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The processing of low-frequency slowly varying signals (e.g. nonelectrical signals measured by sensors) in on-chip signal processing systems is not an easy task due to using of AC coupling between the parts of integrated components (e.g. very large and on-chip nonproductive values of coupling capacity required for separation of the DC component of a signal). One of the solutions to overcome this issue immediately at the input site is to transpose such low-frequency signals to higher frequency bands, for instance, based on the principle of frequency modulation/demodulation (FM) spectral transposition (higher frequency of the processed signal means lower value of coupling capacity). This paper focuses on the improvement of a voltage-controlled oscillator (VCO) for phase-locked loop (PLL) based FM demodulator for processing and measurement of signals with slow changes. There is introduced a novel concept of adjustability of the oscillation condition performed by a special analog multiplier. It brings reduction of complexity of the resulting topology and the designed oscillator operates with linearly adjustable (by DC voltage) frequency range of one decade from 4 kHz up to 43 kHz. This VCO is applied in a demodulator of FM modulated waveforms based on PLL methodology employing the same active cells (integrated multipliers and buffers). The proposed and realized concept is suitable for specific low-frequency applications and the presented example improves propagation of low-frequency signals of mechanical vibrations and biomedical signals through signal-processing systems integrated on chip (e.g. a sensed electrocardiogram wave) where fabrication of large coupling capacity values on chip represents significant issue. Active cells fabricated in ON Semiconductor 0.35 mu m I3T25 3.3 V process were used for experimental verification.