An apparatus and a method using no switching elements for multiplexing and reading arrays of sensors whose electrical resistance is modulated by the signals to be measured are proposed. Sensor elements are arranged in groups and columns where each column is fed with a continuous voltage waveform of different amplitude, frequency and phase characteristics which then produce current signals that are modulated by the variable resistance signals to be measured. Modulated currents are summed row-wise and collected at the read-out circuits, either by applying a constant voltage to each row of the array or by connecting a capacitor and converting these current summations into output voltage signals. The read-out circuits de-multiplex each individual sensor signal to be measured by lock-in demodulation according to the frequencies and phases employed for the stimulation of each column.