The inverting configuration is one of the fundamental applications of operational amplifiers, often referred to as op amps. When studying operational amplifiers, after understanding the ideal model, the inverting and non-inverting input terminals, and the concept of feedback, the inverting configuration is one of the first truly practical circuits used to design amplification, attenuation, summing, current-to-voltage conversion, and active filtering stages.
This article is intended as an in-depth extension of the operational amplifier guide published on MST Tutorial, where the main op amp terminals, the ideal model with very high input resistance and very low output resistance, and the basic configurations such as inverting, non-inverting, voltage follower, summing amplifier, differential amplifier, differentiator, and integrator are introduced.
Structure of the Inverting Configuration
In an inverting circuit, the input signal is applied to the inverting terminal of the op amp through an input resistor. The non-inverting terminal is normally connected to ground, or to a virtual ground when the circuit operates from a single supply. A second resistor, called the feedback resistor, connects the output of the op amp back to the inverting terminal.
The minimum structure therefore consists of:
- an operational amplifier;
- an input resistor, usually indicated as R1 or Rin;
- a feedback resistor, usually indicated as R2 or Rf;
- a reference on the non-inverting terminal, often GND in dual-supply circuits;
- a single or dual power supply compatible with the selected component.
The key characteristic of this configuration is that the output signal is phase-inverted with respect to the input signal. If the input signal is positive, the output tends to become negative; if the input signal is negative, the output tends to become positive, within the limits imposed by the supply voltage and the output swing of the op amp.
Operating Principle
The operation of the inverting configuration is based on negative feedback. The op amp adjusts its output in order to keep its two inputs at approximately the same potential. If the non-inverting terminal is connected to ground, the inverting terminal is ideally held very close to zero volts. This node is known as a virtual ground.
The virtual ground is not a real physical connection to GND: it is the result of negative feedback. From a voltage point of view, the inverting node behaves as if it were connected to ground, but it must not be used as a ground point to power or reference other circuits.
Ideal equation for the inverting gain: Av = Vout / Vin = - Rf / Rin Where: Av = voltage gain Rf = feedback resistor Rin = input resistor The minus sign indicates a 180-degree phase inversion.
Since the op amp input ideally draws no current, the current flowing through the input resistor must also flow through the feedback resistor. This makes it possible to determine the gain almost entirely from the ratio between the two resistors.
Why It Is Called an Inverting Configuration
The term “inverting” comes from the fact that the output is shifted by 180 degrees with respect to the input. In DC operation, this means that a positive input voltage produces a negative output voltage. In AC operation, a positive half-cycle at the input corresponds to a negative half-cycle at the output.
This inversion can be either an advantage or a disadvantage depending on the application. In audio circuits, for example, the phase inversion of a single stage is not always a problem; however, it becomes important when multiple signals must be summed or compared with each other. In control systems, on the other hand, the sign of the gain is essential to avoid unwanted feedback effects.
Difference Between Real Ground and Virtual Ground
One of the most important concepts to understand is the difference between real ground and virtual ground. Real ground is a physical node connected to the circuit reference. Virtual ground, instead, is a node that assumes a potential close to ground due to the action of the op amp and negative feedback.
In an ideal inverting circuit, the inverting terminal remains close to the potential of the non-inverting terminal. In practice, however, errors are introduced by offset voltage, input bias currents, open-loop gain limitations, noise, resistor tolerances, and limited bandwidth.
Choosing Rin and Rf
The choice of resistors should not be based only on the Rf/Rin ratio. Two different pairs of resistor values may produce the same gain, but they can behave differently in terms of noise, offset, current drawn from the signal source, bandwidth, and stability.
Example of an inverting gain equal to -10: Case A: Rin = 10 kOhm Rf = 100 kOhm Av = -100 kOhm / 10 kOhm = -10 Case B: Rin = 1 kOhm Rf = 10 kOhm Av = -10 kOhm / 1 kOhm = -10 Both cases provide the same ideal gain, but they are not equivalent: - Case A loads the source less; - Case B is less sensitive to thermal noise from the resistors; - Case B requires more current from the input signal; - Case A may be more sensitive to bias currents and parasitic capacitances.
In many audio or general-purpose signal circuits, resistor values typically range from a few kiloohms to a few hundred kiloohms. Values that are too low increase source loading and current consumption; values that are too high increase noise, sensitivity to bias currents, and possible stability issues.
