FM Bandwidth Calculator
Broadcast FM with 75 kHz deviation and 15 kHz audio needs 180 kHz by Carson’s rule, with β = 5.
180 kHz
- Modulation index β = Δf/f_m
- 5
- Type
- wideband FM
- Significant sideband pairs ≈ β + 1
- 6
| n | Jₙ(β) | Power share Jₙ² |
|---|---|---|
| 0 | -0.177597 | 0.03154 |
| 1 | -0.327579 | 0.2146 |
| 2 | 0.0465651 | 0.004337 |
| 3 | 0.364831 | 0.2662 |
| 4 | 0.391232 | 0.3061 |
| 5 | 0.261141 | 0.1364 |
| 6 | 0.131049 | 0.03435 |
| 7 | 0.0533764 | 0.005698 |
Step-by-step solution
- β = Δf ÷ f_m = 75 ÷ 15 = 5
- Carson’s rule: B = 2(Δf + f_m) = 2 × (75 + 15) kHz = 180 kHz
FM Bandwidth Formula
B ≈ 2(Δf + f_m), β = Δf/f_m
sideband n has amplitude Jₙ(β) of the unmodulated carrier
Worked Example
Broadcast FM with 75 kHz peak deviation and 15 kHz audio:
- β = Δf ÷ f_m = 75 ÷ 15 = 5
- Carson’s rule: B = 2(Δf + f_m) = 2 × (75 + 15) kHz = 180 kHz
Type: wideband FM · Significant sideband pairs ≈ β + 1: 6
| n | Jₙ(β) | Power share Jₙ² |
|---|---|---|
| 0 | -0.177597 | 0.03154 |
| 1 | -0.327579 | 0.2146 |
| 2 | 0.0465651 | 0.004337 |
| 3 | 0.364831 | 0.2662 |
| 4 | 0.391232 | 0.3061 |
| 5 | 0.261141 | 0.1364 |
| 6 | 0.131049 | 0.03435 |
| 7 | 0.0533764 | 0.005698 |
GATE tip
Narrowband FM (β < 0.3) has the same bandwidth as AM, 2f_m. Frequency multipliers multiply both the carrier and the deviation, so β scales too.
More Communication Calculators
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m = (V_max − V_min)/(V_max + V_min), Pₜ = P_c(1 + m²/2)
each sideband P_c m²/4; efficiency m²/(2 + m²); bandwidth 2f_m
Example: An AM envelope swinging between 15 V and 5 V on a 100 W carrier with 5 kHz audio: Modulation index m = 0.5.
-
PCM Bit Rate Calculator
R = n fₛ × channels
L = 2ⁿ levels; SQNR = 6.02n + 1.76 dB; minimum bandwidth R/2
Example: Telephone-quality speech: 8 bits at 8 kHz, one channel: Bit rate = 64 kbit/s.
Frequently asked questions
How accurate is Carson’s rule?
It captures about 98 % of the power. Counting sidebands above 1 % of the carrier gives a slightly wider figure.
When does the carrier vanish?
When J₀(β) = 0, first at β = 2.405. Engineers use this to calibrate deviation.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). FM Bandwidth Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/fm-bandwidth-calculator/
IEEE
Scientific Converters, "FM Bandwidth Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/fm-bandwidth-calculator/