We have designed and characterized a cryogenic amplifier for use in $^3$He NMR spectrometry. The amplifier, with a power consumption of $sim 2.5$ mW, works at temperatures down to 4~K. It has a hi-impedance input for measuring a signal from NMR resonant circuit, and a 50 $mathrm{Omega}$ differential input which can be used for pick-up compensation and gain calibration. At 4.2 K, the amplifier has a voltage gain of 45, output resistance 146 $mathrm{Omega}$ and a 4.4 MHz bandwidth starting from DC. At 1 MHz, the voltage and current noise amount to 1.3 $mbox{nV}/sqrt{mbox{Hz}}$ and 12 $mbox{fA}/sqrt{mbox{Hz}}$, respectively, which yields an optimal source impedance of $sim 100$ k$mathrm{Omega}$.
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