AM/FM Modulation Simulator Back
Signal Processing

AM/FM Modulation Simulator

Learn how a message signal such as audio is "carried" by a radio wave through modulation. Switch between amplitude modulation (AM) and frequency modulation (FM), and adjust the carrier frequency, message frequency and modulation index to watch the modulated waveform, frequency spectrum and occupied bandwidth update in real time.

Parameters
Modulation type
AM varies amplitude, FM varies instantaneous frequency
Carrier frequency f_c
Hz
High-frequency reference wave that carries the information
Message frequency f_m
Hz
Low-frequency signal (e.g. audio) placed on the carrier
Modulation index
For AM: modulation depth μ (overmodulation above 1) / For FM: index β
Results
Occupied bandwidth (Hz)
Carrier frequency (Hz)
Modulation index
Overmodulation
Power efficiency (%)
Message frequency (Hz)
Modulated waveform animation

The scrolling wave is the modulated signal s(t). In AM the amplitude swells and shrinks within the envelope (dashed). In FM the amplitude is constant and the wave bunching shows the instantaneous frequency change.

Time waveform — modulated signal s(t)
Frequency spectrum
Theory & Key Formulas

$$\text{AM: }s(t)=[1+\mu\,m(t)]\cos(2\pi f_c t)$$

Amplitude modulation. The carrier cos(2πf_c t) has its amplitude varied by the message m(t). μ is the modulation depth; μ>1 collapses the envelope into overmodulation. The occupied bandwidth is fixed at 2f_m.

$$\text{FM: }s(t)=\cos\!\big(2\pi f_c t+\beta\sin(2\pi f_m t)\big),\quad B_{FM}=2(\beta+1)f_m$$

Frequency modulation. The instantaneous frequency varies; the occupied bandwidth follows Carson's rule B_FM=2(β+1)f_m. β is the FM modulation index and Δf=β·f_m is the frequency deviation.

The AM occupied bandwidth is fixed at 2f_m regardless of the modulation index, while the FM bandwidth grows with the modulation index β. This is the basis of the trade-off "FM gains noise immunity at the cost of wider bandwidth".

What is AM/FM Modulation?

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I always thought "AM" and "FM" on a radio were just types of station. What actually makes them different?
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Roughly speaking, they are two ways of putting audio onto a radio wave. A low-frequency signal like audio cannot be radiated efficiently from an antenna on its own, so we make a high-frequency "carrier" carry it — that is modulation. AM varies the carrier's amplitude in time with the audio. FM keeps the amplitude constant and instead makes the carrier's frequency speed up and slow down with the audio.
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So amplitude versus frequency. Looking at the waveform on the left, in AM the height of the wave ripples up and down. When I switch to FM the height stays the same but the spacing of the wave changes.
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Exactly that. The dashed line wrapping the AM waveform is the "envelope", and it is the original audio shape itself. A receiver just traces the envelope to recover the audio — which is why an AM radio can use a very simple, cheap circuit. In FM, you see the wave getting dense and then sparse, right? Dense means a high instantaneous frequency, sparse means a low one. The audio amplitude has been converted into a "frequency shift".
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If AM is simpler, why do we even have FM?
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AM has a weakness. Noise basically rides on a radio wave as "amplitude fluctuation". Because AM puts the information in the amplitude, noise turns straight into audible noise — that crackle on an AM radio during a thunderstorm is exactly this. FM puts the information in the frequency, and the receiver can simply clip away the amplitude. So FM resists noise and sounds clean. In practice FM broadcasting suits music, while AM travels far and suits news and emergency broadcasts.
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Then FM wins on everything. Is there any reason AM is still used?
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FM has a cost too. Look at the "Frequency spectrum" below. AM has just one pair of sidebands either side of the carrier, with an occupied bandwidth fixed at 2f_m. But raise the FM modulation index β and many sideband pairs spread out, eating up bandwidth fast. Spectrum is a finite resource, so FM — using a wide band per station — fits fewer stations. AM is narrow-band, power-efficient and cheap to build. So where you want to reach widely and thinly, AM is still in service.
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When I push the modulation index μ above 1, a red warning appears on the waveform. What is happening there?
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That is "overmodulation". In AM, setting μ>1 makes the envelope 1+μ·m(t) go negative for an instant. An envelope detector cannot handle a negative value, so that part folds over and the sound distorts. The spectrum also spreads further and interferes with the next station. That is why real AM broadcast stations keep μ around 0.7-0.9 and tightly control peaks so they never exceed 100%. Try moving the slider around 1.0 and watch the bottom of the waveform flip over.

Frequently Asked Questions

AM (amplitude modulation) varies the carrier's amplitude with the message signal: s(t)=[1+μ·m(t)]·cos(2πf_c t). FM (frequency modulation) varies the carrier's instantaneous frequency with the message: s(t)=cos(2πf_c t+β·sin(2πf_m t)). AM uses simple circuits and cheap receivers but is noise-sensitive because noise rides directly on the amplitude, and overmodulation clips the envelope. FM keeps a constant amplitude, so it resists amplitude noise and sounds clean, but it occupies a wider bandwidth.
In AM, overmodulation occurs when the modulation index (modulation depth) μ exceeds 1. The envelope 1+μ·m(t) goes negative for part of the cycle, and an envelope detector folds that region over, distorting the recovered waveform. The spectrum also spreads and interferes with adjacent channels. Practical AM broadcast keeps μ below 1 (roughly 0.7-0.9) so that peaks never exceed 100%. This simulator flags overmodulation whenever μ>1.
FM bandwidth is estimated with Carson's rule, B_FM = 2·(β+1)·f_m, where β is the FM modulation index and f_m is the message frequency. Increasing β raises the peak frequency deviation Δf=β·f_m and the number of significant sideband pairs (about β+1), widening the band. By contrast, the occupied bandwidth of AM is always 2·f_m regardless of the modulation index. This contrast shows how FM trades wider bandwidth for higher fidelity and noise immunity.
An FM wave cos(2πf_c t+β·sin(2πf_m t)) can be expanded with trigonometric identities into the carrier f_c plus an infinite set of sidebands at f_c±n·f_m (n=1,2,3…). The amplitude of each sideband is given by the Bessel function of the first kind J_n(β). For small β only up to J_1 is significant, giving a three-line spectrum close to AM; the larger β is, the more high-order sidebands appear. This simulator approximates J_n(β) with a series to draw the spectrum.

