📚 Electronics | 电子学
Electronics is a branch of physics that deals with the control of electric current using non‑linear devices such as semiconductors to process information or control energy. In CIE A‑Level Physics, the electronics topic focuses on practical circuits built around operational amplifiers (op‑amps), sensors, and output transducers. Understanding these components allows us to design systems that sense physical quantities, compare signals, amplify weak voltages, and drive output devices such as LEDs and relays. This article covers the essential principles and applications required by the syllabus, including op‑amp comparators, inverting and non‑inverting amplifiers, negative feedback, and output stages.
电子学是物理学的一个分支，研究如何利用半导体等非线性器件控制电流，以实现信息处理或能量控制。在 CIE A‑Level 物理课程中，电子学专题主要围绕运算放大器、传感器和输出换能器构建实用电路。理解这些元器件后，我们可以设计出感知物理量、比较信号、放大微弱电压并驱动 LED 和继电器等输出设备的系统。本文覆盖了考纲要求的基本原理和应用，包括运放比较器、反相与同相放大器、负反馈以及输出级。
1. Sensors and Transducers | 传感器与换能器
Sensors are input devices that convert a physical quantity into an electrical signal. A thermistor changes its resistance with temperature; a negative temperature coefficient (NTC) thermistor decreases its resistance as temperature rises. A light‑dependent resistor (LDR) reduces its resistance when light intensity increases. Strain gauges are used to measure mechanical deformation: a thin wire or foil changes resistance when stretched or compressed. Piezoelectric transducers generate a voltage when mechanically stressed and are often used as pressure sensors or microphones. In all cases, the sensor forms part of a potential divider so that the output voltage varies with the physical stimulus.
传感器是将物理量转换为电信号的输入设备。热敏电阻的阻值随温度变化；负温度系数（NTC）热敏电阻在温度升高时阻值下降。光敏电阻（LDR）在光照增强时阻值降低。应变片用于测量机械形变：当薄金属线或箔被拉伸或压缩时，其电阻发生变化。压电换能器在受到机械应力时产生电压，常被用作压力传感器或麦克风。在所有这些应用中，传感器都作为分压电路的一部分，使得输出电压随物理刺激的变化而变化。
| Sensor | Physical Quantity | Resistance Behaviour |
|---|---|---|
| NTC Thermistor | Temperature | R decreases as T rises |
| LDR | Light intensity | R decreases as light increases |
| Strain gauge | Strain (deformation) | R increases with elongation |
The table above summarises common sensors and their electrical response. When designing a sensing circuit, the sensor is usually placed in one arm of a potential divider, and a variable resistor or fixed resistor in the other arm allows sensitivity adjustment.
上表总结了常见传感器及其电学响应。在设计传感电路时，传感器通常置于分压器的一个臂中，另一个臂中的可变电阻或固定电阻可以调节灵敏度。
2. The Ideal Operational Amplifier | 理想运算放大器
An operational amplifier (op‑amp) is a high‑gain differential voltage amplifier. The ideal op‑amp has infinite open‑loop voltage gain A₀, infinite input impedance (so no current flows into the inverting (−) or non‑inverting (+) input), zero output impedance, and infinite bandwidth. It also has a very high common‑mode rejection ratio, meaning it amplifies only the voltage difference between its two inputs. In practice, real op‑amps such as the TL081 or LM741 approach these properties, and for circuit analysis we treat them as ideal.
运算放大器是一种高增益差分电压放大器。理想运算放大器具有无限大的开环电压增益 A₀、无限大的输入阻抗（因此没有电流流入反相（−）或同相（+）输入端）、零输出阻抗以及无限大的带宽。它还具备很高的共模抑制比，意味着它只放大两个输入端之间的电压差。实际运放（如 TL081 或 LM741）接近这些特性，在电路分析中我们将其视为理想器件。
The output voltage is given by:
Vout = A₀ (V+ – V−)
egative supply rail (typically ±Vsat). This behaviour is exploited in comparator circuits.
由于 A₀ 极大，即使 V+ 与 V− 之间只有微小的电压差，也会使输出饱和到接近正电源或负电源的电压（通常记为 ±Vsat）。这一特性被用于比较器电路。
3. Op‑Amp as a Comparator | 运算放大器作为比较器
When an op‑amp is used without feedback (open‑ sat) depending on which input is higher. If V+ > V−, then Vout ≈ +Vsat; if V+ < V−, then Vout ≈ −Vsat. This produces a binary output that is ideal for threshold detection.
当运算放大器在无反馈（开环）条件下使用时，它充当比较器的角色。根据哪个输入端电压更高，输出会在正饱和电压（+Vsat）和负饱和电压（−Vsat）之间跳变。若 V+ > V−，则 Vout ≈ +Vsat；若 V+ < V−，则 Vout ≈ −Vsat。这种二值输出非常适合阈值检测。
A simple application is a light‑detector: the non‑inverting input is connected to a potential divider with an LDR, and the inverting input is set to a reference voltage Vref from a second potential divider. As light intensity changes, the LDR voltage crosses Vref, causing the output to switch states and turn an LED on or off.
