Dust impacts on spacecraft are commonly detected by antenna instruments as transient voltage perturbations. The signal waveform is generated by the interaction between the impact-generated plasma cloud and the elements of the antenna – spacecraft system. A general electrostatic model is presented that includes the two key elements of the interaction, namely the charge recollected from the impact plasma by the spacecraft and the fraction electrons and cations that escape to infinity. The clouds of escaping electrons and cations generate induced signals, and their vastly different escape speeds are responsible for the characteristic shape of the waveforms. The induced signals are modeled numerically for the geometry of the system and the location of the impact. The model employs a Maxwell capacitance matrix to keep track of the mutual interaction between the elements of the system. A new reduced-size model spacecraft is constructed for laboratory measurements using the dust accelerator facility. The model spacecraft is equipped with four antennas: two operating in a monopole mode, and one pair configured as a dipole. Submicron-sized iron dust particles accelerated to > 20 km/s are used for test measurements, where the waveforms of each antenna are recorded. The electrostatic model provides a remarkably good fit to the data using only a handful of physical fitting parameters, such as the escape speeds of electrons and cations. The presented general model provides the framework for analyzing antenna waveforms and is applicable for a range of space missions investigating the distribution of dust particles in relevant environments.