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We have analyzed a radio-frequency single-electron-transistor (RF-SET) circuit that includes a high-electron-mobility-transistor (HEMT) amplifier, coupled to the single-electron-transistor (SET) via an impedance transformer. We consider how power is transferred between different components of the circuit, model noise components, and analyze the operating conditions of practical importance. The results are compared with experimental data on SETs. Good agreement is obtained between our noise model and the experimental results. Our analysis shows, also, that the biggest improvement to the present RF-SETs will be achieved by increasing the charging energy and by lowering the HEMT amplifier noise contribution. © 2004 American Institute of Physics.