Real-World Applications

Radio broadcasting: The most familiar application. Medium-wave (MW) AM broadcasting occupies a narrow band per station and reaches far via ionospheric reflection, so it is used for wide-area news, weather and disaster information. FM broadcasting takes a large modulation index for high fidelity and suits music programmes and community radio. Even within "radio", AM emphasizes range and spectral economy while FM emphasizes audio quality and noise immunity — two different design philosophies.

Wireless and land-mobile radio: Analog land-mobile and amateur radio have long used narrow-band FM (NFM) for voice. It resists amplitude noise and fading, and the amplitude can be flattened by a limiter, which suits mobile communication. Aviation radio, however, still uses AM: unlike FM — where the "capture effect" lets only one station survive when several transmit at once — overlapping AM transmissions can be heard together, which is actually desirable for safety.

Instrumentation and sensor signal transmission: The FM idea is also applied to telemetry and sensor signals. Voltage-to-frequency (V-F) conversion turns a voltage into a frequency, which is far less affected by amplitude attenuation and noise over long cabling and can be recovered accurately with a frequency counter. From pulse outputs of rotation sensors to analog transmission over optical fiber, there are many cases where "frequency is more robust than amplitude" pays off.

Audio and electronic instruments: FM modulation is also used to create sounds in synthesizers (FM synthesis). The FM synths of the 1980s frequency-modulated an audible carrier with another audible signal, generating metallic, harmonically rich timbres from the abundant sidebands set by Bessel functions. The spreading spectrum you see when you raise the modulation index β in this simulator is exactly the principle behind FM synthesis timbre changes.

Common Misconceptions and Pitfalls

The most common mistake is assuming "the higher the modulation index, the better". In AM, pushing the modulation depth μ toward 1 puts more power into the sidebands and raises transmission efficiency, but the instant μ exceeds 1 the signal is overmodulated, the envelope collapses and the sound distorts. In FM, raising the index β increases the frequency deviation and improves the S/N, but the occupied bandwidth grows without bound according to Carson's rule B=2(β+1)f_m and encroaches on adjacent channels. The modulation index is a trade-off between "efficiency / fidelity" and "bandwidth / interference" — not a parameter to maximize blindly.

Next is believing "in AM the information is in the carrier". In fact the carrier itself carries no information at all. Only the two sidebands carry the information; the carrier is sent merely as a reference for demodulation. This is why the AM power efficiency η=μ²/(2+μ²) tops out at just 33% even at μ=1 — most of the transmitted power is spent on a carrier that conveys nothing. That is exactly why DSB-SC and SSB schemes, which suppress the carrier or one sideband, were developed. This tool handles standard AM, but the low efficiency is an important design starting point.

Finally, the misconception that "FM is better the wider its bandwidth, so we can widen it freely". Wide-band FM does have a better S/N, but once the receiver input S/N drops below a certain threshold, the output degrades abruptly — the "threshold effect" (FM threshold). Widening the bandwidth also lets more noise power into the receiver, which actually worsens the threshold. In a weak field, narrow-band FM is often more robust, so "wide-band FM" does not always mean "high fidelity". Bandwidth must be designed around the S/N of the intended reception environment.

How to Use

  1. Set the carrier frequency (fcNum) between 540 kHz and 1600 kHz for AM, or 88-108 MHz for FM broadcast bands.
  2. Define the message (modulating) frequency (fmNum) typically 300 Hz to 3 kHz for audio signals.
  3. Adjust modulation index (modIndexNum): for AM keep below 1.0 to avoid over-modulation; for FM use 5-15 for typical broadcast quality.
  4. Observe occupied bandwidth in the output: AM bandwidth = 2 × message frequency; FM bandwidth = 2 × (modulation index + 1) × message frequency (Carson's rule).

Worked Example

FM radio station at carrier 101.5 MHz with audio message frequency 2 kHz and modulation index 5: occupied bandwidth = 2 × (5 + 1) × 2 kHz = 24 kHz. An AM broadcast at 680 kHz with 1 kHz audio produces bandwidth = 2 × 1 kHz = 2 kHz. Higher modulation index increases bandwidth and noise immunity but requires wider channel allocation per FCC regulations.

Practical Notes

  1. AM is susceptible to atmospheric noise; use lower modulation indices (0.7-0.9) in industrial environments with high electromagnetic interference.
  2. FM requires 200 kHz channel spacing in broadcast bands; verify your bandwidth does not exceed allocated limits.
  3. Message frequency bandwidth limits: telephone-grade audio uses 300-3400 Hz; high-fidelity FM uses up to 15 kHz, requiring modulation index 4-5 for acceptable signal-to-noise ratio.
  4. Overmodulation (index > 1.0 for AM) causes spectral splatter and adjacent-channel interference; always validate output bandwidth before transmission.