--- title: "Armstrong (indirect) FM generation; pre-emphasis" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:armstrong-indirect-pre-emphasis" source: https://www.bctengineer.com/q/semester_6/communication_systems/armstrong-indirect-pre-emphasis site: BCT Engineering --- # Armstrong (indirect) FM generation; pre-emphasis Communication Systems · Chapter 3: Angle Modulation - Asked in: 2065 Kartik (CS I), 6+2 marks - Video: [ARMSTRONG METHOD || GENERATION OF FM WAVE || ADC || Electronics and Communication Engineering](https://www.youtube.com/watch?v=pGzV1bsXoMk) — Friend's Explanation - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/armstrong-indirect-pre-emphasis - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question How can you generate FM wave using Armstrong modulator (Indirect method)? Explain with the help of block diagram. Why pre-emphasis and de-emphasis networks are used in FM? ## Short answer An Armstrong modulator generates narrowband FM with an integrator, crystal-controlled phase modulator, then multiplies frequency and mixes to obtain wideband FM with stable carrier. Pre‑emphasis (high‑pass, 75 µs) boosts high audio frequencies before modulation to improve SNR; de‑emphasis (low‑pass, 75 µs) at the receiver restores the spectrum and attenuates high‑frequency noise. ## Answer #### Armstrong (indirect) FM modulator In the indirect method, a **narrowband FM** wave is first generated using a crystal-controlled phase modulator, and then **frequency multipliers** and a **mixer** convert it to wideband FM. ```text m(t) +----------+ +----------+ NBFM ---->|Integrator|-->| Balanced |--+ +----------+ | modulator| | +----------+ v ^ +---+ f1, df1 +--------+ +------+ | + |---------+ |Crystal |->|-90deg| +---+ | | osc f1 | +------+ ^ v +--------+--------------+ +-------+ | x n1 | WBFM +-------+ +-------+ +-------+ <-------| x n2 |<--| Mixer |<---------------+ fc, df +-------+ +-------+ ^ [LO fLO] ``` **Working:** 1. **NBFM generation:** for small $\beta$, $$ s(t) \approx A_c\cos\omega_1 t - A_c\,\phi(t)\sin\omega_1 t, \quad \phi(t) = 2\pi k_f\int_0^t m(\tau)d\tau $$ The message is integrated, multiplied with the 90°-shifted crystal carrier in a balanced modulator (giving the DSB-SC term), and the carrier is added. Deviation is kept very small (e.g. $\Delta f_1 \approx 25$ Hz, $\beta < 0.3$) to avoid distortion. 2. **First multiplier ($\times n_1$):** a non-linear device and a BPF multiply the instantaneous frequency, so the carrier becomes $n_1 f_1$ and the deviation becomes $n_1\Delta f_1$. 3. **Mixer:** shifts the carrier to $|f_{LO} - n_1 f_1|$ without changing the deviation. This lets the final carrier be set to the required value. 4. **Second multiplier ($\times n_2$):** gives the final deviation and carrier: $$ \Delta f = n_1 n_2\Delta f_1, \qquad f_c = n_2|f_{LO} - n_1 f_1| $$ Example: $f_1 = 200$ kHz, $\Delta f_1 = 25$ Hz, $n_1 = 64$, $f_{LO} = 10.8$ MHz, $n_2 = 48$ gives $f_c = 48 \times 2$ MHz $= 96$ MHz and $\Delta f = 76.8$ kHz. **Merits:** excellent carrier stability (crystal oscillator, so no AFC is needed). **Demerits:** many multiplier stages, more complexity, and phase noise that is multiplied along with the deviation. #### Why pre-emphasis and de-emphasis are used - After FM detection, the output noise power spectral density is proportional to $f^2$, so noise is heaviest at high audio frequencies. - High-frequency audio components have low amplitude, so their SNR is poor. - **Pre-emphasis** (high-pass RC, 75 μs) at the transmitter boosts high audio frequencies before modulation; **de-emphasis** (low-pass RC, 75 μs) at the receiver restores the original balance and at the same time cuts the high-frequency noise. The overall SNR improves by about 10–13 dB without distorting the message. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the order of generating wideband FM by the indirect method? A. Frequency multipliers first, then an NBFM modulator B. NBFM from a crystal-controlled modulator, then multipliers and a mixer C. A varactor oscillator, then a limiter D. A PLL, then an integrator Answer: B. A small-deviation NBFM wave is produced with a crystal carrier, then multiplier-mixer-multiplier stages raise the deviation and set the carrier. (Key point: Armstrong sequence) 2. What are the final deviation and carrier formulas? A. delta f = (n1 + n2) delta f1; fc = n1 n2 f1 B. delta f = n1 delta f1; fc = f1 + fLO C. delta f = n1 n2 delta f1; fc = n2 |fLO - n1 f1| D. delta f = n2 delta f1; fc = n1 fLO Answer: C. Both multipliers scale the deviation (n1 n2), while the mixer only shifts the carrier before the second multiplier. (Key point: Final deviation and carrier) 3. What is the main merit and demerit of the indirect method? A. Poor stability; very simple B. Good stability from the crystal oscillator; many multiplier stages and complexity C. Large deviation directly; no multipliers D. No integrator; no crystal Answer: B. Crystal control gives excellent stability without AFC, but the many multiplier stages make it complex and multiply phase noise. (Key point: Merit of indirect method) 4. Why is pre-emphasis at the transmitter paired with de-emphasis at the receiver? A. To widen the bandwidth B. To reduce carrier power C. To remove low-frequency noise D. Detected noise rises as f^2, so boosting high audio before modulation and restoring it afterwards improves SNR 10-13 dB without distorting the message Answer: D. De-emphasis returns the message to its original balance and, at the same time, attenuates high-frequency noise. (Key point: Pre-emphasis and de-emphasis) ## Related in Communication Systems - [Need for pre-emphasis and de-emphasis in FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneed-pre-de-emphasis-fm) — 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× - [Armstrong FM modulator: find n1 and n2](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-n1-n2-numerical) — Communication Systems, chapter 3 - [Short note: Pre-emphasis and de-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashort-note-pre-de-emphasis) — Communication Systems, chapter 3, asked 4× - [Limiter-discriminator FM demodulation; need for pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pre-emphasis) — Communication Systems, chapter 3 - [General FM expression; FM using phase modulator](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-general-expression-phase-modulator) — Communication Systems, chapter 3 ## Related in other subjects - [Algorithm and flowchart help; Armstrong flowchart](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Aalgorithm-flowchart-armstrong) — Computer Programming, chapter 2 - [Hydropower generation with block diagram](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ahydropower-generation-block-diagram) — Power System Analysis I, chapter 1 - [DAC square wave generation at 1 kHz](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac-square-wave-1khz) — Instrumentation II, chapter 4