In frequency modulation (FM), the carrier deviation is primarily determined by the modulation frequency and the modulation index. The modulation index, also known as the modulation depth, represents the extent of variation in the carrier frequency due to the modulating signal.
The carrier deviation is a measure of how much the instantaneous frequency of the carrier wave deviates from its nominal or center frequency. In FM, this deviation is directly related to the amplitude of the modulating signal.
The formula for calculating the carrier deviation in FM is given by:
Δf = k * β * A
where: Δf is the carrier frequency deviation, k is a constant that depends on the specific FM system and is typically related to the sensitivity of the modulator or the voltage-controlled oscillator (VCO), β is the modulation index, and A is the amplitude of the modulating signal.
The modulation index (β) is defined as the ratio of the peak frequency deviation (Δf) to the frequency of the modulating signal (fm):
β = Δf / fm
Therefore, the carrier deviation is determined by the product of the modulation index and the amplitude of the modulating signal. As the amplitude of the modulating signal increases, the carrier deviation also increases, resulting in a wider frequency variation around the center frequency of the carrier wave.
The phase and amplitude of the modulating signal do not directly determine the carrier deviation in FM. However, they can affect the shape and characteristics of the modulated waveform, including its frequency spectrum and modulation index, which, in turn, influence the carrier deviation indirectly.