What happens when AM modulation index exceeds 1?

Over-modulation causes envelope distortion and spectral splatter into adjacent channels. The signal can no longer be demodulated correctly with a simple envelope detector.

Why is FM more bandwidth-efficient than AM?

FM trades bandwidth for noise immunity. Carson's rule gives BW = 2(Δf + fm), which is wider than AM's 2·fm, but FM provides much better SNR because information is in frequency variations rather than amplitude.

What is Carson's rule?

Carson's rule estimates FM bandwidth as BW = 2(Δf + fm), where Δf is the peak frequency deviation and fm is the highest modulating frequency. It captures about 98% of the signal power.

How does PM differ from FM?

In PM, the instantaneous phase is proportional to the message signal; in FM, the instantaneous frequency is proportional. Mathematically, PM of a sinusoid produces the same spectrum as FM, but the modulation index scales differently with modulating frequency.

What is sideband power efficiency?

For AM, only the sidebands carry information. Efficiency η = m²/(2 + m²) × 100. At 100% modulation (m = 1), efficiency is only 33.3%, meaning two-thirds of the power is wasted in the carrier.

Why do aircraft use AM instead of FM?

AM allows multiple stations to transmit on the same frequency and be heard simultaneously (the "party line" effect), which is critical for aviation safety. FM exhibits the capture effect, where only the strongest signal is heard.

Modulation Calculator

Calculate AM, FM, and PM modulation index, bandwidth (Carson's rule), sideband frequencies, carrier power, and efficiency for radio signals.

Modulation Type

Carrier Frequency (Hz)

Message Frequency (Hz)

Carrier Amplitude (V)

Message Amplitude (V)

Modulation Index

0.5000

m = Am/Ac

Bandwidth

10.000 kHz

BW = 2·fm

Carrier Power

50.0000 W

Pc = Ac²/2 (normalised R=1Ω)

Total Power

56.2500 W

Pt = Pc(1 + m²/2)

Upper Sideband

1.005 MHz

fc + fm

Lower Sideband

995.000 kHz

fc − fm

Sideband Power

6.2500 W

Psb = Pt − Pc

Efficiency

11.11 %

η = Psb/Pt × 100

Sidebands

2 (upper + lower)

Modulation Depth

50.0%

Frequency Allocation Reference

Band	Range	Modulation	Channel BW
AM Broadcast	530–1700 kHz	AM	10 kHz
Shortwave	3–30 MHz	AM/SSB	6 kHz
FM Broadcast	88–108 MHz	FM	200 kHz
VHF Aviation	118–137 MHz	AM	25 kHz
PMR446	446 MHz	FM	12.5 kHz
Wi-Fi 2.4 GHz	2.4 GHz	OFDM/QAM	20 MHz
LTE Band 7	2.6 GHz	OFDM/QAM	20 MHz
5G mmWave	28 GHz	OFDM/QAM	400 MHz

Planning notes, formulas, and examples

About the Modulation Calculator

Modulation is the process of encoding information onto a carrier wave by varying its amplitude, frequency, or phase. This calculator handles three fundamental types: Amplitude Modulation (AM), Frequency Modulation (FM), and Phase Modulation (PM).

For AM signals, enter carrier and message amplitudes to find the modulation index m = Am/Ac, total power, sideband power, and efficiency. The calculator warns you when over-modulation occurs (m > 1), which causes signal distortion and spectral splatter.

For FM and PM, enter the frequency deviation to compute the modulation index β = Δf/fm and the bandwidth using Carson's rule: BW = 2(Δf + fm). The tool also shows significant sideband counts and carrier frequency allocations for common radio bands from AM broadcast through 5G millimeter wave.

Whether you are designing a radio transmitter, studying for a communications exam, or debugging a modulator circuit, this calculator gives you every key parameter in one place. Preset buttons load typical values for AM broadcast, FM radio, SSB shortwave, and VHF communications.

When This Page Helps

Understanding modulation parameters is essential for radio communication system design. This calculator eliminates working by hand of modulation index, bandwidth, and power for AM, FM, and PM signals.

It is especially useful for students, RF engineers, and amateur radio operators who need to verify modulator designs, estimate channel bandwidth, or compare modulation schemes.

How to Use the Inputs

Select the modulation type: AM, FM, or PM.
Enter the carrier frequency in Hertz.
Enter the message (audio) frequency in Hertz.
Enter the carrier amplitude in volts.
For AM, enter the message amplitude. For FM/PM, enter the frequency deviation.
Read the modulation index, bandwidth, power values, and sideband frequencies.
Use preset buttons to load typical radio scenarios quickly.

Formula used

AM: m = Am/Ac, BW = 2·fm, Pt = Pc(1 + m²/2), η = (m²/2)/(1 + m²/2) × 100.
FM/PM: β = Δf/fm, BW = 2(Δf + fm) (Carson's rule), Pc = Ac²/(2R).
Sidebands: USB = fc + fm, LSB = fc − fm.

Example Calculation

Result: m = 0.50, BW = 10 kHz, Pt = 56.25 W, η = 11.11%

Modulation index m = 5/10 = 0.50. Bandwidth = 2 × 5 kHz = 10 kHz. Carrier power = 50 W. Total power = 50(1 + 0.25/2) = 56.25 W. Efficiency = 6.25/56.25 = 11.1%.

Tips & Best Practices

For AM, keep m between 0.8 and 1.0 for maximum efficiency without over-modulation.
FM broadcast uses ±75 kHz deviation; narrowband FM (e.g., PMR) uses ±5 kHz.
The number of significant FM sidebands is approximately β + 1 on each side of the carrier.
SSB (Single Sideband) transmits only one sideband, halving bandwidth and eliminating carrier waste.
Digital modulation (QAM, OFDM) builds on these fundamentals but modulates both amplitude and phase simultaneously.

When To Use This Calculator

Calculate AM, FM, and PM modulation index, bandwidth (Carson Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

Over-modulation causes envelope distortion and spectral splatter into adjacent channels. The signal can no longer be demodulated correctly with a simple envelope detector.