An op-amp inverting amplifier is a closed-loop operational amplifier circuit where the input signal is applied through a resistor to the inverting (-) terminal, producing an output that is scaled and phase-shifted by 180 degrees. In a real circuit, this topology changes a high-impedance, fragile signal into a robust, low-impedance output while simultaneously flipping its polarity and scaling its amplitude to match your ADC or driver requirements. Beginners frequently confuse it with the non-inverting amplifier; the dead giveaway on a schematic is that the inverting configuration routes the input signal through a resistor to the inverting pin while the non-inverting pin sits at ground, whereas the non-inverting amp feeds the signal directly to the non-inverting (+) pin.
Standard Resistor Pairs and Input Impedance
The gain of an inverting amplifier is dictated entirely by the ratio of the feedback resistor ($R_f$) to the input resistor ($R_{in}$), expressed as $A_v = -R_f / R_{in}$. However, picking arbitrary resistor values that satisfy the ratio is a rookie mistake. You must balance the input impedance (which is simply equal to $R_{in}$) against the op-amp's input bias current and the thermal noise generated by high-value resistors.
The table below provides standard E24 series resistor pairs for common gain targets, optimized for general-purpose audio and sensor applications using bipolar or JFET-input op-amps.
| Target Gain ($A_v$) | $R_{in}$ (Input) | $R_f$ (Feedback) | Actual Gain | Input Impedance ($Z_{in}$) | Best Use Case |
|---|---|---|---|---|---|
| -1 (Inverter) | 10 kΩ | 10 kΩ | -1.00 | 10 kΩ | Phase splitting, audio balancing |
| -10 | 1 kΩ | 10 kΩ | -10.00 | 1 kΩ | Low-noise sensor amps (low $R_{in}$ reduces thermal noise) |
| -10 (High-Z) | 10 kΩ | 100 kΩ | -10.00 | 10 kΩ | Audio preamps (prevents loading the source) |
| -100 | 1 kΩ | 100 kΩ | -100.0 | 1 kΩ | Microphone preamps, high-gain instrumentation |
| -0.5 (Attenuator) | 20 kΩ | 10 kΩ | -0.50 | 20 kΩ | Line-level attenuation, DAC output scaling |
Because the non-inverting (+) pin is tied to physical ground (0V), the op-amp's massive open-loop gain forces the inverting (-) pin to match it. This creates a 'virtual ground' at the inverting node. It sits at 0V, but unlike physical ground, it cannot sink or source current to the power supply rails. All input current flows directly through $R_f$ to the output.
Worked Numeric Example: Audio Preamplifier Stage
Let's design a gain-of-10 inverting stage for an electret microphone capsule using the ubiquitous Texas Instruments NE5532 dual op-amp. The microphone outputs a nominal 50 mV peak signal and has an internal impedance of roughly 2.2 kΩ.
Step 1: Select Resistors
If we use the 1 kΩ / 10 kΩ pair from the table above, the 1 kΩ input impedance will form a voltage divider with the microphone's 2.2 kΩ internal impedance. We would lose over half our signal before it even reaches the op-amp. Instead, we choose the 'High-Z' pair: $R_{in} = 10\text{ k}\Omega$ and $R_f = 100\text{ k}\Omega$.
Step 2: Calculate Output and Impedance
- Gain: $A_v = -100\text{ k}\Omega / 10\text{ k}\Omega = -10$
- Input Impedance: $Z_{in} = R_{in} = 10\text{ k}\Omega$ (The mic now sees a 10 kΩ load, dropping only about 18% of its voltage—a massive improvement).
- Output Voltage: $V_{out} = 50\text{ mV} \times -10 = -500\text{ mV peak}$.
Step 3: Verify Bandwidth (GBP)
The NE5532 has a typical Gain-Bandwidth Product (GBP) of 10 MHz. The closed-loop bandwidth is calculated as $GBP / |A_v|$.
$10,000,000\text{ Hz} / 10 = 1,000,000\text{ Hz}$ (1 MHz).
Since human hearing tops out at 20 kHz, a 1 MHz bandwidth is more than sufficient, ensuring flat frequency response across the audio spectrum.
