📚 Radio Waves: Communication and Modulation | 无线电波：通信与调制
Radio waves are the longest-wavelength, lowest-frequency portion of the electromagnetic spectrum, spanning frequencies from about 3 kHz to 300 GHz. They are generated by accelerating electric charges and have become the backbone of modern wireless communication, including AM/FM radio, television, and mobile networks. Understanding how radio waves are produced, modulated, transmitted, and received is a central topic in A-Level Physics.
无线电波是电磁波谱中波长最长、频率最低的部分，频率范围大约从 3 kHz 到 300 GHz。它们由加速的电荷产生，已成为现代无线通信的支柱，包括调幅/调频广播、电视和移动网络。理解无线电波的产生、调制、发射与接收，是 A-Level 物理中的一个核心主题。
1. What are Radio Waves? | 什么是无线电波？
Radio waves are electromagnetic waves with frequencies below those of infrared radiation. In a vacuum, they travel at the speed of light c = 3.00 × 10⁸ m s⁻¹. Like all electromagnetic waves, they consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation, making them transverse waves.
无线电波是频率低于红外线的电磁波。在真空中，它们以光速 c = 3.00 × 10⁸ m s⁻¹ 传播。与所有电磁波一样，它们由相互垂直且与传播方向垂直的振荡电场和磁场组成，因此属于横波。
The wavelength λ and frequency f of a radio wave are related by the wave equation:
无线电波的波长 λ 与频率 f 满足波动方程：
c = fλ
For example, a radio wave of frequency 100 MHz has a wavelength of 3.0 m. The long wavelengths of radio waves allow them to diffract around obstacles, which is vital for broadcasting.
例如，频率为 100 MHz 的无线电波波长为 3.0 m。无线电波波长较长，能够绕射过障碍物，这对广播至关重要。
2. Frequency Ranges and Wavelengths | 频率范围与波长
Radio waves are divided into several bands for different applications. The table below summarises common bands used in communication:
无线电波被划分为若干波段，用于不同的应用。下表总结了通信中常用的波段：
| Band | Frequency range | Typical use |
| LF (Low Frequency) | 30 – 300 kHz | Navigation, long-range communication |
| MF (Medium Frequency) | 300 kHz – 3 MHz | AM radio (530 – 1600 kHz) |
| HF (High Frequency) | 3 – 30 MHz | Shortwave broadcasting |
| VHF (Very High Frequency) | 30 – 300 MHz | FM radio (88 – 108 MHz), TV |
| UHF (Ultra High Frequency) | 300 MHz – 3 GHz | TV, mobile phones, Wi-Fi |
Notice that AM radio uses MF, while FM radio uses VHF. The higher frequency of FM allows greater bandwidth for higher-fidelity sound, but its shorter wavelength reduces the ability to diffract around large obstacles.
请注意，调幅广播使用中频（MF），而调频广播使用甚高频（VHF）。调频的较高频率允许更大的带宽，从而提供更高保真度的声音，但较短的波长降低了绕射过大障碍物的能力。
3. Generation via Accelerating Charges | 通过加速电荷产生
Any accelerating electric charge emits electromagnetic radiation. In a transmitting antenna, electrons are driven back and forth by an alternating voltage, causing them to oscillate. This produces a time-varying electric field and an associated magnetic field that propagate outward as a radio wave.
任何加速的电荷都会发出电磁辐射。在发射天线中，电子在交变电压的驱动下来回运动，产生振荡。由此产生的时变电场和与之相关的磁场向外传播，形成无线电波。
≈ λ/4. For a 1 MHz (AM) signal, λ ≈ 300 m, so a practical λ/4 antenna would be about 75 m – which is why AM transmitters use tall masts, or the signal is launched from a long wire.
为了有效辐射，天线的长度应约为波长的四分之一，L ≈ λ/4。对于 1 MHz（AM）信号，λ ≈ 300 m，因此实用的 λ/4 天线长度约为 75 m——这就是调幅发射台使用高塔或长导线发射信号的原因。
The power radiated by an oscillating charge is proportional to the square of its acceleration, which explains why higher frequencies are more efficient radiators: the same current produces greater acceleration at higher frequencies.
振荡电荷辐射的功率与其加速度的平方成正比，这解释了为什么更高频率的天线辐射效率更高：同样大小的电流在更高频率下产生更大的加速度。
4. The LC Oscillator and Carrier Signal | LC 振荡器与载波信号
At the heart of a radio transmitter is an oscillator that generates a steady sinusoidal voltage of a selected carrier frequency. A simple LC circuit, consisting of an inductor L and a capacitor C, can produce sustained oscillations when connected to a transistor or other amplifying device to overcome resistive losses.
无线电发射机的核心是一个振荡器，它产生选定载波频率的稳定正弦电压。由一个电感 L 和电容 C 组成的简单 LC 回路，当与晶体管或其他放大器件连接以克服电阻损耗时，可以产生持续的振荡。
The resonant frequency of an LC circuit is given by:
LC 回路的谐振频率由下式给出：
f₀ = 1 / (2π√LC)
By using a variable capacitor, the oscillator can be tuned to produce the desired carrier frequency f₍. This high-frequency 'carrier wave' is a pure sinusoid that, on its own, carries no information. It will later be modulated by an audio or data signal.
