--- title: "Stereo FM encoder and decoder" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:stereo-fm-encoder-decoder" source: https://www.bctengineer.com/q/semester_6/communication_systems/stereo-fm-encoder-decoder site: BCT Engineering --- # Stereo FM encoder and decoder Communication Systems · Chapter 3: Angle Modulation - Asked in: 2079 Chaitra (CS I), 5+5 marks; 2067 Shrawan (CS I), 5+5 marks (asked 2 times) - Video: [CT#28 FM stereo Multiplexing in communication system || EC Academy](https://www.youtube.com/watch?v=1Jh3tK-tDN4) — EC Academy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/stereo-fm-encoder-decoder - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question With functional block diagrams and spectral details explain the operation of stereo encoder and decoder. ## Short answer The stereo encoder combines L+R (0–15 kHz), L-R DSB-SC (23–53 kHz on a 38 kHz suppressed carrier), and a 19 kHz pilot into a composite baseband that FM-modulates the carrier. The decoder extracts L+R via low-pass filter, regenerates the 38 kHz carrier from the pilot, coherently detects the L-R signal, and recovers L and R by addition and subtraction. ## Answer **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) ```text 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 ```text | 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) ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does the stereo decoder get the 38 kHz carrier? A. It filters the 19 kHz pilot and doubles it (or uses a PLL) B. It uses a free-running 38 kHz oscillator C. It takes it from the L+R signal D. It divides the 53 kHz band by two Answer: A. A narrow 19 kHz BPF extracts the pilot, and a doubler or PLL regenerates the phase-locked 38 kHz subcarrier. (Key point: Decoder: recovering the subcarrier) 2. How is L−R recovered? A. LPF at 15 kHz B. Envelope detection of the 23–53 kHz band C. Multiplying the 23–53 kHz band by 38 kHz and low-pass filtering (coherent detection) D. Differentiating the composite Answer: C. L−R is DSB-SC, so it needs coherent detection with the regenerated subcarrier. (Key point: Recovering L−R) 3. How are left and right obtained from L+R and L−R? A. L = (L+R)(L−R), R = (L+R)/(L−R) B. L+R is the left channel and L−R is the right C. Add gives 2L and subtract gives 2R D. Add gives 2R and subtract gives 2L Answer: C. (L+R)+(L−R) = 2L and (L+R)−(L−R) = 2R. (Key point: De-matrixing) 4. Why is the pilot placed at 19 kHz? A. It lies in the empty gap between 15 kHz and 23 kHz, so it is easy to filter B. It is inside the L+R band C. It matches the L−R sideband centre D. It is the FM deviation limit Answer: A. The gap 15–23 kHz is unused, so the pilot does not interfere and is easy to extract. (Key point: Why the pilot sits at 19 kHz) ## Related in Communication Systems - [Stereo FM encoder and decoder block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-encoder-decoder-blocks) — Communication Systems, chapter 3 - [Pre-emphasis in FM broadcasting; stereo encoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apre-emphasis-stereo-encoder) — Communication Systems, chapter 3, asked 2× - [PSD–autocorrelation relation; stereo FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apsd-autocorrelation-stereo-fm) — Communication Systems, chapter 3 - [Narrowband vs wideband FM; stereo FM broadcasting](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anbfm-wbfm-stereo-fm) — Communication Systems, chapter 3 - [Stereo FM transmitter and receiver; output of mono receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-mono-receiver) — Communication Systems, chapter 3 - [Short note: Stereo encoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashort-note-stereo-encoder) — Communication Systems, chapter 3, asked 3× ## Related in other subjects - [Encoder vs decoder; 8-to-3 encoder](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aencoder-decoder-8to3) — Digital Logic, chapter 4 - [Encoder; 4×16 decoder from 2×4 decoders](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aencoder-4x16-decoder) — Digital Logic, chapter 4