---
title: "Armstrong's method of FM generation"
subject: "Communication Systems"
chapter: 3
key: "semester_6/communication_systems:armstrong-fm"
source: https://www.bctengineer.com/q/semester_6/communication_systems/armstrong-fm
site: BCT Engineering
---

# Armstrong's method of FM generation

Communication Systems · Chapter 3: Angle Modulation

- Asked in: 2080 Chaitra, 4 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-fm
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3

## Question

Explain the Armstrong's method for Frequency Modulation.

## Short answer

Armstrong’s indirect FM method first generates narrowband FM (β<0.3) by integrating the message, applying it to a balanced modulator with a 90° phase-shifted carrier, and adding the original carrier. This NBFM is then passed through frequency multipliers and a mixer to increase deviation and set the final carrier frequency, preserving excellent crystal stability.

## Answer

**Armstrong's method** is an indirect method of generating wide-band FM: first a narrow-band FM (NBFM) wave is made with a crystal-controlled phase modulator, then frequency multipliers and a mixer raise the deviation and set the carrier frequency.

```text
 m(t)->[Integrator]->[Balanced]--( Σ )-> NBFM
                     [modulator] ^ -
                         ^       | +
          +--[-90 deg]---+       |
 [Crystal osc fc1]---------------+
          (NB phase modulator)

 NBFM ->[ x n1 ]->[ Mixer ]->[ x n2 ]->[PA]-> WBFM
                      ^
                 [Osc fc2]
```

**Steps**

1. **NBFM generation:** the message is integrated and applied to a balanced modulator with a −90° shifted carrier. The output is added to the carrier, giving

$$
s_{NB}(t) \approx A_c\cos\omega_{c1}t - \beta A_c\sin\omega_mt\,\sin\omega_{c1}t, \quad \beta < 0.3
$$

   which is NBFM. A crystal oscillator keeps $f_{c1}$ very stable.
2. **Frequency multiplication (×n₁):** a non-linear stage multiplies both carrier and deviation: $n_1f_{c1}$, $n_1\Delta f_1$.
3. **Mixer:** shifts the carrier down to a convenient value ($n_1f_{c1} - f_{c2}$) **without changing the deviation**.
4. **Second multiplier (×n₂):** gives the final carrier $f_c = n_2(n_1f_{c1} - f_{c2})$ and deviation $\Delta f = n_1n_2\Delta f_1$ (e.g. 75 kHz).

**Merit:** excellent carrier stability (crystal oscillator). **Demerit:** many multiplier stages; noise and distortion may increase.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What kind of FM generation is Armstrong's method?
   A. Direct FM with a varactor oscillator
   B. Indirect: a crystal-controlled narrow-band phase modulator followed by multipliers and a mixer
   C. AM followed by clipping
   D. A PLL with a VCO
   Answer: B. NBFM is generated from a stable crystal oscillator, then deviation is raised by frequency multiplication. (Key point: Type of method)

2. How is NBFM produced?
   A. Message integrated, balanced-modulated with a −90° shifted carrier, and added to the carrier
   B. Message differentiated and added to a VCO
   C. Message squared and filtered
   D. Message mixed with a 38 kHz carrier
   Answer: A. The integrated message times the quadrature carrier is added to the carrier, giving NBFM with β < 0.3. (Key point: NBFM generation)

3. What does the mixer do in the chain?
   A. Multiplies the deviation
   B. Shifts the carrier frequency without changing the deviation
   C. Removes the carrier
   D. Reduces the deviation
   Answer: B. Mixing translates the carrier but leaves Δf unchanged; multipliers scale both. (Key point: Mixer effect)

4. What is the final deviation after multipliers ×n1 and ×n2?
   A. Δf1/(n1 n2)
   B. n1 + n2 times Δf1
   C. n1 n2 Δf1
   D. n2 Δf1 only
   Answer: C. Each multiplier scales deviation, so Δf = n1 n2 Δf1; the mixer does not change it. (Key point: Final deviation)

## Related in Communication Systems

- [Angle modulation; Armstrong method of FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-modulation-armstrong) — Communication Systems, chapter 3
- [Armstrong (indirect) FM generation; pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-indirect-pre-emphasis) — Communication Systems, chapter 3
- [Angle modulation; single tone FM time and frequency domain](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-single-tone-fm-time-freq) — Communication Systems, chapter 3
- [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
- [Armstrong FM transmitter numerical](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-numerical-200khz-25hz) — Communication Systems, chapter 3
- [Armstrong FM transmitter numerical (Δf1 = 24 Hz)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-numerical-24hz) — Communication Systems, chapter 3

## Related in other subjects

- [Frequency modulation](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afm-explain) — Data Communication, chapter 5
- [Modulation; AM and FM modulated waves](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Amodulation-am-fm-wave) — Basic Electronics Engineering, chapter 5
- [Single tone FM parameters](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afm-single-tone-numeric) — Data Communication, chapter 5