The Non-Inverting Amplifier | 同相放大器

📚 The Non-Inverting Amplifier | 同相放大器

The non-inverting amplifier is one of the standard operational amplifier (op-amp) configurations studied at A-Level. It uses negative feedback to produce a stable voltage gain that is set entirely by two external resistors. Unlike the inverting amplifier, it keeps the output signal in phase with the input and offers a very high input impedance, which makes it useful for buffering and signal conditioning.

同相放大器是 A-Level 阶段学习的标准运算放大器（op-amp）电路之一。它通过负反馈产生稳定的电压增益，该增益完全由两个外部电阻决定。与反相放大器不同，同相放大器使输出信号与输入信号同相，并且提供非常高的输入阻抗，因此常用于缓冲和信号调理。

1. Op-Amp Basics and Ideal Properties | 运算放大器基础与理想特性

An operational amplifier is a high-gain differential voltage amplifier. Its output is proportional to the difference between the non-inverting input, V⁺, and the inverting input, V⁻. For an ideal op-amp used in a linear amplifier, we assume infinite open-loop gain, infinite input impedance, zero output impedance and infinite bandwidth.

运算放大器是一种高增益差分电压放大器。它的输出与同相输入端 V⁺ 和反相输入端 V⁻ 之间的差值成正比。对于用于线性放大器的理想运放，我们假设其开环增益为无穷大、输入阻抗为无穷大、输出阻抗为零、带宽为无穷大。

Because the open-loop gain is huge, even a tiny difference between V⁺ and V⁻ would send the output to saturation. Negative feedback is therefore needed to control the gain and keep the op-amp in its linear region.

由于开环增益极大，即使 V⁺ 和 V⁻ 之间存在极小差值，也会使输出进入饱和状态。因此需要负反馈来控制增益，并使运放工作在线性区。

2. The Non-Inverting Circuit Arrangement | 同相放大器的电路结构

In a non-inverting amplifier, the input signal is applied directly to the non-inverting input terminal. The output is fed back to the inverting input through a feedback resistor R₂. A second resistor R₁ connects the inverting input to ground (0 V). This arrangement is known as series-shunt feedback.

在同相放大器中，输入信号直接施加到同相输入端。输出通过反馈电阻 R₂ 反馈到反相输入端。另一个电阻 R₁ 将反相输入端连接到地（0 V）。这种结构称为串联-并联反馈。

The signal path from input to output keeps the same polarity: a positive input voltage produces a positive output voltage. The closed-loop gain is therefore a positive number. This is different from the inverting amplifier, where the output is 180° out of phase with the input.

从输入到输出的信号通路保持相同极性：正输入电压产生正输出电压。因此闭环增益为正数。这与反相放大器不同，后者的输出与输入相差 180°。

3. Negative Feedback and the Virtual Short | 负反馈与虚短

With negative feedback, the op-amp adjusts its output to make the voltage at the inverting input almost equal to the voltage at the non-inverting input. In the ideal case, V⁻ = V⁺. Since V⁺ is connected directly to the input signal, we have V⁻ = V_in.

在负反馈作用下，运放会调整输出，使反相输入端的电压几乎等于同相输入端的电压。在理想情况下，V⁻ = V⁺。由于 V⁺ 直接连接到输入信号，因此 V⁻ = V_in。

This near-equality of the two input terminals is often called a virtual short. It is not a real short circuit, because no current flows between the two inputs; it is only a voltage equality caused by feedback. We also assume that the op-amp inputs draw no current.

两个输入端的这种近似相等通常称为虚短。它并不是真正的短路，因为两个输入端之间没有电流流动；它只是由反馈引起的电压相等。我们同时假设运放输入端不吸取电流。

Therefore the same current flows through R₁ and R₂, and they form a potential divider from the output to ground. This idea is the key to deriving the voltage gain.

因此，流过 R₁ 和 R₂ 的是同一个电流，它们构成从输出到地的分压器。这一思路是推导电压增益的关键。

4. Deriving the Closed-Loop Voltage Gain | 闭环电压增益的推导

Let the output voltage be V_out. Since R₁ and R₂ are in series, the voltage at the inverting input is the fraction of V_out across R₁:

设输出电压为 V_out。由于 R₁ 与 R₂ 串联，反相输入端的电压是 V_out 在 R₁ 上的分压：

V⁻ = V_out × R₁ ÷ (R₁ + R₂)

But the virtual short gives

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

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