通过使用可变电容器，振荡器可被调谐到所需的载波频率 f₍。这种高频“载波”本身是纯正弦波，不携带任何信息，随后将由音频或数据信号进行调制。
5. Modulation: Why It Is Needed | 调制：为何需要
A typical audio signal has a frequency range from about 20 Hz to 20 kHz. Transmitting such low-frequency electromagnetic waves directly would require antennas thousands of metres long, and the signal would suffer severe attenuation. Moreover, multiple stations would interfere because they would all occupy the same low-frequency band.
典型的音频信号频率范围约为 20 Hz 至 20 kHz。直接发射这样低频的电磁波需要数千米长的天线，并且信号会严重衰减。此外，多个电台将在同一低频段内互相干扰。
Modulation solves these problems: a high-frequency carrier wave is 'modulated' by the lower-frequency information signal. The modulated wave can be transmitted with a reasonably sized antenna, and different stations can be assigned different carrier frequencies, allowing many programmes to be broadcast simultaneously without interference.
调制解决了这些问题：高频载波被较低频率的信息信号“调制”。调制后的波可以用尺寸合理的天线发射，并且不同电台可以分配不同的载波频率，使许多节目能够同时广播而互不干扰。
6. Amplitude Modulation (AM) | 调幅
formation signal (e.g. an audio voltage). If the carrier voltage is v₍ = V₀ sin(2πf₍ t) and the modulating signal is vₘ = Vₘ sin(2πfₘ t), the resulting AM waveform can be expressed as:
在调幅中，高频载波的振幅按照信息信号（例如音频电压）的瞬时振幅变化。如果载波电压为 v₍ = V₀ sin(2πf₍ t)，调制信号为 vₘ = Vₘ sin(2πfₘ t)，则所得 AM 波形可表示为：
vAM = (V₀ + Vₘ sin(2πfₘ t)) sin(2πf₍ t)
rm traces the audio signal. The modulation depth, m = Vₘ / V₀, should be kept below 1 (100% tion. Over-modulation (m > 1) causes the envelope to clip, producing spurious frequencies.
已调波形的包络线跟随音频信号变化。调制深度 m = Vₘ / V₀ 应保持在 1（100%）以下，以避免失真。过调制（m > 1）会使包络削波，产生杂散频率。
The AM spectrum consists of the carrier frequency f₍ and two sidebands: an upper sideband at f₍ + fₘ and a lower sideband at f₍ − fₘ, with fₘ ranging over the entire audio band.
AM 频谱由载波频率 f₍ 和两个边带组成：上边带位于 f₍ + fₘ，下边带位于 f₍ − fₘ，其中 fₘ 覆盖整个音频频段。
7. Frequency Modulation (FM) | 调频
In frequency modulation, the frequency of the carrier is varied by the amplitude of the modulating signal, while the carrier amplitude remains constant. The instantaneous frequency f(t) can be written as:
在调频中，载波的频率按照调制信号的振幅变化，而载波振幅保持恒定。瞬时频率 f(t) 可写为：
f(t) = f₍ + Δf sin(2πfₘ t)
for FM is β = Δf / fₘ. A larger β gives better noise immunity but requires more bandwidth.
此处 Δf 为频偏，与调制信号振幅成正比。FM 的调制指数为 β = Δf / fₘ。β 越大，抗噪声性能越好，但需要更宽的带宽。
FM signals are less susceptible to amplitude disturbances such as lightning or power-line noise, because information is encoded in frequency shifts rather than amplitude. This is why FM radio generally delivers higher sound quality than AM.
FM 信号不易受到振幅干扰（如闪电或电力线噪声）的影响，因为信息被编码在频率偏移而非振幅中。这就是调频广播通常比调幅广播音质更好的原因。
8. Sidebands and Bandwidth | 边带与带宽
For AM, the total bandwidth required is twice the maximum modulating frequency: BW_AM = 2 fₘ_max. If the audio range extends to 5 kHz (mono AM), the bandwidth is 10 kHz. For FM, Carson's rule estimates the bandwidth as BW_FM ≈ 2(Δf + fₘ_max) 75 kHz and audio to 15 kHz, giving BW ≈ 180 kHz, explaining the wider FM channel spacing.
对于 AM，所需的总带宽是最大调制频率的两倍：BW_AM = 2 fₘ_max。如果音频范围延伸到 5 kHz（单声道 AM），带宽为 10 kHz。对于 FM，卡森准则估算带宽为 BW_FM ≈ 2(Δf + fₘ_max)。典型的 FM 广播使用最大频偏 Δf = 75 kHz，音频上限 15 kHz，则带宽约为 180 kHz，这解释了 FM 频道间隔更大的原因。
Sidebands contain all the information of the modulating signal. In an AM signal, the carrier itself carries no information but accounts for a large fraction of the transmitted power. Various schemes (e.g. single-sideband, SSB) suppress the carrier and one sideband to save power and spectrum.
