A frequently occurring subcircuit consists of a loop of a resistor (R), a field-effect transistor (FET), and a capacitor (C). The FET acts as a switch, controlled at its gate terminal by a clock voltage. There may be many such identical circuits connected in parallel, each driven by a different phase of the clock. This subcircuit may be acting as a sample-and-hold (S/H), as a passive mixer (P-M), or as a bandpass filter or bandpass impedance. In this work, we will present a useful analysis that leads to a simple signal flow graph (SFG), which captures the FET-R-C circuit's action completely across a wide range of design parameters. The SFG dissects the circuit into three filtering functions and ideal sampling. This greatly simplifies analysis of frequency response, noise, input impedance, and conversion gain, and leads to guidelines for optimum design. The analysis is extended to multi- path realizations common in RF applications. Part I of this paper focuses on the analyses of a single-path FET-R-C circuit's signal transfer characteristics. Part II extends these analyses to multi- path FET-R-C circuit configurations, which is followed by the noise and driving-point impedance analyses.