Modulation Demodulation Calculator

Calculate modulation parameters for AM, FM, PM, SSB, PSK, FSK and QAM signals. Essential tool for communication engineers and students.

Real-time Calculation
AM
FM
PM
SSB
PSK
FSK
QAM

Amplitude Modulation Formulas:

  • Modulation Index: μ = A_m / A_c
  • Bandwidth: BW = 2 × f_m
  • Total Power: P_t = P_c (1 + μ²/2)
  • Efficiency: η = (μ²/2) / (1 + μ²/2) × 100%
V
Amplitude of the carrier signal
V
Amplitude of the modulating signal
Hz
Frequency of the carrier signal
Hz
Frequency of the modulating signal

Frequency Modulation Formulas:

  • Modulation Index: β = Δf / f_m
  • Bandwidth: BW ≈ 2(β + 1)f_m (Carson's Rule)
  • Frequency Deviation: Δf = k_f × A_m
  • Phase Deviation: Δθ = β
Hz
Frequency of the carrier signal
Hz
Frequency of the modulating signal
Hz
Maximum frequency deviation
Hz/V
Frequency sensitivity constant

Phase Modulation Formulas:

  • Modulation Index: β_p = k_p × A_m
  • Bandwidth: BW ≈ 2(β_p + 1)f_m
  • Phase Deviation: Δθ = k_p × A_m
  • Equivalent Frequency Deviation: Δf = β_p × f_m
Hz
Frequency of the carrier signal
Hz
Frequency of the modulating signal
rad
Maximum phase deviation
rad/V
Phase sensitivity constant

Single Sideband Modulation Formulas:

  • Modulation Index: μ = A_m / A_c
  • Bandwidth: BW = f_m (half of AM)
  • Total Power: P_t = P_c × μ²/4
  • Efficiency: η = 100% (theoretically)
V
Amplitude of the carrier signal
V
Amplitude of the modulating signal
Hz
Frequency of the carrier signal
Hz
Frequency of the modulating signal
Select which sideband to transmit

Phase Shift Keying Formulas:

  • Phase Shift: Δφ = 2π/M (for M-PSK)
  • Bandwidth: BW = R_b / log₂(M)
  • Symbol Rate: R_s = R_b / log₂(M)
  • BER (approx): 0.5 × erfc(√(E_b/N₀) × sin(π/M))
bps
Data transmission rate in bits per second
Number of phase states
Hz
Frequency of the carrier signal
dB
Energy per bit to noise power spectral density ratio

Frequency Shift Keying Formulas:

  • Frequency Separation: Δf = |f₁ - f₀|
  • Bandwidth: BW ≈ 2Δf + R_b (for binary FSK)
  • Modulation Index: h = 2Δf / R_b
  • BER (approx): 0.5 × erfc(√(E_b/(2N₀))) for coherent detection
bps
Data transmission rate in bits per second
Hz
Carrier frequency for binary '0'
Hz
Carrier frequency for binary '1'
dB
Energy per bit to noise power spectral density ratio

Quadrature Amplitude Modulation Formulas:

  • Symbol Rate: R_s = R_b / log₂(M)
  • Bandwidth: BW = R_s (with ideal filtering)
  • Constellation Points: M = 2ⁿ (where n is even)
  • BER (approx): (4/log₂(M)) × (1-1/√M) × Q(√(3×SNR/(M-1)))
bps
Data transmission rate in bits per second
Number of points in the constellation diagram
Hz
Frequency of the carrier signal
dB
Signal-to-noise ratio at receiver
Advanced Options
Thermal noise density in dBm/Hz (default: -174 dBm/Hz)
Transmitter power in dBm
Total path loss in dB
Receiver antenna gain in dBi
Calculating...

Understanding Modulation Techniques

Modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted.

Key Modulation Parameters:

  • Carrier Signal: High-frequency signal that carries the information
  • Modulating Signal: Information-bearing signal (voice, data, video)
  • Modulation Index: Measure of the extent of modulation
  • Bandwidth: Range of frequencies occupied by the modulated signal
  • BER (Bit Error Rate): Probability of bit errors in digital communication

Modulation Types Comparison

Type Parameter Varied Bandwidth Efficiency Noise Immunity Power Efficiency Applications
AM Amplitude Low Poor Low AM radio broadcasting
FM Frequency Medium Good Medium FM radio, TV audio
PM Phase Medium Good Medium Some digital communications
SSB Amplitude (Single Sideband) High Poor High Maritime, amateur radio
PSK Phase High Good High Wi-Fi, satellite, cable modems
FSK Frequency Low Good Medium Telemetry, paging, RFID
QAM Amplitude & Phase Very High Medium Medium Cable modems, Wi-Fi, Digital TV

System Performance Metrics

1

Bit Error Rate (BER): The probability that a transmitted bit will be received in error. Lower BER indicates better system performance.

2

Signal-to-Noise Ratio (SNR): Ratio of signal power to noise power. Higher SNR means better signal quality and lower BER.

3

Bandwidth Efficiency: Data rate per unit bandwidth (bps/Hz). Higher efficiency means more data transmitted in limited bandwidth.

4

Power Efficiency: Amount of power needed to achieve a specific BER. Important for battery-powered devices.

5

Spectral Efficiency: Combination of bandwidth and power efficiency. Maximizing spectral efficiency is key in modern wireless systems.

Technical Note: The choice of modulation technique depends on application requirements: bandwidth availability, power constraints, noise environment, and implementation complexity. Modern communication systems often use adaptive modulation that changes based on channel conditions.

Frequently Asked Questions

AM (Amplitude Modulation) varies the amplitude of the carrier signal in proportion to the modulating signal. FM (Frequency Modulation) varies the frequency of the carrier signal. AM is simpler but more susceptible to noise, while FM provides better noise immunity at the cost of greater bandwidth.

Modulation index measures the extent of modulation. For AM, it's the ratio of modulating amplitude to carrier amplitude (μ = A_m/A_c). For FM, it's the ratio of frequency deviation to modulating frequency (β = Δf/f_m). It determines signal quality, bandwidth, and power distribution. In AM, μ > 1 causes distortion (overmodulation).

FM bandwidth is typically estimated using Carson's rule: BW ≈ 2(Δf + f_m), where Δf is the frequency deviation and f_m is the highest modulating frequency. For commercial FM broadcasting with Δf = 75 kHz and f_m = 15 kHz, bandwidth ≈ 2(75 + 15) = 180 kHz.

QAM (Quadrature Amplitude Modulation) modulates both amplitude and phase, allowing multiple bits per symbol. This provides high bandwidth efficiency. 16-QAM carries 4 bits/symbol, 64-QAM carries 6 bits/symbol. However, QAM requires higher signal-to-noise ratio and more complex transceivers compared to simpler modulation schemes.

Narrowband FM has a modulation index β < 1 and relatively small frequency deviation. It uses less bandwidth but has poorer noise immunity. Wideband FM has β > 1, larger frequency deviation, uses more bandwidth but provides better noise immunity. Commercial FM broadcasting uses wideband FM (β ≈ 5, Δf = 75 kHz) for high fidelity.