Signal Modulation

The core principle of signal modulation

Introduction

Modulation is the process of loading low-frequency information signals (such as voice and data) onto a high-frequency carrier signal. Its physical essence is changing the amplitude, frequency, or phase of the carrier wave so that it changes in accordance with the information signal. 


Why is modulation necessary?


1. Antenna size limitations:

Antenna length must be proportional to the wavelength (typically 1/4 of the wavelength). Low-frequency signals (e.g., 1kHz) have extremely long wavelengths, requiring antennas tens of kilometers high; after modulation to higher frequencies (e.g., 1GHz), the antenna can be shortened to the centimeter level.


2. Spectrum allocation:

Allows multiple transmitters to transmit simultaneously on different frequencies (frequency division multiplexing) without interference.


3. Transmission distance and noise immunity:

High-frequency signals have better propagation characteristics in space, and specific modulation methods (e.g., digital modulation) can effectively resist noise.

Common Modulation Techniques


Modulation is mainly divided into two categories: analog modulation and digital modulation:


Analog Modulation

Used for transmitting continuous analog signals (such as traditional broadcasting).

  • AM (Amplitude Modulation): Changes the amplitude of the carrier wave. Simple circuitry, but susceptible to noise interference.

The general AM equation:
$$ y(t) = \big[A + m(t)\big] \cdot \cos(2\pi f_c t) $$

If the modulating signal is a sine wave: $ m(t) = A_m \cos(2\pi f_m t) $
Then:
$$ y(t) = \big[A + A_m \cos(2\pi f_m t)\big] \cdot \cos(2\pi f_c t) $$

Where:
  • $ A $ = carrier amplitude
  • $ A_m $ = modulating amplitude
  • $ f_c $ = carrier frequency (Hz)
  • $ f_m $ = modulating frequency (Hz)

Modulation index $ m = A_m / A $ (must be ≤ 1 for no overmodulation).
Expanded form:
$$ y(t) = A\cos(2\pi f_c t) + \frac{A_m}{2} \cos\big(2\pi (f_c+f_m)t\big) + \frac{A_m}{2} \cos\big(2\pi (f_c-f_m)t\big) $$


  • FM (Frequency Modulation): Changes the frequency of the carrier wave. Better sound quality and stronger anti-interference capability.

For FM, the instantaneous frequency varies sinusoidally:
$$ y(t) = A \cos\left(2\pi f_c t + \frac{\Delta f}{f_m} \sin(2\pi f_m t)\right) $$ Where:

  • $ \Delta f $ = peak frequency deviation
  • Modulation index $ \beta = \Delta f / f_m $

So: $$ y(t) = A \cos\big(2\pi f_c t + \beta \sin(2\pi f_m t)\big) $$


  • PM (Phase Modulation): Changes the phase of the carrier wave.

For a sine wave carrier modulated by a sine wave message:
$$ y(t) = A_c \cos\big[2\pi f_c t + \phi(t)\big] $$ Where $\phi(t)$ is the phase deviation proportional to the message signal.

With sine wave message:
$$ m(t) = A_m \cos(2\pi f_m t) $$

The phase deviation is: $$ \phi(t) = k_p \cdot m(t) = k_p A_m \cos(2\pi f_m t) = \Delta \phi \cdot \cos(2\pi f_m t) $$ Where:

  • $ k_p $ = phase sensitivity (rad/volt)
  • $ \Delta \phi $ = peak phase deviation (radians) = $ k_p A_m $

Final PM signal: $$ y(t) = A_c \cos\big[2\pi f_c t + \Delta \phi \cos(2\pi f_m t)\big] $$



Signal and modulations of AM, FM, and PM.

Digital Modulation

Used for transmitting discrete binary data (0 and 1), and is the foundation of modern communications (Wi-Fi, 5G, Zigbee).

  • ASK (Amplitude Shift Keying): Uses the presence, absence, or different amplitudes of the carrier wave to represent 0 and 1.
  • FSK (Frequency Shift Keying): Uses different frequencies to represent 0 and 1.
  • PSK (Phase Shift Keying): Uses phase shifts to represent data. For example, BPSK (2 phases) or QPSK (4 phases).
  • QAM (Quadrature Amplitude Modulation): Simultaneously changes amplitude and phase, significantly improving spectral efficiency, and is widely used in high-speed networks.



Resonance in RLC Circuit
Communication via energy transfer