Short note: Threshold effect in FM

The threshold effect in FM is the sharp drop in output signal-to-noise ratio of an FM receiver when the input carrier-to-noise ratio (CNR) falls below a certain value, called the threshold, typically about 10 dB (about 13 dB in some texts).

Above threshold

When the carrier is much stronger than the noise, noise only causes small phase perturbations. The output SNR grows linearly with input CNR and FM gives a large improvement over AM:

$$(SNR)_o=\frac{3}{2}\beta^2\,(SNR)_c\quad(\text{tone modulation})$$

Below threshold

 (SNR)o dB
   |              /  FM above threshold
   |             /
   |            /
   |     ------/  <- knee (threshold, ~10 dB CNR)
   |    /
   |   /   sharp fall below threshold
   +---------------------------> (SNR)c dB

When noise amplitude occasionally exceeds the carrier amplitude, the resultant phasor can encircle the origin, causing a sudden $2\pi$ phase jump. The discriminator output (derivative of phase) then shows sharp impulses, heard as clicks. As CNR falls, clicks become frequent, the noise rises rapidly, and the signal is "captured" by noise. The output SNR then falls much faster than the input CNR and the FM advantage is lost.

Consequences and remedies

• Large $\beta$ improves SNR above threshold but needs more bandwidth, so more noise enters and the threshold rises; this sets a practical limit on $\beta$.
• Threshold extension (lowering the threshold by a few dB) uses an FM demodulator with feedback (FMFB) or a phase-locked loop demodulator, which track the signal with a narrower effective bandwidth.
• Pre-emphasis/de-emphasis improves SNR above threshold but does not remove the threshold.