We report on the behaviour of a low-noise two-stage SQUID amplifier, which is strongly coupled to high-Q electrical resonators operating at audio frequencies. The behaviour of the system has been made stable, without adding noise, by means of a damping network. Thanks to the very high quality factor of the resonator, it is possible to evaluate the back action noise of the SQUID amplifier. The additive noise is evaluated as usual by measuring the open input noise. From measurements of back action and additive noises, performed in the temperature range 1.33 K–4.17 K and at 1.67 kHz and 11 kHz, the approximate noise temperature T′_n of the SQUID amplifier is evaluated and its minimum value corresponds to 120 quanta. Besides providing a full noise characterization of the SQUID amplifier, this system constitutes a simulator of a cryogenic resonant gravitational wave detector as regards operation frequency, quality factors and stability problem. On the basis of these results the operation of a resonant gravitational wave detector with an amplifier with energy sensitivity better than 100 ℏ seems achievable.