📚 Rectification | 整流
Rectification is the fundamental process of converting alternating current (AC), which periodically reverses direction, into direct current (DC), which flows in only one direction. In everyday electronics, the mains supply provides AC, but most circuits – from mobile phone chargers to computer power supplies – require a steady DC voltage. Therefore, rectification is an essential step in almost every power supply unit.
整流是将周期性地改变方向的交流电（AC）转换为单向流动的直流电（DC）的基本过程。在日常生活中，市电提供的是交流电，而绝大多数电路——从手机充电器到计算机电源——都需要稳定的直流电压。因此，整流是几乎所有电源装置中必不可少的一个环节。
1. The Semiconductor Diode – The Heart of Rectification | 半导体二极管——整流的核心
A diode is a semiconductor device that allows current to pass in one direction only. It consists of a p–n junction: p-type material with an excess of holes and n-type material with an excess of electrons. When forward-biased (p-side connected to the positive terminal), the depletion layer narrows and current flows easily once the applied voltage exceeds the threshold voltage (approximately 0.7 V for silicon diodes). Under reverse bias, the depletion layer widens, and only a tiny leakage current flows until the breakdown voltage is reached.
二极管是一种只允许电流单向导通的半导体器件。它由p–n结组成：p型材料含有大量空穴，n型材料含有大量自由电子。当正向偏置（p侧接正极）时，耗尽层变窄，一旦外加电压超过阈值电压（硅二极管约为0.7 V），电流就能轻松通过。在反向偏置下，耗尽层变宽，只有极小的漏电流流过，直到达到击穿电压为止。
Because of this one-way conduction property, a diode acts as an electronic check valve. When placed in series with an AC source and a load, it only conducts during the half-cycles that forward-bias it, blocking current in the opposite half-cycles. This behaviour is the foundation of rectification.
正因为这种单向导电特性，二极管理论上相当于一个电子单向阀。当二极管与交流电源和负载串联时，它仅在使其正向偏置的半周期导通，在相反的半周期阻断电流。这一特性就是整流的基础。
2. Half-Wave Rectification | 半波整流
A half-wave rectifier uses a single diode in series with the load. During the positive half-cycle of the AC input, the diode is forward-biased and conducts, developing a voltage across the load. During the negative half-cycle, the diode is reverse-biased and blocks current, so the load voltage is zero. The output is a unidirectional but pulsating voltage that contains only the positive halves of the input waveform.
半波整流器采用一个与负载串联的二极管。在交流输入的正半周期间，二极管正向偏置并导通，负载上产生电压。在负半周期间，二极管反向偏置并阻断电流，因此负载电压为零。输出是一个单向但脉动的电压，仅包含输入波形的正半部分。
The main disadvantages of half-wave rectification are its low efficiency – roughly 40% at best – and a high ripple content because power is delivered only half of the time. The output frequency of the ripple is equal to the mains frequency (e.g. 50 Hz). Moreover, the transformer must handle DC magnetisation, which can lead to core saturation unless the core is specially designed.
半波整流的主要缺点是效率低——最高约40%——以及因只在半个周期内传递功率而导致的高纹波含量。输出纹波的频率等于电源频率（如50 Hz）。此外，变压器需要承受直流磁化，除非铁心经过特殊设计，否则可能导致磁饱和。
3. Full-Wave Rectification Using a Centre-Tap Transformer | 中心抽头变压器全波整流
A full-wave centre-tap rectifier requires a transformer with a centre-tapped secondary winding and two diodes. The centre tap acts as the common (ground) point. During one half-cycle, the top end of the winding is positive with respect to the centre tap, forward-biasing diode D₁, while the bottom end is negative, reverse-biasing D₂. In the next half-cycle, the polarity reverses, so D₂ conducts and D₁ is off. In both cases, current flows through the load in the same direction, giving an output on every half-cycle.
