What is an Inverting Amplifier?

I. Working Principle of Inverting Amplifier

The inverting amplifier circuit has the function of amplifying the input signal and inverting the output. "Inverted" means that the positive and negative signs are reversed. This amplifier uses negative feedback technology. The so-called negative feedback is to return a part of the output signal to the input. In the circuit shown in the figure, the connection method of connecting (returning) the output Vout to the inverting input terminal (-) via R2 is negative feedback.

Operational amplifiers have the following characteristics. When the power supply voltage is not applied to the output terminal, the non-inverting input terminal (+) and the inverting input terminal (-) are considered to have the same voltage applied, that is to say, it can be considered as a virtual short circuit. Therefore, when the positive input terminal (+) is 0V, the voltage at point A is also 0V.

The input impedance of the operational amplifier is extremely high, and there is basically no current in the inverting input terminal (-). Therefore, when flows to R2 via point A, the currents of I1 and I2 are basically equal. Based on the above conditions, using Ohm's law for R2, we get Vout=-I1×R2. I1 is negative because I2 flows from point A where the voltage is 0V. From another point of view, when the input voltage of the inverting input terminal (-) rises, the output will be inverted and amplified greatly in the negative direction. Since the output voltage in this negative direction is connected to the inverting input terminal via R2, the voltage rise of the inverting input terminal (-) will be blocked. Both the inverting input terminal and the positive input terminal voltage become 0V, and the output voltage is stable.

Gain Calculation

Calculate the gain through the relationship between the input and output in this amplifier circuit. The gain is the ratio of Vout and Vin, that is, Vout/Vin = (-I1×R2) / (I1×R1) =-R2/R1. The resulting gain is -, which means the waveform is inverted.

Special attention should be paid to this formula, the gain is only determined by the resistance ratio of R1 and R2. In other words. We can easily change the gain by changing the resistance. Apply negative feedback to an operational amplifier with high gain, and by adjusting the resistance value, the desired gain circuit can be obtained.

Types of Inverting Amplifier Circuits

Due to the different ratios of the input resistance (R1) to the feedback resistance (R2), the inverting amplifier can be categorized into three distinct types of circuits:

1. Inverter (Unity Gain Inverter)

When R2 = R1, the gain magnitude equals 1.

• The output signal has the same amplitude as the input but with opposite polarity

• Gain = -R2/R1 = -1

• Example: If R1 = R2 = 10kΩ, an input of +2V produces an output of -2V

2. Inverting Amplifier

When R2 > R1, the circuit amplifies the signal.

• The output signal has greater amplitude than the input with opposite polarity

• Gain = -R2/R1 (magnitude greater than 1)

• Example: If R1 = 10kΩ and R2 = 100kΩ, gain = -10, an input of +0.5V produces an output of -5V

3. Inverting Attenuator

When R2 < R1, the circuit attenuates the signal.

• The output signal has smaller amplitude than the input with opposite polarity

• Gain = -R2/R1 (magnitude less than 1)

• Example: If R1 = 100kΩ and R2 = 10kΩ, gain = -0.1, an input of +2V produces an output of -0.2V

Among them, the inverter is also called the inverter circuit, which is named because the output and output change trends are opposite and their absolute values are equal; the inverting amplifier has the dual function of signal inversion and amplification; the inverting attenuator has the signal inversion and the dual role of attenuation. All three types of circuits have universal applications.

Circuit Analysis

The starting point of analyzing its circuit principle is still playing the leading role in the series resistor divider, and the op-amp device is a supporting role. Or it can be analyzed from the perspective of input current. As shown in the figure above, the bias circuit is drawn separately to better explain the problem.

In Figure 2, R1 and R2 form a voltage divider network. The signal polarity determines the direction of current flow—from the input signal source through R1 to the inverting input node, and then through R2 to the output terminal. This current path is essential to understanding the operation of the inverting amplifier.

Since the same current flows into R1 and R2, R1=R2, and the voltage divider point is 0V, it can be inferred that the OUT terminal must be -1V. The -1V of the output terminal (0V of the voltage division point) is determined by the conduction degree of the output stage Q2, and is adjusted by itself according to the input signal.

To analyze this from another perspective, consider the current flow: When a signal current of +1mA flows through R1 toward the inverting input (node A), this same current must flow through R2 away from node A (since the op-amp input impedance is extremely high and negligible current flows into the op-amp terminal).

For node A to maintain 0V (virtual ground):

• - Current entering node A through R1: I₁ = Vin/R1

• - Current leaving node A through R2: I₂ = (0V - Vout)/R2

• - By Kirchhoff's Current Law at node A: I₁ + I₂ = 0

• - Therefore: Vin/R1 + (0V - Vout)/R2 = 0

• - This gives us: Vout = -Vin × (R2/R1)

The operational amplifier automatically adjusts its output voltage until the inverting input reaches 0V (virtual ground). This is the fundamental control mechanism of the inverting amplifier configuration.

It can be deduced from this that when R2>R1, in order to obtain the reverse current flowing through R2, the current is still equal to R1, and the OUT terminal must be adjusted to -3V; when R2<R1, to obtain the reverse current flowing through R2 the current is still equal to the reverse current of R1, and the OUT terminal must be adjusted to output -0.5V.    

