  This paper presents a low noise amplifier for large arrays of silicon
photomultipliers (SiPMs) operated in cryogenic environments, especially liquid
argon (87 K) and liquid nitrogen (77 K). The goal is for one amplifier to read
out a total photosensitive surface of tens of cm$^2$ while retaining the
capability to resolve single photoelectron signals. Due to the large
capacitance of SiPMs, typically a few nF per cm$^2$, the main contributor to
noise is the series (voltage) component. A silicon-germanium heterojunction
bipolar transistor (HBT) was selected as the input device of the cryogenic
amplifier, followed by a fully differential operational amplifier, operated in
an unconventional feedback configuration. The input referred voltage noise of
the circuit at 77 K is just below 0.4 nV/$\surd$Hz white (above 100 kHz) and 1
nV/$\surd$Hz at 10 kHz. The value of the base spreading resistance of the HBT
at 77 K was determined from noise measurements at different bias currents.
Power consumption of the full circuit is about 2.5 mW. The design gives the
flexibility to optimally compensate the feedback loop for different values of
the input capacitance, and obtain a gain-bandwidth product in the GHz range.
The signal-to-noise ratio obtained in reading out SiPMs is discussed for the
case of a 300 kHz low pass filter and compared with the upper limit that would
derive from applying optimum filtering algorithms.