中心抽头全波整流器需要一个带有中心抽头的次级变压器和两只二极管。中心抽头作为公共（接地）点。在某个半周期内，绕组上端相对于中心抽头为正，使二极管D₁正向偏置，而下端为负，使D₂反向偏置。在下一个半周期，极性反转，因此D₂导通而D₁截止。两种情况下，流过负载的电流方向都相同，使得每个半周期都有输出。
This arrangement effectively uses both halves of the AC wave, roughly doubling the average DC output voltage and the efficiency compared with half-wave rectification. However, the centre-tapped transformer is heavier and more expensive. Additionally, each diode must withstand a peak inverse voltage (PIV) of twice the peak secondary voltage, because when one diode is off, it sees the full voltage across the entire secondary winding.
这种电路有效利用了交流波的两个半部分，与半波整流相比，平均直流输出电压和效率大致提高了一倍。然而，中心抽头变压器更重、更贵。此外，每个二极管必须承受两倍次级峰值电压的峰值反向电压（PIV），因为当一个二极管截止时，它所承受的是整个次级绕组两端的电压。
4. The Bridge Rectifier | 桥式整流
The bridge rectifier uses four diodes arranged in a bridge configuration and does not require a centre-tapped transformer. During the positive half-cycle of the input, two diodes conduct and direct current through the load in one direction. During the negative half-cycle, the other two diodes conduct, again sending current through the load in the same direction. Thus, full-wave rectification is achieved with a simple two-wire transformer secondary.
桥式整流器使用四只以桥式方式连接的二极管，无需中心抽头变压器。在输入的正半周，两个二极管导通，将电流以一个方向引导通过负载。在负半周，另外两个二极管导通，再次使电流以相同方向流过负载。因此，只需一个简单的两线变压器次级就能实现全波整流。
The bridge rectifier offers several advantages: the transformer is simpler and cheaper; the PIV across each diode is equal to the peak supply voltage (rather than twice that); and the output voltage is almost the full secondary voltage minus two diode drops. Its main drawback is the need for four diodes, and the fact that current always flows through two conducting diodes in series, causing a slightly larger voltage drop (about 1.4 V for silicon diodes).
桥式整流器有几个优点：变压器更简单、更便宜；每个二极管的PIV等于电源峰值电压（而非两倍）；输出电压几乎是整个次级电压减去两个二极管的压降。其主要缺点是需要四只二极管，而且电流总是流经两个串联的导通二极管，因此压降稍大（硅二极管约为1.4 V）。
Today, bridge rectifiers are available as single integrated components with four terminals, making them extremely convenient for power supply design.
如今，桥式整流器可制成具有四个端子的单一集成器件，在电源设计中极为方便。
5. Smoothing – The Need for Filtering | 平滑——滤波的必要性
The output of any rectifier is not a steady DC voltage but a pulsating waveform that fluctuates between a peak value and zero (or near zero). If such a voltage were applied directly to sensitive electronic circuits, it would cause hum, malfunction or damage. Smoothing is therefore introduced to reduce these fluctuations and produce a more stable DC level.
任何整流器的输出都不是平稳的直流电压，而是一个在峰值和零（或接近零）之间波动的脉动波形。如果将这样的电压直接加在敏感的电子电路上，会造成嗡嗡声、工作失常甚至损坏。因此，需要引入平滑措施来减小这些波动，产生更稳定的直流电平。
The simplest and most common smoothing method uses a large-value electrolytic capacitor connected in parallel with the load. When the rectified voltage rises, the capacitor charges up rapidly through the low resistance of the conducting diodes. When the rectified voltage begins to fall, the capacitor discharges relatively slowly through the load, releasing its stored energy and maintaining the output voltage between peaks.
最简单、最常用的平滑方法是在负载两端并联一个大容量的电解电容。当整流后的电压上升时，电容通过导通二极管的低电阻快速充电。当整流电压开始下降时，电容通过负载相对缓慢地放电，释放储存的能量，在波峰之间维持输出电压。
This charging–discharging action reduces the depth of the voltage dip, resulting in a smoother waveform with a small alternating component called ripple.
这一充放电过程降低了电压下降的深度，从而得到更平滑的波形，其中仅含有一个较小的交流分量，称为纹波。
6. Ripple Voltage and Its Approximate Calculation | 纹波电压及其近似计算
The remaining AC fluctuation superimposed on the DC level is called the ripple voltage. It is usually measured as the peak-to-peak variation, denoted Vripple(pp). A smaller ripple is desirable for a stable power supply. The ripple depends on the load current, the capacitance, and the frequency of the rectified waveform.