一个简单的应用是光检测器：同相输入端连接包含 LDR 的分压器，反相输入端由另一个分压器提供参考电压 Vref。当光照强度变化时，LDR 上的电压越过 Vref，导致输出状态改变，进而点亮或熄灭 LED。
4. Negative Feedback and the Virtual Earth Concept | 负反馈与虚拟接地概念
To obtain linear amplification rather than switching, we apply negative feedback by connecting a resistor from the output back to the inverting input. Negative feedback reduces the overall gain but greatly improves bandwidth, input and output resistance, and linearity. Because the open‑loop gain is extremely high, the voltage difference between the two inputs becomes vanishingly small when the output is not saturated. In an inverting amplifier configuration with the non‑inverting input grounded, this forces the inverting input to be almost at ground potential—a condition called a virtual earth.
为了获得线性放大而非开关状态，我们施加负反馈，即用一个电阻将输出端连接到反相输入端。负反馈降低了总增益，但大大改善了带宽、输入输出电阻和线性度。由于开环增益极高，在输出未饱和时，两个输入端的电压差变得极小。在非反相端接地的反相放大器配置中，这迫使反相输入端几乎处于地电位，这种状态被称为虚拟接地。
No current flows into the op‑amp inputs, so the current through the input resistor Rin must equal the current through the feedback resistor Rf. This current relationship together with the virtual earth concept allows us to derive the closed‑loop gain.
由于没有电流流入运放输入端，流经输入电阻 Rin 的电流必定等于流经反馈电阻 Rf 的电流。利用这一电流关系和虚拟接地概念，我们可以推导出闭环增益。
5. Inverting Amplifier | 反相放大器
ier, the input voltage Vin is applied through resistor Rin to the inverting input. The non‑ verting input is held at 0 V. The current through Rin is Vin / Rin, and the same current flows through Rf, giving an output voltage Vout = –(Rf / Rin) × Vin. Thus the voltage gain is:
G = Vout / Vin = – Rf / Rin
在反相放大器中，输入电压 Vin 通过电阻 Rin 接到反相输入端。同相输入端接地。反馈电阻 Rf 连接在输出端和反相输入端之间。根据虚拟接地原理，反相输入端保持为 0 V。流经 Rin 的电流为 Vin / Rin，该电流同样流经 Rf，得到输出电压 Vout = –(Rf / Rin) × Vin。因此电压增益为上述公式。
The negative sign indicates a phase inversion of 180°. The input impedance of the inverting amplifier is simply Rin, which is relatively low. This circuit is widely used when a fixed gain and phase inversion are needed, for example in audio pre‑amplifiers.
负号表示输出与输入反相 180°。反相放大器的输入阻抗等于 Rin，相对较低。当需要固定增益和反相时，这种电路得到广泛应用，例如在音频前置放大器中。
6. Non‑Inverting Amplifier | 同相放大器
The non‑inverting amplifier has the input signal applied directly to the non‑ ed by Rf and R1 feeds back a fraction of the output to the inverting input. Because the op‑ nd this same current flows through Rf, giving Vout = Vin × (1 + Rf / R1). Hence the closed‑loop gain is:
G = 1 + Rf / R1
同相放大器的输入信号直接加在同相输入端。由 Rf 和 R1 组成的分压器将一部分输出电压反馈回反相输入端。由于运放保持两个输入端电压近似相等，反相输入端电压就等于 Vin。流经 R1 的电流为 Vin / R1，该电流同样流过 Rf，于是 Vout = Vin × (1 + Rf / R1)。因此闭环增益如上述公式。
This amplifier has a very high input impedance because the signal is fed straight into the non‑inverting input. It is ideal for buffering sensors that cannot supply much current, such as strain gauge bridges.
这种放大器具有极高的输入阻抗，因为信号直接送入同相输入端。它非常适合对不能提供大电流的传感器（如应变片电桥）进行缓冲。
7. Output Devices | 输出设备
Op‑amp outputs can deliver only a few milliamps, so external driving circuits are often needed to power output devices. Common output transducers include light‑emitting diodes (LEDs), piezoelectric buzzers, and electromagnetic relays. An LED requires a series resistor to limit current and turns on when the op‑amp output goes high (+Vsat). A transistor, such as an NPN bipolar junction transistor, can be used as a switch: a base resistor limits current, and the collector circuit can drive a relay coil or a buzzer.
运算放大器的输出只能提供几毫安的电流，因此通常需要外部驱动电路来为输出设备供电。常见的输出换能器包括发光二极管（LED）、压电蜂鸣器和电磁继电器。LED 需要串联一个限流电阻，当运放输出为高电平（+Vsat）时点亮。NPN 双极型晶体管等三极管可以用作开关：基极电阻限制电流，集电极回路可以驱动继电器线圈或蜂鸣器。
A relay allows a low‑power electronic circuit to control a high‑power mains device, providing electrical isolation. A reverse‑biased diode is placed across the relay coil to protect the transistor from the back‑EMF generated when the coil current is switched off.
