Alternating Current Experiments and Oscilloscope Observation | 交流电实验与示波器观察

📚 Alternating Current Experiments and Oscilloscope Observation | 交流电实验与示波器观察

An alternating current (AC) circuit is fundamentally different from a direct current (DC) circuit because the voltage and current change direction and magnitude periodically. The oscilloscope is the most powerful instrument for visualising these time-varying signals, allowing students to measure waveform shape, amplitude, frequency, and phase relationships directly.

交流电（AC）电路与直流电（DC）电路有着本质区别，因为交流电的电压和电流会周期性地改变方向和大小。示波器是观察这些随时间变化信号的最有力工具，它能够让学生直接测量波形形状、幅值、频率以及相位关系。

1. Key Parameters of Alternating Current | 交流电的关键参数

An AC waveform is usually described by its period, frequency, peak value, and root-mean-square (RMS) value. The period ‘T’ is the time taken for one complete cycle, measured in seconds. The frequency ‘f’ is the number of cycles per second, measured in hertz (Hz), and is given by the equation f = 1/T.

交流波形通常由周期、频率、峰值和有效值（RMS）来描述。周期 T 是完成一次完整循环所需的时间，单位为秒。频率 f 是每秒完成的循环次数，单位为赫兹（Hz），其关系式为 f = 1/T。

f = 1/T

For a sinusoidal AC voltage, the peak value V₀ is the maximum voltage reached. The RMS value V_rms is the equivalent DC voltage that would dissipate the same power in a resistor, given by V_rms = V₀ / √2 ≈ 0.707 V₀.

对于正弦交流电压，峰值 V₀ 是达到的最大电压。有效值 V_rms 是在电阻上产生相同功率的等效直流电压，其关系为 V_rms = V₀ / √2 ≈ 0.707 V₀。

V_rms = V₀ / √2 ≈ 0.707 V₀

2. The Function of an Oscilloscope | 示波器的功能

An oscilloscope displays an instantaneous voltage against time on a screen. The horizontal axis represents time, while the vertical axis represents voltage. Modern digital oscilloscopes sample the signal and reconstruct the waveform, while analogue oscilloscopes use a cathode-ray tube to trace the beam.

示波器在屏幕上显示瞬时电压随时间的变化。横轴表示时间，纵轴表示电压。现代数字示波器对信号进行采样并重建波形，而模拟示波器则利用阴极射线管使电子束在屏幕上扫描。

The key advantage of using an oscilloscope is that it shows the actual shape of the AC waveform, revealing distortions, asymmetries, and phase shifts that are invisible to a multimeter. This makes it essential for understanding AC experiments.

使用示波器的主要优势在于它能显示交流波形的实际形状，揭示万用表无法察觉的失真、不对称和相移。这使得示波器成为理解交流电实验不可或缺的工具。

3. Oscilloscope Controls and Calibration | 示波器的控制与校准

Before conducting an experiment, the student must understand the main controls: the vertical sensitivity (volts per division, V/div), the time base (seconds per division, s/div), and the trigger level. These controls allow the waveform to be displayed at a suitable size and stable position.

在进行实验之前，学生必须了解主要控制旋钮：垂直灵敏度（伏/格，V/div）、时基（秒/格，s/div）以及触发电平。这些控制可以使波形以合适的尺寸和稳定位置显示在屏幕上。

Vertical scale: determines how many volts each division represents.

垂直标度：决定每一格代表多少伏电压。
Horizontal scale (time base): determines how many seconds each division represents.

水平标度（时基）：决定每一格代表多少秒时间。
Trigger: stabilises the waveform by setting a voltage level and slope where the sweep starts.

触发：通过设置扫描起始的电压电平和斜率来稳定波形。

Calibration is usually performed with a built-in 1 kHz square wave reference. The probe compensation should be adjusted until the square wave appears perfectly flat on top, ensuring accurate measurements.

通常使用内置的 1 kHz 方波参考信号进行校准。应调整探头补偿，使方波顶部看起来完全平坦，以确保测量准确。

4. Observing a Sinusoidal AC Waveform | 观察正弦交流波形

Connect the output of a signal generator (or a laboratory AC power supply via an isolating transformer) to the oscilloscope input using a coaxial cable. Set the signal generator to produce a sine wave at a frequency such as 50 Hz or 1 kHz and a few volts amplitude.