Where You Meet the Inverting Amplifier in Practice
You will rarely see an inverting amplifier built just to flip a signal's polarity. Its true value emerges in topologies that exploit the virtual ground at the inverting input.
Audio Summing Mixers
Because the inverting input is a virtual ground, multiple input signals can be fed into the node through separate input resistors. The signals sum as currents, not voltages. This prevents 'crosstalk'—where one channel's signal bleeds back into another channel's source—making it the foundational circuit inside analog mixing consoles.
Transimpedance Amplifiers (TIA)
A transimpedance amplifier is a circuit topology that converts an input current into a proportional output voltage, typically using a feedback resistor. By replacing $R_{in}$ with a photodiode (which generates current proportional to light), the inverting op-amp forces the photodiode's voltage to remain at 0V (eliminating parasitic capacitance effects) while converting the tiny nanoamp current into a usable voltage via $R_f$. This is how fiber optic receivers and laser rangefinders operate.
R-2R DAC Buffering
Discrete R-2R resistor ladder DACs have an output impedance that varies depending on the digital code being output. If you drive a load directly, the varying impedance causes severe non-linearity. Slapping an inverting amplifier with a fixed $R_{in}$ on the output forces the DAC to see a constant load impedance, while the op-amp provides the low-impedance drive needed for the next stage.
Bench Troubleshooting and Edge Cases
When your inverting amplifier misbehaves on the bench, it is almost never the basic gain equation failing. It is usually a secondary op-amp parameter clashing with your component choices.
DC Offset from Input Bias Current
Bipolar op-amps like the NE5532 or LM741 require a small DC current to flow into or out of their input pins to bias the internal transistors. If your $R_f$ is large (e.g., 1 MΩ), this bias current flowing through the feedback resistor generates a massive DC offset voltage at the output ($V_{offset} = I_{bias} \times R_f$). The fix: Switch to a JFET or CMOS input op-amp like the TL072 or OPA2134, which have bias currents in the picoamp range, rendering the offset negligible.
Slew Rate Limiting on Fast Transients
If you feed a 100 kHz square wave into an inverting amp and the output looks like a triangle wave, you have hit the op-amp's slew rate limit. The slew rate is the maximum speed the output voltage can change, measured in Volts per microsecond (V/μs). The LM741 maxes out at a sluggish 0.5 V/μs. If your circuit needs to output a 10V peak signal at 100 kHz, you need a minimum slew rate of $2 \times \pi \times f \times V_{peak} = 6.28\text{ V/}\mu\text{s}$. The fix: Use a high-speed op-amp like the AD8055 (1500 V/μs) for video or fast pulse applications.
Instability and Oscillation
If your output is ringing or oscillating at high frequencies, check your physical layout. The inverting input is a high-impedance node highly susceptible to stray capacitance. If you place a massive 1 MΩ feedback resistor with long, sweeping leads, the parasitic capacitance creates a pole in the feedback loop, destroying phase margin. The fix: Keep $R_f$ physically as close to the op-amp pins as possible, and consider adding a small 10 pF to 33 pF compensation capacitor in parallel with $R_f$ to roll off high-frequency gain.
Frequently Asked Questions
Why can't I just use a voltage divider to attenuate a signal instead of an inverting amp with gain < 1?
A voltage divider attenuates the signal, but it also raises the output impedance. If your downstream circuit (like an ADC or a long cable) has a relatively low input impedance, it will load the divider and ruin your attenuation ratio. An inverting amplifier with a gain of -0.5 provides precise attenuation while maintaining a near-zero output impedance, isolating the source from the load.
Does the 180-degree phase shift matter in DC circuits?
In pure DC circuits (like scaling a 0-5V sensor down to 0-3.3V for an ESP32 ADC), a 180-degree phase shift simply means the output voltage moves in the opposite direction of the input (e.g., as the sensor voltage rises, the op-amp output falls). If your microcontroller expects a positive correlation, you simply invert the math in your firmware, or add a second inverting amplifier with a gain of -1 to flip the polarity back to normal.
