Testing and Designing an External Differentiator to Shorten the Response from Silicon Photomultipliers

The Antihydrogen Trap (ATRAP) experiment has recently exchanged the vacuum photo multiplier tubes (PMT) in their apparatus for silicon photomultipliers (SIMP). The SIMP have a long response pulse, about 1$\mu$s, which results in a lower date of detection. In this paper the testing and designing of a differentiator is described. The final design of this differentiator circuit is two high-pass filters each followed by a amplifier. The circuit was a success as it reduced the the pulse length to less than 100ns, and amplified the pulse by a factor of 2. Two tests were done to see if the new differentiator resulted in a higher rate of detection, the first was done with a DG353 pulse generator and a summing circuit, the second was done with a nanosecond laser pulser. The first was unsuccessful due to a limited bandwidth of a device used in the apparatus. The second was preformed on an updated circuit that condensed the summer and amplifier of the SIMP with only a single stage of differentiation. The SIMP could detect pulses that were 20ns apart.