Input Impedance
An often overlooked aspect is that, in the inverting configuration, the input impedance seen by the source is approximately equal to Rin. This differs from the non-inverting configuration, where the input impedance can be very high because the signal is applied directly to the non-inverting terminal of the op amp.
For this reason, the inverting configuration is very predictable in terms of gain, but it can load the source if Rin is too low. If the source has a high impedance, it may be preferable to use a buffer or a non-inverting stage before the inverting amplifier.
Fields of Application
The inverting configuration is widely used because it is simple, stable, easy to calculate, and highly extendable. Its most common applications include signal amplifiers, audio preamplifiers, analog mixers, summing amplifiers, active filters, current-to-voltage converters, sensor conditioning stages, and analog signal processing circuits.
In audio circuits, it is used to set gain, invert phase, sum multiple sources, or create active filters. In measurement systems, it can be used to adapt the level of a sensor signal to the input of an analog-to-digital converter. In circuits using photodiodes, a variation of the inverting configuration is used as a transimpedance amplifier, converting current into voltage.
Main practical applications: 1. Inverting voltage amplifier Vout = -Vin * Rf / Rin 2. Inverting attenuator Rf lower than Rin Example: Rf = 10 kOhm, Rin = 100 kOhm, Av = -0.1 3. Inverting summing amplifier Multiple inputs, each with its own resistor 4. Audio mixer A variation of the inverting summing amplifier 5. Current-to-voltage converter Typical with photodiodes and current-output sensors 6. Active filter By inserting capacitors in the input or feedback network 7. Integrator and differentiator By replacing resistors with capacitors in the appropriate positions
Advantages Compared to the Non-Inverting Configuration
Compared to the non-inverting configuration, the inverting stage offers several important advantages. The gain is determined very directly by the ratio between two resistors. In addition, the virtual-ground inverting node makes it easy to sum multiple signals, making this configuration ideal for analog mixers and summing amplifiers.
- Gain is simple to calculate.
- Analog summing circuits are easy to implement.
- Excellent linearity when the op amp operates within its limits.
- Possibility of obtaining gains lower than, equal to, or greater than unity.
- The virtual-ground input node is useful in current-to-voltage converters.
- Good predictability in small-signal operation.
Disadvantages Compared to the Non-Inverting Configuration
The main disadvantage is that the input impedance is limited by Rin. If the source cannot properly drive this resistance, the signal may be attenuated or distorted. In addition, the signal is phase-inverted, which may require a second inverting stage if the original phase must be restored.
- Lower input impedance compared to the non-inverting configuration.
- 180-degree phase inversion.
- Greater care required when choosing Rin if the source is weak or has high impedance.
- Possible increase in noise when high-value resistors are used.
- A proper virtual ground is required in single-supply circuits.
Comparison with Voltage Follower, Summing Amplifier, and Differential Amplifier
The voltage follower has unity non-inverting gain and very high input impedance. It is ideal as a buffer, but it does not allow an arbitrary gain to be set using the ratio between two resistors.
The inverting summing amplifier is derived directly from the inverting configuration. By adding multiple input resistors, each connected to a different signal, the currents are summed at the virtual node and the output provides the weighted sum of the signals, with phase inversion.
The differential amplifier amplifies the difference between two signals and is useful when common-mode components need to be rejected. However, it is more sensitive to the accuracy of resistor ratios and requires more careful design if a good CMRR is desired.
Summary comparison: Inverting configuration: - gain: Av = -Rf/Rin - phase: inverted - input impedance: approximately Rin - typical use: amplification, summing, filters, transimpedance Non-inverting configuration: - gain: Av = 1 + Rf/Rg - phase: non-inverted - input impedance: very high - typical use: amplified buffer, interface with weak sources Voltage follower: - gain: Av = 1 - phase: non-inverted - input impedance: very high - typical use: impedance matching Inverting summing amplifier: - gain: weighted for each input - phase: inverted - typical use: mixer, analog summing, resistive DACs Differential amplifier: - gain: proportional to the difference between two inputs - typical use: differential measurement, common-mode rejection
Practical Use with the TL072
The TL072 is a widely used dual operational amplifier in audio circuits and low-noise analog applications. It is appreciated for its FET input stage, low bias current, and slew rate suitable for many audio applications. It is suitable when the source has medium-to-high impedance or when the design requires minimizing errors caused by input bias currents.
