An inverting amplifier takes an input voltage, scales it by a set amount, and flips its polarity. A positive input produces a negative output, and a negative input produces a positive output. The amount of amplification (or reduction) depends entirely on two resistors in the circuit, making it one of the most straightforward and widely used configurations for operational amplifiers.
How the Signal Gets Flipped
The core job of an inverting amplifier is multiplying the input signal by negative one, then scaling it. If you feed in +33 millivolts with a gain of 10, you get -330 millivolts out. Feed in -0.5 volts, and you get +5 volts out. This polarity flip is what “inverting” means.
For sine waves, inversion looks identical to shifting the wave by half a cycle (180 degrees). But technically, inversion and phase shifting are not the same thing. Inversion multiplies every point of the signal by -1 at the same instant in time. A true 180-degree phase shift delays the signal by half its period. The distinction only matters for complex waveforms with a mix of harmonic frequencies. For a pure sine wave, or any signal built only from odd harmonics like a square wave, the two are indistinguishable. For most practical purposes in audio and instrumentation, you can think of it as a polarity flip.
The Gain Formula
An inverting amplifier uses two resistors: one at the input (often called R1) and one in the feedback path from the output back to the input (called Rf). The voltage gain of the circuit is:
Gain = -Rf / R1
The negative sign represents the inversion. The ratio of the two resistors sets how much the signal gets amplified. If Rf is 10 kilohms and R1 is 1 kilohm, the gain is -10, meaning the output is ten times larger than the input and opposite in polarity. If Rf equals R1, the gain is -1, and the circuit simply flips the signal without changing its size. If Rf is smaller than R1, the circuit actually attenuates the signal while still inverting it.
This clean, predictable relationship is what makes the inverting amplifier so useful. You don’t need to know anything about the op-amp’s internal electronics. The behavior is set almost entirely by two external components you choose.
Virtual Ground: Why It Works
The circuit relies on a concept called virtual ground. In an inverting amplifier, the non-inverting input (the + terminal) connects to ground. Because the op-amp has extremely high internal gain and uses negative feedback, it forces its two input terminals to sit at nearly the same voltage. Since the + terminal is at zero volts, the – terminal also sits at essentially zero volts, even though it’s not physically connected to ground.
This virtual ground is the key to the whole circuit. The input signal pushes current through R1 toward that zero-volt point. Since virtually no current flows into the op-amp’s input (its internal impedance is enormous), all of that current must flow through Rf instead. The op-amp adjusts its output to whatever voltage is needed to push exactly that much current back through Rf. The result is the gain formula above.
Input Impedance Trade-Offs
One important characteristic of an inverting amplifier: its input impedance equals R1. Because the inverting terminal sits at virtual ground, the entire input voltage drops across R1, and the signal source “sees” only that resistance. This creates a design tension. If you want high gain, you need Rf to be much larger than R1. But if R1 is small, the circuit presents a low impedance to whatever is driving it, which can load down a weak signal source.
A non-inverting amplifier avoids this problem because its input connects directly to the op-amp’s high-impedance terminal, giving it an extremely high input impedance regardless of gain. So when you need both high gain and high input impedance, the non-inverting configuration is often a better choice. The inverting amplifier shines when you want precise, resistor-controlled gain and the source can handle the loading, or when you specifically need that polarity inversion.
On the output side, negative feedback gives the inverting amplifier very low output impedance, meaning it can drive reasonable loads without its output voltage sagging.
Bandwidth Shrinks as Gain Increases
Every op-amp has a fixed gain-bandwidth product. This is a constant number: if you multiply the gain by the bandwidth, you always get the same value, equal to the op-amp’s unity-gain frequency (the frequency where its open-loop gain drops to 1). An op-amp with a gain-bandwidth product of 1 MHz set to a gain of -10 will work accurately up to about 100 kHz. Set it to a gain of -100, and that usable bandwidth drops to just 10 kHz.
The practical takeaway is that higher gain costs you frequency range. At the upper edge of the amplifier’s bandwidth, the output drops to about 70.7% of its expected level (a 3 dB reduction). Beyond that point, the amplifier can no longer keep up. If your application involves high-frequency signals, you need to balance gain against the bandwidth your circuit requires.
Output Limits and Clipping
The output of an inverting amplifier cannot exceed the power supply voltages (called the rails). If you’re powering the op-amp with +12V and -12V, the output will typically swing close to those values but not quite reach them. The exact maximum depends on the specific op-amp. Some “rail-to-rail” op-amps can get within millivolts of the supply voltage, while older designs might fall a volt or two short.
When the calculated output would exceed the supply rails, the amplifier clips. The output simply flatlines at the maximum or minimum voltage it can produce, and the signal gets distorted. If you’re amplifying a sine wave with a gain that pushes peaks beyond the rails, those peaks get chopped off into flat plateaus. Avoiding clipping means choosing a gain and supply voltage combination that keeps the output within range for your expected input levels.
Common Applications
The inverting amplifier’s most powerful extension is the summing amplifier. By connecting multiple input signals through separate input resistors to the same inverting terminal, you can add them together in a single output. Each input gets its own resistor, so each signal can be weighted differently. This is exactly how analog audio mixers combine vocals, instruments, and other channels into one signal before sending it to a power amplifier. Each channel’s volume is controlled by the ratio of the feedback resistor to that channel’s input resistor.
Beyond audio mixing, summing amplifiers appear in instrumentation. A temperature sensor, for example, might output a voltage that doesn’t read zero at a convenient reference point. By summing in a negative offset voltage through a second input resistor, you can shift the output so that 0 volts corresponds to the freezing point or any other baseline you need.
The inverting configuration also works as a current-to-voltage converter. With the input resistor removed and a current source connected directly to the virtual ground node, the input impedance drops to essentially zero ohms, which is ideal for measuring current. The feedback resistor converts the input current into a proportional (and inverted) output voltage.
Choosing Resistor Values
While the gain depends only on the ratio of Rf to R1, the actual resistance values still matter. Very low resistor values draw more current from the op-amp and the signal source, which can cause problems. Very high values (above a few hundred kilohms) introduce thermal noise and interact with stray capacitance on the circuit board. That extra capacitance in the feedback path adds phase shift, which can erode the amplifier’s stability margins and cause oscillation at high frequencies.
A common starting point is to pick resistor values in the range of 1 kilohm to 100 kilohms. For a gain of -10, that might mean R1 = 10 kilohms and Rf = 100 kilohms. This keeps current consumption reasonable, noise low, and parasitic effects manageable. From there, you adjust based on the specific demands of your signal source impedance and frequency range.