使用同轴电缆将信号发生器（或通过隔离变压器连接的实验室交流电源）的输出连接到示波器输入。将信号发生器设置为产生例如 50 Hz 或 1 kHz、幅度为几伏的正弦波。

Adjust the time base so that two or three complete cycles are visible across the screen. Adjust the vertical sensitivity so that the waveform occupies about half to two-thirds of the vertical scale. The resulting trace should clearly show the sinusoidal variation of voltage with time.

调整时基，使屏幕上显示两到三个完整周期。调整垂直灵敏度，使波形约占垂直标度的二分之一到三分之二。得到的扫描线应清晰显示电压随时间呈正弦变化。

Note that the oscilloscope shows the voltage between its input terminal and ground. If neither side of the AC source is grounded, the displayed waveform may float or contain noise. A ground reference must be established to interpret the trace correctly.

注意，示波器显示的是其输入端与地之间的电压。如果交流电源的两端均未接地，显示波形可能会浮动或包含噪声。必须建立接地参考才能正确解读扫描线。

5. Measuring Period and Frequency | 测量周期与频率

To measure the period, count the number of horizontal divisions covered by one complete cycle. Multiply this number by the time base setting. For example, if one cycle spans 4 divisions and the time base is 2 ms/div, then T = 4 × 2 ms = 8 ms = 0.008 s.

要测量周期，可数出一个完整周期所占的水平格数，再乘以时基设定值。例如，如果一个周期占据 4 格，时基为 2 ms/格，则 T = 4 × 2 ms = 8 ms = 0.008 s。

T = horizontal divisions per cycle × time base setting

周期 = 每周期水平格数 × 时基设定

The frequency is then calculated using f = 1/T. In the example above, f = 1 / 0.008 = 125 Hz. This method is often called the ‘division counting’ method and is accurate to within one division if the trace is adjusted properly.

然后利用 f = 1/T 计算频率。在上例中，f = 1 / 0.008 = 125 Hz。这种方法通常称为“数格法”，如果扫描线调整得当，精度可以控制在一格以内。

6. Measuring Peak Voltage and RMS Value | 测量峰值电压与有效值

To measure the peak voltage of a sinusoidal waveform, count the number of vertical divisions from the central horizontal line to the highest point of the waveform. Multiply by the vertical sensitivity. If the peak-to-peak voltage V_pp is measured instead, the peak voltage is half of that: V₀ = V_pp / 2.

要测量正弦波的峰值电压，数出从中心水平线到波形最高点之间的垂直格数，再乘以垂直灵敏度。如果测量的是峰峰值电压 V_pp，则峰值电压为其一半：V₀ = V_pp / 2。

V₀ = V_pp / 2

Once V₀ is known, the RMS value is V_rms = V₀ / √2. For a sine wave with V₀ = 10 V, V_rms ≈ 7.07 V. This value should match the reading of an AC voltmeter if the signal is a pure sinusoid.

知道 V₀ 后，有效值为 V_rms = V₀ / √2。对于 V₀ = 10 V 的正弦波，V_rms ≈ 7.07 V。如果信号是纯正弦波，该值应与交流电压表的读数一致。

7. Observing Phase Difference with a Dual-Channel Oscilloscope | 用双通道示波器观察相位差

A dual-channel oscilloscope can display two signals simultaneously, making it possible to measure the phase difference between voltages across different components in an AC circuit. For example, in a series RC circuit, the voltage across the resistor leads the voltage across the capacitor by a certain angle.

双通道示波器可以同时显示两个信号，从而可以测量交流电路中不同元件两端电压之间的相位差。例如，在串联 RC 电路中，电阻两端的电压超前电容两端电压一定角度。

To measure phase difference, set both channels to the same vertical sensitivity and use the time base to display a full cycle of the reference signal. Count the horizontal distance ‘d’ between the points where the two waveforms cross the zero axis in the same direction. If one full cycle has length ‘D’, then the phase difference φ is given by:

要测量相位差，将两个通道设置为相同的垂直灵敏度，用时基显示参考信号的一个完整周期。数出两个波形在相同方向穿过零轴的点之间的水平距离 d。如果一个完整周期的长度为 D，则相位差 φ 由下式给出：

φ = (d / D) × 360°

For example, if d = 1 division and D = 10 divisions, then φ = 36°. This method is widely used in AC experiments to verify the relationships between voltage and current in capacitors and inductors.

