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A detailed analysis of the tunability of a radio-frequency quantum point contact setup using a C - LCR circuit is presented. We calculate how the series capacitance influences resonance frequency and charge-detector resistance for which matching is achieved as well as the voltage and power delivered to the load. Furthermore, we compute the noise contributions in the system and compare our findings with measurements taken with an etched quantum point contact. While our considerations mostly focus on our specific choice of matching circuit, the discussion of the influence of source-to-load power transfer on the signal-to-noise ratio is valid generally.