Electrical Modulation
Electrical modulation is the process of varying one or more properties of a high-frequency carrier signal—such as amplitude, frequency, or phase—in proportion to a lower-frequency information signal. It is fundamental to all modern communication systems because modulated carriers can travel long distances with minimal energy loss and can be multiplexed to share a single channel. Applications include AM/FM radio, cellular networks, Wi-Fi, and satellite communications.
Key Formula
s(t) = Ac * [1 + ka * m(t)] * cos(2*pi*fc*t)
LaTeX: s(t) = A_c \left[1 + k_a m(t)\right] \cos(2\pi f_c t)
| Symbol | Meaning | Unit |
|---|---|---|
| s(t) | Modulated signal | V |
| A_c | Carrier amplitude | V |
| k_a | Amplitude sensitivity | V⁻¹ |
| m(t) | Message (baseband) signal | V |
| f_c | Carrier frequency | Hz |
Worked Example
Problem
An AM transmitter has a carrier amplitude A_c = 10 V and carrier frequency f_c = 1 MHz. The message signal is m(t) = 3 cos(2π × 1000t) V and the amplitude sensitivity k_a = 0.2 V⁻¹. Find the modulation index μ and the bandwidth of the AM signal.
Solution
Step 1: Calculate modulation index μ = k_a × A_m, where A_m = 3 V is the peak message amplitude. μ = 0.2 × 3 = 0.6 Step 2: Since μ = 0.6 < 1, the signal is under-modulated (no distortion). Step 3: AM bandwidth = 2 × f_m, where f_m = 1000 Hz. BW = 2 × 1000 = 2000 Hz = 2 kHz.
Answer
Modulation index μ = 0.6; Bandwidth = 2 kHz
Comparison of Common Modulation Schemes
| Scheme | Varied Property | Bandwidth | Noise Immunity | Application |
|---|---|---|---|---|
| AM | Amplitude | 2f_m | Low | Medium-wave radio |
| FM | Frequency | 2(Δf + f_m) | High | VHF radio, audio |
| PM | Phase | 2(Δφ + 1)f_m | High | Digital links |
| QAM | Amplitude + Phase | Narrow | Moderate | Cable, Wi-Fi |
| OFDM | Multi-carrier | Flexible | Very High | 4G/5G, Wi-Fi 6 |
Interactive Tools
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Related Terms
Antenna (electrical)
An antenna is a transducer that converts between guided electromagnetic waves in a transmission line and freely propagating electromagnetic waves in space, enabling wireless transmission and reception of signals. Key performance parameters include gain, radiation pattern, bandwidth, polarisation, and impedance; these are governed by the antenna's geometry, size relative to the operating wavelength, and surrounding environment. Antennas are central to radio broadcasting, mobile communications, radar, satellite links, and wireless sensor networks.
Transmission Line (electrical)
An electrical transmission line is a distributed-parameter structure—such as a coaxial cable, twisted pair, or microstrip—designed to guide electromagnetic energy from a source to a load with minimal radiation and reflection losses. At high frequencies, the physical length of the line becomes comparable to the signal wavelength, making lumped-circuit analysis invalid; instead, the line is modelled using the telegrapher's equations that treat resistance, inductance, capacitance, and conductance as distributed per-unit-length quantities. Impedance matching between the line and its terminations is critical to prevent standing waves and power loss.
Digital Signal Processing
Digital Signal Processing (DSP) is the mathematical manipulation of discrete-time, discrete-amplitude representations of signals—obtained by sampling and quantising an analogue source—to extract information, filter noise, compress data, or transform the signal into a desired form. Core operations include convolution, Fourier analysis via the FFT, FIR/IIR filtering, and modulation; these are implemented in real time on dedicated DSP chips or general-purpose microprocessors. DSP underpins audio processing, medical imaging, telecommunications, radar, sonar, and machine learning inference at the edge.
From Latin "modulatio" (a measuring, rhythmical measure), derived from "modulari" (to measure, regulate), from "modulus" (a small measure). In electronics, the term was adopted in the early 20th century when engineers began encoding audio onto radio carriers.