fully described by a two port network model and associated impedance matrix. Noise and sensitivity behavior are studied for the four measuring configurations, corresponding to four terms of the impedance matrix. The model yields a good description of experimental data from noise measurements. The magnetic noise spectral density is dominated either by the excitation or detection stages, depending upon whether the excitation currents are high or low. The nontrivial noise behavior exhibited by each configuration leads to better understanding of the noise limitations of GMI magnetometers. The configuration in which the signal at the coil terminals is measured (often called offdiagonal) is the most efficient in decreasing the equivalent output magnetic noise spectral density.