继电器使得低功率电子电路能够控制高功率的市电设备，同时提供电气隔离。在继电器线圈两端反向并联一个二极管，可以保护晶体管免受线圈电流关断时产生的反向电动势（反激电压）的冲击。
8. Temperature Monitoring and Control Circuit | 温度监测与控制电路
A practical system can combine a sensor, a comparator, and an output driver. Consider a temperature controller: an NTC thermistor Rtherm and a variable resistor Rset form a potential divider connected to the inverting input of an op‑amp. The non‑inverting input is held at a fixed reference voltage Vref from another potential divider. When the temperature is low, Rtherm is high, so the voltage at the inverting input is low (below Vref); the op‑amp output goes to +Vsat. This high output turns on an NPN transistor, energising a relay that switches on a heater. As the temperature rises, Rtherm falls, raising the inverting voltage. Once it exceeds Vref, the op‑amp output swings to −Vsat, turning off the transistor and relay, thereby disconnecting the heater.
一个实用系统可以将传感器、比较器和输出驱动器组合在一起。考虑一个温度控制器：NTC 热敏电阻 Rtherm 和可变电阻 Rset 形成分压器，连接到运放的反相输入端。同相输入端由另一个分压器提供固定的参考电压 Vref。温度较低时，Rtherm 较大，反相输入端电压较低（低于 Vref）；运放输出变为 +Vsat。这个高电平使 NPN 晶体管导通，驱动继电器吸合，接通加热器。温度升高后，Rtherm 下降，反相输入端电压上升。一旦超过 Vref，运放输出跳变到 –Vsat，关断晶体管和继电器，从而断开加热器。
Adjusting Rset changes the temperature threshold. This arrangement is an on‑off temperature control that uses the op‑amp as a comparator.
调节 Rset 可以改变温度阈值。这种配置是利用运放作为比较器的开关式温度控制。
9. Schmitt Trigger for Noise Immunity | 施密特触发器抗干扰
A basic comparator can suffer from rapid oscillation when the input voltage hovers near the threshold voltage due to electrical noise. The Schmitt trigger solves this by using positive feedback to create two distinct threshold levels (hysteresis). In the non‑inverting Schmitt trigger, the input signal goes to the non‑inverting input through a potential divider formed by R1 and R2, while the inverting input is grounded. The output toggles between +Vsat and −Vsat depending on whether the voltage at the non‑inverting input crosses the upper trip point Vth+ or the lower trip point Vth−.
当输入电压在阈值附近徘徊时，基本的比较器可能因电气噪声而产生快速振荡。施密特触发器通过引入正反馈产生两个不同的阈值电平（迟滞）来解决这一问题。在非反相施密特触发器中，输入信号经过由 R1 和 R2 组成的分压器进入同相输入端，反相输入端接地。输出根据同相输入端的电压是否越过上门限 Vth+ 或下门限 Vth− 在 +Vsat 和 −Vsat 之间切换。
The trip points are given by:
Vth+ = (R1 / (R1 + R2)) × (+Vsat)
Vth− = (R1 / (R1 + R2)) × (−Vsat)
The hysteresis width is Vth+ − Vth−. This makes the circuit immune to small noise fluctuations, providing clean switching in sensor applications.
迟滞宽度为 Vth+ − Vth−。这使得电路对小的噪声波动免疫，在传感器应用中提供干净的开关动作。
10. Summary and Design Considerations | 总结与设计要点
Electronic systems typically consist of an input sensor stage, a signal processing block (often an op‑amp), and an output transducer. The choice of sensor depends on the physical quantity to be measured; the op‑amp can be configured as a high‑gain amplifier or comparator; output devices require appropriate current amplification. Negative feedback stabilises the gain and extends the linear range, while positive feedback in a Schmitt trigger introduces hysteresis to avoid chatter. When designing circuits, one must also consider power supply voltages, the need for decoupling capacitors, and the maximum current ratings of the devices.
电子系统通常由输入传感器级、信号处理模块（常为运放）和输出换能器组成。传感器的选择取决于待测物理量；运放可配置为高增益放大器或比较器；输出设备需要适当的电流放大。负反馈能稳定增益并扩展线性范围，而施密特触发器中的正反馈则引入迟滞以避免抖动。在设计电路时，还必须考虑电源电压、去耦电容的需要以及器件的最大电流额定值。
Mastering op‑amp circuits and sensor interfacing not only prepares students for the CIE Electronics examination questions but also builds a foundation for understanding modern measurement and control systems.
掌握运算放大器电路和传感器接口，不仅为 CIE 电子学考题做好准备，也为理解现代测量与控制系统打下基础。
Published by TutorHao | Electronics Revision Series | aleveler.com
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