Modulation and Demodulation of Signals (Part 1): The Essence of Modulation – The "Transformation" Art of Signals Breaking Through Physical Constraints

When we make a video call on our mobile phones, when a radio plays clear music, or when a satellite transmits space observation data back to Earth, there is a key operation behind it all—modulation. In the era of digital intelligence, we have long been accustomed to the instant long-distance transmission of information, yet we rarely stop to think: why can the originally "sluggish" low-frequency useful signals travel across mountains and seas? The answer lies in the "transformative magic" of modulation technology—it equips low-frequency signals with high-frequency "wings," breaking through physical limitations and becoming the technological cornerstone of information dissemination. In this article, we will first uncover the basic logic of modulation, elaborate on the precise principles of analog modulation, and look back at the technological foundation-laying path of the analog communication era.

I. Why is modulation necessary? Three unavoidable physical problems

The useful signals in our daily lives, whether they are audible audio (20Hz - 20kHz) or temperature and pressure data collected by sensors (DC-10kHz), all belong to low-frequency signals. If these signals are directly transmitted wirelessly, they will encounter three "fatal bottlenecks", and modulation is the core solution to solve these problems:

1. Physical Limits of Antenna Size: The "Fetter of Long-Distance Travel" for Low-Frequency Signals

For a signal to be effectively radiated through an antenna, it must satisfy the physical law that "antenna length ≈ signal wavelength / 4" — this is a fundamental principle of electromagnetic radiation and cannot be violated. We can clearly see the difference through precise calculations:

20Hz audio signal: wavelength λ = speed of light c / frequency f (3×10⁸m/s ÷ 20Hz) = 15,000km, which is equivalent to 3/4 of the Earth's equatorial circumference. Such a huge antenna is completely impossible to manufacture;

1MHz radio signal: wavelength λ = 3×10⁸m/s ÷ 10⁶Hz = 300m. Building a 300-meter-high broadcast tower can achieve effective radiation, which is also the technical basis of early medium-wave broadcasting. For example, the height of the Beijing Central Radio and Television Tower is close to 300 meters, which is designed to adapt to the radiation of medium-wave signals.

One of the core functions of modulation is to "load" low-frequency useful signals onto high-frequency carriers, enabling the signals to adapt to the achievable antenna size—just like equipping a hiker with an off-road vehicle, making previously insurmountable distances feasible. The "loading" here is not a simple superposition, but rather involves "encoding" the information of the useful signal into the carrier by changing a certain parameter (amplitude, frequency, phase) of the high-frequency carrier. This encoding process is a precise modulation process. For example, the sound of our speech (low-frequency), after being converted into an electrical signal by a microphone, must be modulated and loaded onto a high-frequency carrier before it can be transmitted through a mobile phone antenna to achieve long-distance communication.

2. Efficient utilization of spectrum resources: a key design to avoid "traffic congestion"

The frequency spectrum is a limited public resource, just like the roads in a city. If all low-frequency signals are transmitted in the low-frequency band, serious "crosstalk" interference will occur—similar to vehicles from multiple lanes mixing together, making it impossible to distinguish them. Modulation technology, through the "frequency division multiplexing" mechanism, allocates exclusive high-frequency "lanes" (carrier frequencies) to different signals, enabling the orderly utilization of the frequency spectrum:

• FM broadcasting: It exclusively uses the 88 - 108MHz frequency band, with adjacent radio stations separated by 200kHz, ensuring that signals of different programs do not interfere with each other. For example, when we switch between FM93.8 and FM101.1 in a car, we can clearly hear different programs, which benefits from this frequency band division.

• WiFi 2.4GHz frequency band: It is divided into 14 independent channels with a channel spacing of 5MHz. If a home router experiences signal lag, switching the channel often restores smoothness because it avoids channel conflicts with neighboring routers.

3. Essential improvement in anti-interference capability: the "natural advantage" of high-frequency signals

The anti-interference ability of low-frequency signals is extremely poor, just like a whisper that is easily drowned out by noise; while the frequency characteristics of high-frequency signals make it easier to achieve "selective reception" through filter circuits - similar to how we can accurately capture a whistle of a specific frequency in a noisy environment. For example, in a factory workshop, the low-frequency noise generated by the operation of motors can interfere with many devices, but the walkie-talkies in the workshop use high-frequency signals for transmission, which can penetrate the noise to achieve clear communication; in addition, high-frequency signals have higher radiation efficiency and can achieve longer transmission distances under the same transmission power, which is also the core reason why satellite communications and long-distance broadcasting all use high-frequency carriers.

Modulation and demodulation of signals

II. Accurate Analysis: Core Principles and Processes of Analog Modulation

Analog modulation is the "founding father" of modulation technology, and its core logic is "to accurately map changes in low-frequency analog signals to a certain parameter (amplitude, frequency, phase) of high-frequency carriers". It is like painting on rice paper with different brush techniques; although the techniques are different, they can all accurately convey the changing details of information. The following is an analysis of the precise processes of three classic analog modulations, accompanied by daily scene cases to help understand:

Amplitude Modulation (AM): A "precise mapping" where the amplitude fluctuates synchronously with the signal

The core of AM is "the instantaneous value of the carrier amplitude and the modulation signal (low-frequency useful signal) changes precisely synchronously", and its mathematical model is: s(t) = Ac[1 + m·m(t)]·cos(2πfc t). The physical meaning of each parameter and the precise details of the modulation process are as follows:

