--- title: "Stereo FM encoder and decoder block diagram" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:stereo-fm-encoder-decoder-blocks" source: https://www.bctengineer.com/q/semester_6/communication_systems/stereo-fm-encoder-decoder-blocks site: BCT Engineering --- # Stereo FM encoder and decoder block diagram Communication Systems · Chapter 3: Angle Modulation - Asked in: 2076 Baisakh (CS I), 8 marks - 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-blocks - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question Draw the block diagram of stereo FM encoder and decoder. Explain each block briefly. ## Short answer Stereo FM encoder: matrix yields L+R and L−R; L−R DSB-SC on 38 kHz subcarrier from doubled 19 kHz pilot. Composite: L+R (0–15 kHz), 19 kHz pilot, 23–53 kHz sidebands. Decoder: LPF gives L+R; pilot extracted and doubled yields 38 kHz for coherent detection of L−R; matrix recovers L and R. ## Answer **Stereo FM** carries left (L) and right (R) audio on one FM carrier as a composite baseband signal, keeping compatibility with mono receivers. #### Encoder ```text L --+-->(+)--L+R-->[LPF]----------->( Σ )--> | ^ ^ ^ to FM R --|----+ | | mod. +-->(-)--L-R-->[LPF]-->[Bal.mod]--+ | ^ (R) ^ 38k | [19k osc]->[x2] | | | +--19 kHz pilot----+ ``` - **Matrix (adder/subtractor):** forms $L+R$ and $L-R$. - **LPF (15 kHz) and pre-emphasis:** band-limit each audio signal and boost high frequencies. - **19 kHz pilot oscillator:** crystal-controlled reference. - **Frequency doubler (×2):** gives the 38 kHz sub-carrier, phase-locked to the pilot. - **Balanced modulator:** DSB-SC modulates $L-R$ on 38 kHz, producing 23–53 kHz. - **Adder:** sums $L+R$, the DSB-SC $L-R$ and a low-level 19 kHz pilot into the composite signal, which drives the FM modulator. $$ m(t) = (L+R) + (L-R)\cos(2\pi\,38\text{k}\,t) + A_p\cos(2\pi\,19\text{k}\,t) $$ ```text | L+R pilot L-R DSB-SC |______ | ____ ____ | | | | | | | +------+------+---+----+--+----+---> f (kHz) 0 15 19 23 38 53 ``` #### Decoder ```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 ---+ ``` - **FM discriminator:** recovers the composite signal. - **LPF (0–15 kHz):** extracts $L+R$ (mono signal). - **Narrow BPF (19 kHz):** extracts the pilot. - **Doubler (×2):** regenerates a 38 kHz carrier in phase with the transmitter's. - **BPF (23–53 kHz):** selects the $L-R$ DSB-SC signal. - **Product detector and LPF:** coherent detection with 38 kHz gives $L-R$. - **Matrix:** $(L+R)+(L-R) = 2L$, $(L+R)-(L-R) = 2R$. - **De-emphasis and AF amplifiers:** restore flat response and drive the left and right speakers. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which set of components forms the composite stereo FM baseband signal? A. L+R (0-15 kHz), 19 kHz pilot, and L-R DSB-SC around 38 kHz B. L+R at 38 kHz, L-R baseband, and a 19 kHz pilot C. L and R sent as two separate FM carriers D. L-R baseband, R at 38 kHz DSB-SC, and a 38 kHz pilot Answer: A. The sum L+R stays at baseband for mono compatibility, L-R is DSB-SC on 38 kHz (23-53 kHz), and a 19 kHz pilot is added. (Key point: Composite signal) 2. Why does the transmitter obtain 38 kHz by doubling the 19 kHz oscillator? A. Because a 38 kHz crystal does not exist B. To reduce the bandwidth of L-R C. So the subcarrier is phase-locked to the pilot D. To pre-emphasize the L-R signal Answer: C. Deriving both from one oscillator keeps their phase relationship fixed, letting the receiver regenerate the carrier. (Key point: Doubler) 3. Why can a mono receiver still play a stereo broadcast properly? A. It demodulates the L-R DSB-SC signal and ignores L+R B. It subtracts the pilot from the composite signal C. Its 0-15 kHz low-pass filter picks out L+R, which is the full mono program D. It decodes the 38 kHz subcarrier with a fixed oscillator Answer: C. L+R occupies 0-15 kHz at baseband, so a simple LPF recovers the mono signal and the higher components are filtered out. (Key point: Mono compatibility) 4. In the decoder matrix, how are the left and right outputs obtained? A. (L+R)+(L-R) gives 2R and (L+R)-(L-R) gives 2L B. L+R and L-R are used directly as L and R C. (L-R) is divided by the pilot to obtain R D. (L+R)+(L-R) gives 2L and (L+R)-(L-R) gives 2R Answer: D. Adding the two signals cancels R and leaves 2L; subtracting cancels L and leaves 2R. (Key point: Decoder matrix) ## Related in Communication Systems - [Stereo FM encoder and decoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-encoder-decoder) — Communication Systems, chapter 3, asked 2× - [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