We have designed a fluxgate magnetometer which utilizes the detection of ultra-low DC fields down to (even less) 3 nT. In addition to high sensitivity, it also has quite a large dynamical measurement range. The second harmonic voltage used as the sensor signal shows linear dependence on the applied field up to 1 Oe. We report some critical factors affecting the noise level and sensitivity of magnetometer. The core diameter and magnetic properties are some of them. We will report optimal core dimensions resulting in minimal electrical noise. During experiments, we have recognized that ring-shaped six-layered ribbon core must be well attached to the template, since otherwise, it may vibrate on its original position as a function of the excitation frequency. Thus, additional electrical noises become unavoidable.