叠加在直流电平上的剩余交流波动称为纹波电压，通常以峰峰值变化来衡量，记作Vripple(pp)。对于稳定的电源，纹波越小越好。纹波的大小取决于负载电流、电容值以及整流波形的频率。
An approximate formula used in A-Level Physics is:
Vripple(pp) ≈ Iload / (fripple × C)
where Iload is the average load current, C is the smoothing capacitance, and fripple is the frequency of the rectified pulses: for half-wave rectification fripple = fmains (e.g. 50 Hz), and for full-wave rectification fripple = 2 × fmains (e.g. 100 Hz). This formula assumes a constant load current and a sufficiently large capacitor so that the discharge is roughly linear.
A-Level物理中使用的近似公式为：
Vripple(pp) ≈ Iload / (fripple × C)
其中Iload为平均负载电流，C为平滑电容，fripple为整流脉冲的频率：半波整流时fripple = fmains（如50 Hz），全波整流时fripple = 2 × fmains（如100 Hz）。该公式假定负载电流恒定且电容足够大，以使放电近似线性。
rent of 0.5 A and a smoothing capacitance of 2000 μF (2 × 10⁻³ F), the ripple voltage is Vripple eak-to-peak. If the required ripple must be below 0.5 V, a larger capacitor or a lower load current would be needed.
举例：对于使用50 Hz市电的全波整流器，负载电流为0.5 A，平滑电容为2000 μF（2 × 10⁻³ F），纹波电压为Vripple ≈ 0.5 / (100 × 2×10⁻³) = 0.5 / 0.2 = 2.5 V峰峰值。若要求纹波低于0.5 V，则需要更大的电容或更小的负载电流。
7. Effect of Load Resistance and Capacitance on Ripple | 负载电阻与电容对纹波的影响
The ripple voltage increases when the load draws a larger current because the capacitor discharges more between charging peaks. In terms of the load resistance RL, since Iload ≈ VDC / RL, the ripple is approximately proportional to 1 / (fripple × C × RL). Therefore, a heavier load (smaller RL) gives larger ripple.
当负载汲取更大电流时，纹波电压会增加，因为电容在充电峰值之间的放电更多。从负载电阻RL来看，由于Iload ≈ VDC / RL，纹波电压近似与1/(fripple × C × RL)成正比。因此，负载越重（RL越小），纹波越大。
Similarly, increasing the capacitance C increases the time constant RL g the rate at which the voltage falls. Hence, a larger capacitor reduces ripple. In practice, electrolytic capacitors of several hundred or thousand microfarads are commonly used, and designers may also add smaller high-frequency capacitors in parallel to filter out fast transients.
同理，增大电容C会增加放电回路的时间常数RL × C，从而降低电压下降的速率。因此，更大的电容能减小纹波。在实践中，通常使用几百到几千微法的电解电容，设计者还可能并联较小的高频电容以滤除快速瞬变。
The choice of capacitance is a compromise between ripple performance, physical size, cost, and start-up surge current. Very large capacitances draw enormous charging current pulses when the supply is first switched on, requiring surge-limiting components.
电容的选择需要在纹波性能、体积、成本以及启动浪涌电流之间权衡。非常大的电容在首次接通电源时会引发巨大的充电电流脉冲，往往需要限流器件。
8. Comparison of Rectifier Topologies | 整流拓扑结构比较
The table below summarises the key differences among the three main rectifier types for a single-phase AC supply. The peak inverse voltage (PIV) is the maximum reverse voltage a diode must block without breaking down, and it is a critical rating when selecting diodes.
