Stereo FM encoder and decoder

Stereo FM sends two audio channels, left (L) and right (R), on one FM carrier using a composite baseband signal. It stays compatible with mono receivers because the sum $L+R$ is sent in the normal 0–15 kHz band.

Stereo 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: an adder and a subtractor form $L+R$ and $L-R$.
2. LPF and pre-emphasis: each signal is limited to 15 kHz and pre-emphasized.
3. Balanced modulator: $L-R$ DSB-SC modulates a 38 kHz sub-carrier. Since the carrier is suppressed, its power goes into useful sidebands (23–53 kHz).
4. Pilot: a 19 kHz crystal oscillator gives the 38 kHz sub-carrier through a frequency doubler. The 19 kHz pilot itself is also added at low level (about 10% of deviation). It lies in an empty gap (15–23 kHz), is easy to filter, and tells the receiver the exact frequency and phase of the 38 kHz sub-carrier.
5. Adder: forms the composite signal that frequency-modulates the RF carrier:

$$m(t) = [L(t)+R(t)] + [L(t)-R(t)]\cos(2\pi\,38\text{k}\,t) + A_p\cos(2\pi\,19\text{k}\,t)$$

Spectrum of the composite baseband

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

The composite bandwidth is 53 kHz (with optional SCA services up to about 75 kHz).

Stereo 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 ---+

1. The FM discriminator output is the composite signal $m(t)$.
2. LPF (0–15 kHz) gives $L+R$. A mono receiver stops here.
3. Narrow BPF at 19 kHz extracts the pilot; a frequency doubler (or PLL) regenerates the 38 kHz sub-carrier, locked in phase with the transmitter.
4. BPF (23–53 kHz) selects the $L-R$ DSB-SC signal. It is multiplied by the 38 kHz carrier and low-pass filtered (coherent detection), giving $L-R$.
5. De-matrixing:

$$(L+R) + (L-R) = 2L, \qquad (L+R) - (L-R) = 2R$$

6. Each channel is de-emphasized and amplified to its own speaker. A stereo indicator lamp lights when the pilot is detected.

Advantages: full mono compatibility, small extra bandwidth, simple pilot-based synchronization. Drawback: the stereo SNR is somewhat lower than mono, since the $L-R$ channel sits at higher baseband frequencies where FM noise is larger.