  We propose a new type of cryogenic current amplifiers, in which low-frequency
power spectrum of current can be measured through a measurement of microwave
response of a superconducting resonant circuit shunted by a series array of
Josephson junctions. From numerical analysis on the equivalent circuit, the
numerical value of the input-referred current noise of the proposed amplifier
is found to be two orders of magnitude lower than the noise floor measured with
the conventional cryogenic current amplifiers based on high-electron-mobility
transistors or superconducting quantum interference devices. Our proposal can
open new avenues for investigating low-temperature solid-state devices that
require lower noise and wider bandwidth power spectrum measurements of current.
