An upgrade of an AMPTEK soft X-ray spectrometer with a silicon drift detector (SDD) to boost the output count rate is presented in the paper. Enhanced count rate is provided by a shaping electronic amplifier which forms pulses with  a short rise time from step-wise impulse responses of SDD charge sensitive preamplifier. The rise time of the amplifier pulses is about a half of that used in the AMPTEK amplifier. The output noise of the amplifier equals the noise of  the AMPTEK amplifier. The spectrometer is tested with the developed amplifier and amplifier in its digital pulse processing (DPP) unit and SDD radiated by an isotope 55Fe source. The results of the test are compared in terms of the  rise time and amplitudes of the response pulses as well as trapezoidal pulses at various peaking and flat top times. The developed amplifier is capable to provide the count rate of output pulses increased by a factor of 1.5 in regards  with the standard methods at the same energy resolution.