• Parameter definition: Ac is the initial amplitude of the carrier, fc is the carrier frequency, m(t) is the modulation signal (such as audio), and m is the modulation index (ranging from 0 to 1, which determines the depth of amplitude change);

• Modulation process: When m(t) is at the positive peak, the carrier amplitude reaches the maximum value Ac(1+m); when m(t) is at the negative peak, the carrier amplitude drops to the minimum value Ac(1-m); when m(t)=0, the carrier maintains the initial amplitude Ac, forming an AM waveform where the "envelope" is completely consistent with the modulation signal;

• Key note: The modulation index m must be controlled between 0 and 1. If m > 1, it will cause "over-modulation distortion" — at this time, the carrier amplitude will have zero-point clipping, resulting in severe distortion when restoring the signal, which is a core taboo in the design of AM modulation circuits;

• Bandwidth characteristics: The bandwidth of the AM signal is B = 2fm (fm is the highest frequency of the modulation signal). For example, when transmitting a 20kHz audio signal, a spectrum width of 40kHz is required, and the spectrum efficiency is low.

The advantage of AM is that the circuit implementation is simple (only diodes, capacitors, and resistors are needed to build a basic modulation circuit) and the cost is low; the disadvantage is poor anti-interference ability — external amplitude interference (such as lightning, motor radiation) will be directly superimposed on the carrier amplitude, leading to distortion of the restored signal. Nowadays, AM is still used in medium-wave broadcasting (530 - 1700kHz). For example, the simple radios we use in rural areas receive AM signals. When encountering thunderstorms, the signals become messy because the amplitude interference generated by lightning affects AM demodulation.

Amplitude Modulation (AM)

Frequency Modulation (FM): "Dynamic adjustment" where the frequency precisely shifts with the signal

The core of FM is "the precise deviation of the carrier frequency with the instantaneous value of the modulation signal" rather than amplitude changes. Its mathematical model is: s(t) = Ac·cos[2πfc t + 2πkf ∫m(τ)dτ]. The precise details of the modulation process are as follows:

• Core parameters: kf is the frequency sensitivity (unit: Hz/V, representing the carrier frequency deviation caused by the modulation signal per unit voltage), and ∫m(τ)dτ is the integral of the modulation signal, reflecting the cumulative effect of frequency deviation.

• Modulation process: When m(t) reaches the positive peak, the carrier frequency reaches the maximum value fc + Δf (Δf = kf·|m(t)|max, called the maximum frequency deviation); when m(t) reaches the negative peak, the carrier frequency drops to the minimum value fc - Δf; when m(t) = 0, the carrier frequency remains unchanged at fc, and the frequency deviation is proportional to the instantaneous value of the modulation signal.

• Anti-interference advantage: Since the information of the FM signal is carried in the frequency rather than the amplitude, external amplitude-type interference can be directly filtered out through a limiting circuit (the limiting circuit can clamp the signal amplitude at a fixed value without affecting the frequency change). Therefore, the anti-interference ability of FM is far superior to that of AM, and the sound quality is clearer (it can transmit full-band audio from 30Hz to 15kHz).

FM is widely used in scenarios such as frequency modulation broadcasting (88 - 108MHz) and analog TV audio. The most common example in daily life is the car FM radio. Even when the vehicle is driving on a bumpy road, with engine noise and electromagnetic interference from other vehicles, the radio programs can still be heard clearly, which is an intuitive manifestation of FM's strong anti-interference ability. Early analog TV audio also used FM modulation to ensure that viewers could hear clear sound while watching the picture.

Frequency Modulation (FM)

Phase Modulation (PM): The "hidden coding" where the phase is precisely deflected with the signal

PM and FM both belong to "angle modulation," with the core being that "the carrier phase is precisely deflected according to the instantaneous value of the modulation signal." The mathematical model is: s(t) = Ac·cos[2πfc t + kp·m(t)] (where k_p is the phase sensitivity, with the unit rad/V). The key to the modulation process is that the phase deflection Δφ = kp·m(t) is directly related to the instantaneous value of the modulation signal, rather than an integral relationship — this is the core difference between PM and FM.

PM has limited applications in analog communication (phase changes are not easily perceived directly), but it has become a core foundation in digital communication. However, in early analog walkie-talkies, some models used PM modulation to achieve short-distance communication. For example, old walkie-talkies used in construction sites and shopping malls have stable signal transmission and are not easily affected by amplitude interference, which is precisely due to the characteristics of PM modulation. In digital communication, PSK (Phase Shift Keying) technology is a digital extension of PM modulation, using different phase deflections to represent 0 and 1, laying the theoretical foundation for the development of digital modulation technology.

Analog Modulation —— The Technical Foundation and Era Value of Information Dissemination

Although analog modulation technology is no longer the mainstream of current communications, it has accomplished the pioneering mission of "enabling signals to transcend physical limitations". From early medium-wave broadcasting to FM radio stations, from analog television to the first generation of mobile communications (1G), analog modulation, with its simple and reliable principles, realized long-distance wireless transmission of information for the first time, breaking the geographical constraints on information interaction and laying a technical foundation for human society to enter the information age. In today's era of rapid development of digital technology, the core logics of analog modulation - "parameter mapping" and "frequency division multiplexing" - are still in use. It is not only the "source of living water" for communication technology, but also has accumulated core technical experience in parameter mapping and frequency division multiplexing for the field of signal processing. These valuable technical accumulations have also laid a key foundation for the innovation of subsequent digital modulation technologies.