  A superconducting optoelectronic neuron will produce a small current pulse
upon reaching threshold. We present an amplifier chain that converts this small
current pulse to a voltage pulse sufficient to produce light from a
semiconductor diode. This light is the signal used to communicate between
neurons in the network. The amplifier chain comprises a thresholding Josephson
junction, a relaxation oscillator Josephson junction, a superconducting
thin-film current-gated current amplifier, and a superconducting thin-film
current-gated voltage amplifier. We analyze the performance of the elements in
the amplifier chain in the time domain to calculate the energy consumption per
photon created for several values of light-emitting diode capacitance and
efficiency. The speed of the amplification sequence allows neuronal firing up
to at least 20\,MHz with power density low enough to be cooled easily with
standard $^4$He cryogenic systems operating at 4.2\,K.