边带包含了调制信号的全部信息。在 AM 信号中，载波本身不携带信息，却占用了发射功率的很大一部分。多种方案（如单边带 SSB）会抑制载波和一个边带，以节省功率和频谱。
9. Radio Wave Transmission and Antennas | 无线电波发射与天线
After modulation, the signal is amplified and fed to a transmitting antenna. For efficient radiation, the antenna must be impedance-matched to the transmission line. The power radiated by a dipole antenna is proportional to the square of the current amplitude and the radiation resistance.
调制后的信号经放大后馈入发射天线。为有效辐射，天线必须与传输线阻抗匹配。偶极天线辐射的功率与电流振幅的平方以及辐射电阻成正比。
Radio waves propagate from the antenna by three main mechanisms: ground (surface) waves for lower frequencies, sky waves that refract off the ionosphere for HF, and space (line-of-sight) waves for VHF and above. AM waves can reflect off the ionosphere at night, allowing long-distance reception beyond the horizon.
无线电波从天线以三种主要方式传播：较低频率的地波（表面波）；高频天波，通过电离层折射；以及 VHF 及以上频段的空间波（视距传播）。AM 电波在夜间可经电离层反射，实现超视距远距离接收。
10. Reception: Tuning and Demodulation | 接收：调谐与解调
A receiving antenna intercepts a tiny fraction of the transmitted power, inducing a small alternating voltage that is a mixture of all transmitted signals. The first stage of a radio receiver is a tuned circuit, typically a parallel LC circuit, which selects one carrier frequency by resonance:
接收天线截获发射功率的极小部分，感应出包含所有发射信号混合的微小交流电压。接收机的第一级是一个调谐回路，通常为并联 LC 回路，通过谐振选择一个载波频率：
fres = 1 / (2π√LC)
By adjusting a variable capacitor, the listener can select the desired station. The sharpness of tuning is described by the quality factor Q: a high Q gives better selectivity but may distort sidebands, so a practical compromise is needed.
通过调节可变电容，听众可选择所需电台。调谐的尖锐程度由品质因数 Q 描述：高 Q 值提供更好的选择性，但可能使边带失真，因此需要在实际中折衷处理。
After selection, the signal must be demodulated to recover the original audio. For AM, a simple diode detector rectifies the signal, and a capacitor charges to the envelope and discharges through a resistor to follow the audio waveform. For FM, a discriminator or phase-locked-loop circuit converts frequency variations into voltage variations.
选定信号后，需要解调以恢复原始音频。对于 AM，简单的二极管检波器对信号进行整流，电容充电至包络电平并通过电阻放电，跟随音频波形。对于 FM，鉴频器或锁相环电路将频率变化转换为电压变化。
11. Propagation Properties: Diffraction and Reflection | 传播特性：衍射与反射
ound hills and buildings, whereas an FM wave with λ ≈ 3 m behaves more like light, being blocked by obstacles and requiring a relatively clear line of sight.
由于无线电波的波长远大于可见光，它们表现出显著的衍射效应。波长为 300 m 的 AM 波可以绕射过山丘和建筑物，而波长约为 3 m 的 FM 波则更像光，容易被障碍物阻挡，需要相对清晰的视距。
Reflection from the ionosphere allows long-range HF communication. The ionosphere is a region of ionised gases that reflects radio waves at frequencies below about 30 MHz. TV and FM signals (VHF/UHF) usually pass straight through, so communication is limited to the horizon unless satellites or repeaters are used.
电离层反射使得远距离高频通信成为可能。电离层是电离气体区域，可反射频率低于约 30 MHz 的无线电波。电视和 FM 信号（VHF/UHF）通常直接穿透，因此通信范围限于地平线以内，除非使用卫星或中继站。
12. AM versus FM: A Comparison | AM 与 FM 比较
The table below highlights key differences between amplitude modulation and frequency modulation as used in commercial radio broadcasting.
下表突出了商业无线电广播中调幅与调频的主要差异。
| Feature | AM | FM |
| Carrier frequency band | MF (530 – 1600 kHz) | VHF (88 – 108 MHz) |
| Bandwidth per channel | ~ 10 kHz | ~ 200 kHz |
| Noise immunity | Poor (affected by amplitude noise) | Excellent (amplitude limiters remove noise) |
| Audio quality | Limited fidelity, often mono | High fidelity, stereo possible |
| Range (typical) | Long, especially at night via skywave | Line-of-sight, ~ 50–100 km |
| Transmitter complexity | Simple | More complex |
| Receiver complexity | Simple (diode detector) | More complex (discriminator) |
The choice between AM and FM involves a trade-off between coverage and quality. AM's long range makes it suitable for national and international broadcasting, while FM's superior sound quality makes it the preferred choice for music stations serving metropolitan areas.
选择 AM 还是 FM 需要在覆盖范围与质量之间进行权衡。AM 的远距离传输能力使其适合全国及国际广播，而 FM 优越的音质使其成为服务大都市区域音乐电台的首选。
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