3.4.1 Frequency Deviation

The frequency deviation (∆f) of an FM waveform is the maximum shift of the carrier frequency from its resting frequency caused by the modulating signal. For example, if an FM system has a deviation of ±50 kHz, a 100 MHz carrier varies between 99.95 MHz and 100.05 MHz.

From Equation (3.22) we can see that the deviation is proportional to the amplitude of the modulating signal voltage and the frequency-deviation constant such that:

Δ f = f_{Δ} V_{m}

(3.26)

Unlike AM, which has a defined upper limit, FM has no theoretical upper bound on deviation. In practice, however, every system specifies a rated system deviation $Δ f_{m a x}$ , to limit the occupied bandwidth and ensure compatibility with channel allocations. Typical deviations range from tens of kilohertz in narrowband systems to several megahertz in satellite or video links.

3.4.2 Modulation Index And Deviation Ratio

The modulation index (m_f) of an FM wave is the ratio of the frequency deviation of the carrier to the modulating frequency:

m_{f} = \frac{Δ f}{f_{m}}

(3.27)

The modulation index determines the amplitudes of the various frequency components (sidebands) in the FM spectrum, as discussed earlier. It is also commonly denoted by β and is dimensionless, though it represents an angular deviation in radians. Because the modulation index depends on the frequency of the modulating signal, its value changes as the modulation frequency varies. It is therefore not a fixed design parameter for an FM system.

We therefore define the deviation ratio as the value of the modulation index when both the frequency deviation and the modulating frequency are at their maximum values:

D = \frac{Δ f_{m a x}}{f_{m (𝑚𝑎𝑥)}}

(3.28)

The deviation ratio is specified during system design and remains constant for a given FM system. Typical values depend on application—narrowband FM systems use D<1, while wideband systems (such as broadcast or satellite FM) may have D≫1.