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A superconducting current transformer with a maximum DC current of 28 kA has been used for Nb3Sn cable testing at self-fields under various experimental conditions. A fast data acquisition system was developed and used for accurate measurements of the secondary current. Test results are shown for thirty cables made of MJR, RRP and PIT strands, along with a description of the SC transformer, sample preparation and test procedure. It was found that premature quenches at currents significantly lower than the expected critical currents at low fields were due to electromagnetic instabilities in the superconductor.