A spectrometer for measuring the complex impedance spectrum of tissue comprises: a multi-frequency excitation current generator; a demodulation signal generator; two identical amplification/demodulation circuits; an A/D converter; and a microprocessor for signal processing. In use, the current generator excites the tissue sample and a series-connected reference impedance. The voltages generated in the tissue and reference are measured, demodulated, and digitized in parallel using the demodulation signal generator, the two amplification/demodulation circuits, and the A/D converter. Demodulation is done using the same demodulation signal generated at a frequency with a preset difference from the excitation signal, which allows measurements to be made at a low frequency independent of the excitation frequency. The microprocessor then calculates the complex impedance spectrum in relation to the reference signal. Because the measurements are relative, they are independent of both the excitation current amplitude of the phase of the excitation and demodulation signals.