Scale factor nonlinearity in an open loop Fiber Optic Gyroscope (FOG) indicates the maximum inaccuracy of rotation rates within the whole measurement range. Because of the non-linearity of the phase modulation, scale factor non-linearity of open loop FOG is inherent and will become worse if the bandwidth of preamplifier is limited. This paper educed theoretically the facts that will make the nonlinearity of scale factor even worse when all harmonic components are amplified dissimilarly. Finally, experiment indicates that 20 multiples of the base frequency bandwidth of a preamplifier with a 1st-order RC low-pass filter is needed if scale factor nonlinearity we wanted is less than 500 ppm or better.