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Narrowband vs wideband FM; stereo FM broadcasting

Short answer

NBFM has modulation index β < 0.3, bandwidth ≈ 2f<sub>m</sub>; WBFM has β >> 1, bandwidth ≈ 2(Δf+f<sub>m</sub>). Stereo FM transmits a composite baseband: L+R (0–15 kHz), 19 kHz pilot, and L–R DSB-SC on 38 kHz subcarrier (23–53 kHz). A mono receiver uses L+R; a stereo decoder recovers L and R via matrix.

Differentiate between Narrow Band FM and Wide Band FM. Describe stereo FM broadcasting with its block diagram and spectral details.

NBFM versus WBFM

PointNarrow band FMWide band FM
Modulation indexβ≪1\beta \ll 1 (< 0.3)β≫1\beta \gg 1
Bandwidth≈2fm\approx 2f_m (like AM)≈2(Δf+fm)\approx 2(\Delta f + f_m)
SidebandsCarrier + one pairMany significant pairs
Max deviationSmall (~5 kHz)Large (75 kHz in broadcast)
Noise performanceLittle better than AMMuch better SNR
UseMobile radio, police, Armstrong first stageFM broadcast, TV sound

Stereo FM broadcasting

Stereo FM transmits left (L) and right (R) audio on one carrier, while mono receivers can still receive the program.

Encoder (transmitter)

 L --+-->(+)--L+R-->[LPF]----------->( Σ )-->
     |    ^                            ^ ^  to FM
 R --|----+                            | |  mod.
     +-->(-)--L-R-->[LPF]-->[Bal.mod]--+ |
          ^ (R)                 ^ 38k    |
                  [19k osc]->[x2]        |
                      |                  |
                      +--19 kHz pilot----+
  1. Matrix makes L+RL+R and L−RL-R, each limited to 15 kHz and pre-emphasized.
  2. L−RL-R DSB-SC modulates a 38 kHz sub-carrier (balanced modulator).
  3. 38 kHz is obtained by doubling a 19 kHz oscillator; the 19 kHz pilot is added at low level for receiver synchronization.
  4. The composite signal
m(t)=(L+R)+(L−R)cos⁡(2π 38k t)+Apcos⁡(2π 19k t)m(t) = (L+R) + (L-R)\cos(2\pi\,38\text{k}\,t) + A_p\cos(2\pi\,19\text{k}\,t)

frequency-modulates the RF carrier (peak deviation 75 kHz).

Spectrum

 |  L+R      pilot    L-R DSB-SC
 |______       |    ____    ____
 |      |      |   |    |  |    |
 +------+------+---+----+--+----+---> f (kHz)
 0     15     19  23   38      53

Decoder (receiver)

FM    +->[LPF 0-15k]------------L+R--+->(+)--> 2L
demod |                              |   ^
out --+->[BPF 23-53k]-->( X )->[LPF]-+   |
      |                   ^      L-R  |  |
      |                   | 38k       +--|-->(-)--> 2R
      +->[BPF 19k]-->[ x2 ]              |
         (pilot)                  L-R ---+
  • LPF gives L+RL+R (mono output).
  • Pilot is filtered and doubled to 38 kHz; the 23–53 kHz band is coherently detected to give L−RL-R.
  • Adding and subtracting give 2L2L and 2R2R.

✓ Answer checked by Claude Opus 5.5 (high effort)

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