The periodical-in-voltage features of the negative differential conductance (NDC) region in the current-voltage characteristics of a high-quality GaAs/AlAs terahertz resonant-tunneling diode have been detected. The found oscillations are considered taking account of the LO-phonon excitation stimulated by tunneling of electrons through the quantum active region in the resonance nanostructure where an undoped quantum well layer is sandwiched between two undoped barrier layers. Rearrangements in the I-V characteristics of the resonant-tunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp have been experimentally studied and analyzed. The revealed substantial changes in the current-voltage characteristics of the resonant-tunneling diode are discussed schematically using Kirchhoff's voltage law.