例如，如果 d = 1 格，D = 10 格，则 φ = 36°。这种方法在交流电实验中广泛用于验证电容和电感中电压与电流的关系。

8. Lissajous Figures and Frequency Comparison | 李萨如图形与频率比较

When the oscilloscope operates in X-Y mode, one signal is applied to the X input and another to the Y input. The resulting pattern is called a Lissajous figure. If the two frequencies are equal and in phase, the figure is a straight line or an ellipse depending on the phase difference.

当示波器工作在 X-Y 模式时，一个信号加在 X 输入，另一个信号加在 Y 输入，得到的图形称为李萨如图形。如果两个频率相等且同相，图形是一条直线；若相位差不同，则可能是椭圆或其他形状。

Lissajous figures can determine the ratio of two frequencies. If the figure has ‘m’ horizontal tangencies and ‘n’ vertical tangencies, then:

李萨如图形可以确定两个频率之比。如果图形有 m 个水平切点和 n 个垂直切点，则：

f_y / f_x = m / n

This technique is especially useful when comparing an unknown frequency with a known standard source. However, it is less accurate than direct frequency counting for complex waveforms.

这种技术在将未知频率与已知标准源比较时特别有用。然而，对于复杂波形，其精度不如直接频率计数。

9. Practical Considerations and Safety | 实验注意事项与安全

When performing AC experiments with an oscilloscope, always check the input voltage rating of the oscilloscope and the probe attenuation. Most probes have a 10× setting that reduces the signal by a factor of 10; the vertical sensitivity must be multiplied accordingly.

使用示波器进行交流电实验时，务必检查示波器的输入电压额定值以及探头的衰减。大多数探头有 10× 档，将信号衰减为原来的十分之一；此时垂直灵敏度必须相应乘以 10。

Never connect an oscilloscope directly to the mains supply without an isolation transformer or a differential probe, because the ground clip of the probe is connected to the earth, creating a short circuit risk. Always use a signal generator or a properly isolated auxiliary coil in laboratory experiments.

切勿在没有隔离变压器或差分探头的情况下将示波器直接连接到市电电源，因为探头的接地夹与大地相连，会产生短路风险。在实验室实验中，务必使用信号发生器或经过适当隔离的辅助线圈。

Set the intensity and focus controls before reading the trace.

在读取扫描线之前先调节亮度和聚焦控制。
Use a known calibration signal before taking measurements.

在进行测量之前使用已知校准信号。
Disconnect the equipment after the experiment and store probes properly.

实验结束后断开设备并妥善存放探头。

10. Sources of Error and Their Reduction | 误差来源及其减小方法

Common errors in oscilloscope measurements include parallax error when reading the scale, incorrect probe compensation, and finite bandwidth of the oscilloscope leading to amplitude attenuation at high frequencies. The unknown internal impedance of the probe can also load the circuit and alter the measured signal.

示波器测量中的常见误差包括读数时的视差误差、探头补偿不正确，以及示波器有限的带宽导致高频时幅度衰减。探头未知的输入阻抗也可能对电路产生负载效应，从而改变被测信号。

To reduce errors, read the trace directly from the front when the screen graticule is aligned, verify probe compensation before each session, and choose an oscilloscope bandwidth at least five times the signal frequency. For low-amplitude signals, use the 10× probe to reduce loading and improve accuracy.

为了减少误差，应在屏幕刻度对齐时正视读取扫描线，每次使用前验证探头补偿，并选择带宽至少为信号频率五倍的示波器。对于低幅度信号，使用 10× 探头可减少负载效应并提高精度。

11. Summary | 总结

The oscilloscope provides a direct visual representation of alternating current, allowing students to measure period, frequency, peak value, RMS value, and phase difference with straightforward techniques. Mastery of the basic controls and an understanding of the relationship between time base, vertical sensitivity, and the displayed waveform are essential for all AC circuit experiments.

示波器为交流电提供了直接的可视化表示，使学生能够通过简单的技术测量周期、频率、峰值、有效值和相位差。掌握基本控制旋钮，并理解时基、垂直灵敏度与显示波形之间的关系，是所有交流电路实验的基础。

By combining theoretical calculations with actual oscilloscope observations, students can confidently analyse AC circuits, predict component behaviour, and verify fundamental laws such as Ohm’s law and Kirchhoff’s rules in the context of alternating signals.

通过将理论计算与实际示波器观察相结合，学生可以自信地分析交流电路、预测元件行为，并在交流信号背景下验证欧姆定律和基尔霍夫定律等基本定律。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Alternating Current Experiments and Oscilloscope Observation | 交流电实验与示波器观察