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Inverting AmplifierEdit

An inverting amplifier is a foundational circuit in analog electronics that uses an op-amp to produce a scaled and inverted version of an input signal. In this configuration, the input signal is fed through a resistor Rin to the inverting input of an op-amp, while a second resistor Rf provides feedback from the output back to that same input. The non-inverting input is typically connected to a reference potential, often ground. When the device operates in its linear region and with adequate open-loop gain, the circuit behaves predictably and can deliver a precise, inverted gain set by the ratio Rf/Rin.

Because of the negative feedback path, the inverting amplifier establishes a virtual ground at the inverting input, meaning this node is held at a potential very close to the reference at the non-inverting input. This property, together with the op-amp’s high open-loop gain, makes the closed-loop gain largely independent of the input source and the op-amp’s internal characteristics within limits. The ideal transfer is Vout = - (Rf/Rin) Vin, so the output is inverted and scaled by the chosen resistor ratio. In practice, designers exploit this simple relationship to build a wide range of signal-processing stages, from precision scaling to phase inversion for subsequent stages. For broader context, see op-amp and Negative feedback.

The inverting configuration also fixes the input impedance of the stage to Rin, which can be advantageous when you want to present a known impedance to a source. This is in contrast to the non-inverting amplifier, which typically presents a much higher input impedance but involves a different gain behavior. The choice between these configurations often hinges on whether a controlled input loading and predictable gain are paramount. See also the discussion on Non-inverting amplifier for comparison.

Overview

  • Stable, predictable gain in a compact form, with the gain set by the resistor ratio Rf/Rin.
  • Phase inversion: the output is 180 degrees out of phase with the input.
  • Input impedance approximately equal to Rin, allowing deliberate loading of the source.
  • Commonly used as a building block in broader signal-processing chains, including Active filter designs and instrumentation stages.
  • Easy to implement with standard components, and compatible with a wide range of op-amps such as the family around legacy parts and modern rail-to-rail devices like some op-amp.
  • In practice, non-idealities of the op-amp (finite open-loop gain and finite bandwidth) constrain the usable gain and frequency range.

From a pragmatic engineering standpoint, the inverting amplifier is valued for its simplicity and reliability. In environments where a stable, repeatable gain is essential and source impedance is well-controlled, this topology delivers robust results at modest cost. When a higher input impedance is required or when a non-inverting phase is needed, designers may route signals through a buffer or choose the alternative configuration. See Voltage gain and Input impedance for related concepts.

Operation and Theory

The basic circuit places Rin between Vin and the inverting input, and Rf between Vout and the same node. The non-inverting input is tied to a fixed reference, usually 0 V. Because the op-amp strives to keep its inputs at the same potential under negative feedback, the inverting input is driven to a virtual ground. Applying Kirchhoff’s laws at the inverting node gives:

(Vin − V−)/Rin + (Vout − V−)/Rf = 0

With V− ≈ V+ ≈ 0, this reduces to Vout ≈ −(Rf/Rin) Vin. This ideal result assumes an infinite open-loop gain and unlimited bandwidth. In real devices, the closed-loop gain deviates slightly due to finite open-loop gain and the op-amp’s finite gain-bandwidth product; the more demanding the frequency content of Vin, the more the actual gain departs from the ideal. See virtual ground for the fundamental concept behind the “zero” potential at the inverting input under feedback, and compare to the non-inverting case via Non-inverting amplifier.

Non-idealities to consider include input bias currents and input offset voltage, which, when multiplied by Rin, can produce an output offset that may require compensation in precision applications. The finite output drive capability and the load presented by connected circuitry also shape the usable range of Vout. For design practice, consider the op-amp’s stability with capacitive loads and the potential need for compensation or isolation (an occasional small resistor in series with the load can help). See Input bias current and Offset voltage for more detail.

Design considerations

  • Gain choice: select Rin and Rf to achieve the desired magnitude and sign of the gain, remembering that the magnitude is |Rf/Rin| and the sign is negative.
  • Input loading: Rin sets the input impedance; a larger Rin minimizes loading on the source, while a smaller Rin can improve noise performance at high source impedances but increases loading.
  • Bandwidth and stability: the closed-loop bandwidth roughly tracks the op-amp’s gain-bandwidth product divided by the magnitude of the closed-loop gain. At higher gains, the usable frequency range narrows. See Gain-bandwidth product.
  • Non-ideal offsets: input offset voltage and input bias currents produce an output error proportional to Rin; sometimes a small trimming or offset-cancellation strategy is used in precision circuits.
  • Output integrity: if the load is capacitive, stability can be challenging; a small series resistor (isolation resistor) with the load often improves stability and reduces the risk of oscillation. See op-amp stability.
  • Variants and extensions: this topology can be used as a summing amplifier by feeding multiple Vin signals through separate Rin paths, each contributing a weighted amount to the inverting input. See Summing amplifier for related configurations.

Real-world variants and practical tips

  • Capacitance at the input or in the feedback path can limit bandwidth and introduce phase shifts; designers often balance component values to maintain phase margin.
  • For high-precision work, matching Rin and Rf to tight tolerances minimizes gain error due to resistor mismatches; temperature coefficients matter for stable operation across environmental ranges.
  • When speed matters, ensure the chosen op-amp’s slew rate and bandwidth are sufficient to preserve the desired waveform without distortion; consult the device’s data sheet for the relevant figures of merit such as the slew rate and the gain-bandwidth product.
  • In practice, engineers may cascade stages or add buffering to reconcile the desire for high gain with the need for wide bandwidth and low distortion.

Applications for the inverting amplifier span a broad spectrum, from simple signal scaling to more complex signal-conditioning chains. It is a common choice where a known, inverted gain is required, and it often serves as a practical building block in active filters, instrumentation front-ends, and ADC interfaces. Related concepts include Active filter, Non-inverting amplifier, and Instrumentation amplifier for more sophisticated signal chaining.

See also