下表总结了单相交流电源三种主要整流器类型之间的关键差异。峰值反向电压（PIV）是二极管在截止时所能承受且不击穿的最大反向电压，是选型时的重要参数。
| Property 性质 |
Half-wave 半波 |
Full-wave centre-tap 全波中心抽头 |
Bridge 桥式 |
| Number of diodes 二极管数量 |
1 | 2 | 4 |
| Transformer requirement 变压器要求 |
Simple 简单 |
Centre-tapped secondary, heavier 中心抽头，较重 |
Simple, lower cost 简单，成本低 |
| Ripple frequency 纹波频率 |
fmains (e.g. 50 Hz) 市电频率 |
2 × fmains (e.g. 100 Hz) 两倍市电频率 |
2 × fmains (e.g. 100 Hz) 两倍市电频率 |
| DC output voltage (approx) 直流输出电压（近似） |
0.45 × Vsec(rms) 0.45 × Vsec(rms) |
0.90 × Vsec(rms) (each half) 0.90 × Vsec(rms)（每半部分） |
0.90 × Vsec(rms) 0.90 × Vsec(rms) |
| Peak Inverse Voltage (PIV) per diode 每只二极管的PIV |
Vpeak Vpeak |
2 × Vpeak 2 × Vpeak |
Vpeak Vpeak |
| Efficiency (approx) 效率（近似） |
~40% | ~81% | ~81% |
| Typical application 典型应用 |
Low-power, battery charging 低功率、电池充电 |
Older high-current supplies 旧式大电流电源 |
Most common in modern PSUs 现代电源中最常见 |
Note: Vsec(rms) refers to the RMS voltage of the transformer secondary winding (or the relevant section for the centre-tap type).
注：Vsec(rms) 指变压器次级绕组（或中心抽头类型的相应部分）的RMS电压。
9. Practical Considerations and Further Filtering | 实际考量与进一步滤波
A simple capacitor filter is rarely sufficient for precision circuits. The residual ripple can be further reduced by adding an inductor (choke) in series or by using active voltage regulators (e.g. linear regulators or switch-mode ICs). Passive LC filters (inductor–capacitor) can smooth the output to very low ripple levels but are bulky and expensive.
对于精密电路，仅靠简单的电容滤波往往不够。可通过串联电感（扼流圈）或使用有源稳压器（如线性稳压器或开关型集成电路）进一步降低残余纹波。无源LC滤波器（电感–电容）可将输出平滑至极低的纹波水平，但体积大且成本高。
In modern power supply design, a bridge rectifier followed by a smoothing capacitor and a voltage regulator is a standard combination. The regulator not only reduces ripple but also compensates for variations in load and input voltage, providing a fixed, stable DC output.
在现代电源设计中，桥式整流器后接平滑电容和稳压器是一种标准组合。稳压器不仅减小纹波，还能补偿负载和输入电压的波动，提供固定且稳定的直流输出。
Another important consideration is the diode surge current. When a power supply is first switched on, the discharged capacitor appears as a short circuit, and the diodes must be able to withstand a very large initial current surge without damage. Designers often include a negative temperature coefficient (NTC) thermistor or a soft-start circuit to limit inrush current.
另一个重要考量是二极管浪涌电流。电源接通的瞬间，未充电的电容相当于短路，二极管必须能够承受极大的初始电流冲击而不损坏。设计人员常加入负温度系数（NTC）热敏电阻或软启动电路以限制浪涌电流。
10. Summary and Connection to the Wider Syllabus | 总结及与大纲的联系
Rectification transforms AC into DC using the one-way conduction of diodes. Half-wave rectifiers are simple but inefficient and produce large ripple. Full-wave rectifiers, whether centre-tap or bridge, offer higher efficiency, smaller ripple, and are the standard for most DC power supplies. Adding a smoothing capacitor reduces ripple, and the approximate ripple voltage can be estimated using Vripple(pp) ≈ Iload / (fripple s is crucial for topics such as power supplies, electronics, and even electromagnetic applications where stable DC is required from an AC source.
整流利用二极管的单向导电性将交流电转换为直流电。半波整流器结构简单但效率低且纹波大。全波整流器，不论是中心抽头还是桥式，都具有更高的效率、更小的纹波，是大多数直流电源的标准选择。加入平滑电容可减少纹波，其近似纹波电压可用Vripple(pp) ≈ Iload / (fripple × C)估算。理解这些原理对电源、电子学，乃至需要从交流源获得稳定直流的电磁应用等主题都至关重要。
In the Cambridge International A-Level Physics syllabus, students are expected to describe the action of diodes in half-wave and full-wave bridge rectification, explain the use of a capacitor for smoothing, and apply the ripple formula in simple calculations. Mastery of rectification provides a solid
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
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