The entire op-amp circuit is a game of series resistor divider. As long as you master the analysis ability of the resistor series voltage divider circuit, you have found the golden key to analyze the principle of the operational amplifier circuit.

Virtual Ground Concept

The inverting amplifier is a circuit structure in which the non-inverting terminal is grounded (or grounded via a bias resistor), and the input signal enters from the inverting input terminal. From the "virtual short" relationship between the two input terminals (due to the grounding of the non-inverting terminal), the concept of "virtual ground" can be derived, and this concept only refers to the inverting amplifier. Due to the different considerations of the designer, the input of the non-inverting terminal is directly grounded, and there are also those connected to the ground by adding a bias resistor R3, and there is no difference in the analysis of the circuit principle and the troubleshooting.

Obviously, because the non-inverting input terminal is grounded, the final control purpose of the amplifier is to always make the inverting input terminal become 0V ground level under the dynamic adjustment of the output stage in the amplification area, no matter what the input signal is. In the above figure, R1 is the input resistance, R2 is the feedback resistance, and the voltage amplification factor of the circuit = R2/R3.

Basic Characteristics of Normal Operation

1. Input Terminal Voltages

Both input terminals are 0V to ground.

2. Signal Relationship

The input and input signal voltages show a reverse trend, and the magnitude depends on the proportional relationship between R1 and R2.

If you need to analyze or get a detection judgment, you must first determine the circuit in the figure. What point is the signal input terminal?

Due to the "virtual ground" characteristic of the inverting amplifier, the two input terminals of the op-amp device itself are at 0V ground level and do not change with the input signal voltage change (or only transient changes, which are extremely difficult to capture in the measurement). Obviously, the right end of the input resistance R1 is not the signal input end, but the left end is the signal input end, so R2/R1=-VOUT/VIN- (the input voltage at the left end of R1).

Or you can think of it like this: In the circuit shown above, both ends of R1 are the input voltage, and both ends of R2 are the reverse output voltage. The voltage of the circuit is amplified and whether it is good or bad. Just use two test leads to clear the two. That's it-the voltage across VR1 is the input voltage; the voltage across VR2 is the reverse output voltage.

II. Inverting Amplifier Troubleshooting

1. Normal Working State

That is to meet two fundamental characteristics:

a. Both input terminals are 0V to ground.

b. The input and input signal voltages show a reverse trend, and the magnitude depends on the proportional relationship between R1 and R2.

Not for this, that is, a fault state.

2. Repair Principles

The principle of repairing non-inverting amplifiers still applies to inverting amplifiers.

a. After the "virtual ground" principle is not met, first check according to the comparator principle. If it meets it, the op-amp device is good, and the peripheral components are faulty.

b. If the principle of the comparator is not met, the op-amp device is broken.

III. Applications of Inverting Amplifier

1. Integrator Circuit

The integrator is created by replacing the feedback resistor R2 with a capacitor C.

Circuit Configuration

• Input resistance: R1 connects to the inverting input

• Feedback element: Capacitor C instead of R2

• Output relationship: Vo = -(1/RC)∫Vi dt

Practical Applications

• Waveform generation

• Low-pass filtering

• Analog computing

• Signal processing in control systems

Design Example

For an integrator with R1 = 10kΩ and C = 1μF, the integration time constant is 10ms, suitable for integrating signals with frequency components above 16Hz.

2. Differentiator Circuit

The differentiator is formed by replacing the input resistor R1 with a capacitor C.

Circuit Configuration

• Input element: Capacitor C instead of R1

• Feedback resistance: R2 maintains its position

• Output relationship: Vo = -RC(dVi/dt)

Practical Applications

• Edge detection in signal processing

• Rate-of-change measurement

• High-pass filtering

• Pulse generation

Note

Practical differentiators typically include an additional resistor in series with the capacitor to limit high-frequency gain and reduce noise sensitivity.

3. Summing Amplifier (Adder)

The summing amplifier combines multiple input signals into a single output.

Circuit Configuration

• Multiple input resistors (R1, R2, R3, etc.) connect to the inverting input

• Single feedback resistor Rf

• When R1 = R2 = R3 = ... = Rn = Rf, output becomes: Vo = -(V1 + V2 + V3 + ... + Vn)

Practical Applications

• Audio mixing

• Analog computation

• Signal combining in sensor systems

• Weighted addition (by varying resistor values)

Design Example

For a three-input adder with equal weighting, using R1 = R2 = R3 = Rf = 10kΩ:

• If V1 = 1V, V2 = 2V, V3 = 3V

• Then Vo = -(1V + 2V + 3V) = -6V

References

• Analog Devices. (n.d.). Inverting op amp. https://www.analog.com/en/resources/glossary/inverting-op-amp.html

• ElectronX Lab. (2022, April 19). Introduction to inverting op AMP circuits [Video]. YouTube. https://www.youtube.com/watch?v=Zxu1N3DfVaI

• All About Circuits. (n.d.). Basic amplifier configurations: The inverting amplifier - Video tutorial. https://www.allaboutcircuits.com/video-tutorials/the-basic-op-amp-inverting-amplifier/