Indicative TL072 data, TL07xx family, according to Texas Instruments documentation: Type: dual operational amplifier Number of channels: 2 Total supply voltage indicated by TI for TL072: min 7 V, max 30 V Typical GBW: 3 MHz Typical slew rate: 13 V/us Maximum offset voltage at 25 °C: 6 mV Typical quiescent current per channel: 1.4 mA Typical voltage noise at 1 kHz: 37 nV/sqrt(Hz) Maximum input bias current: 200 pA Typical CMRR: 100 dB Operating temperature, catalog version: -40 °C / 85 °C Note: TL072, TL072A, TL072B, TL072H, and versions from different manufacturers may have different values. Always check the datasheet for the exact part number being used.
A classic example is a small inverting audio stage with a gain of -2. This circuit can be used to moderately increase the level of a line-level signal or a signal coming from a previous stage, while maintaining a suitable input impedance.
Practical example with TL072: inverting audio amplifier Goal: obtain a gain of -2 Components: Rin = 22 kOhm Rf = 44 kOhm, or 47 kOhm as a standard commercial value Op amp = TL072 Recommended supply for classic audio use: dual supply, for example +/-12 V or +/-15 V Calculation: Av = -Rf / Rin With Rf = 44 kOhm: Av = -44 kOhm / 22 kOhm = -2 With Rf = 47 kOhm: Av = -47 kOhm / 22 kOhm = approximately -2.14 Notes: - use decoupling capacitors close to the supply pins; - add a resistor from the non-inverting terminal to ground; - avoid long wires or traces on the inverting node; - check that the output signal does not saturate with the available supply voltages.
Practical Use with the RC4558
The RC4558 is a widely used dual bipolar operational amplifier found in general-purpose audio circuits, guitar pedals, active filters, and low-cost gain stages. Compared to the TL072, it has a much higher input bias current because it uses a bipolar input stage, but it can still provide good performance in audio applications where circuit impedances are not too high.
Indicative RC4558 data according to Texas Instruments documentation: Type: general-purpose dual operational amplifier Number of channels: 2 Total supply voltage: min 10 V, max 30 V Typical GBW indicated in the product table: 3 MHz Typical slew rate: 1.7 V/us Maximum offset voltage at 25 °C: 6 mV Typical quiescent current per channel: 1.25 mA Typical voltage noise at 1 kHz: 8 nV/sqrt(Hz) Typical THD + N at 1 kHz: 0.0005 % Architecture: bipolar Typical CMRR: 90 dB Maximum input bias current: 500000 pA Operating temperature, catalog version: -40 °C / 85 °C Note: The datasheet also reports typical characteristics related to audio applications. When designing a circuit, always verify package, manufacturer, datasheet revision, and test conditions.
A practical example with the RC4558 is an inverting stage for an audio effect or a moderate-gain preamplifier, using resistor values that are not too high in order to reduce the effect of input bias current.
Practical example with RC4558: general-purpose inverting audio stage Goal: gain of approximately -4.7 Components: Rin = 10 kOhm Rf = 47 kOhm Op amp = RC4558 Typical supply: dual supply, for example +/-9 V, +/-12 V, or +/-15 V, if compatible with the design Calculation: Av = -Rf / Rin Av = -47 kOhm / 10 kOhm Av = -4.7 Notes: - moderate resistor values help reduce errors caused by input bias current; - check the slew rate if the output signal is large and high in frequency; - verify the margin before saturation; - use local supply decoupling; - avoid directly driving very low-impedance loads from the output.
Design with a Dual Supply
A dual supply is the simplest condition for understanding the inverting circuit. With a symmetrical supply, for example positive and negative voltages referenced to ground, the non-inverting terminal can be connected directly to GND. The signal can swing above and below zero, and the output can do the same within the limits of the op amp.
Example with dual supply: Power supply: +Vcc = +12 V -Vcc = -12 V GND = central reference Non-inverting node: connected to GND Input: signal centered at 0 V Output: inverted signal, centered at 0 V, limited by the available output swing
In traditional analog audio circuits, this is often the cleanest solution because it avoids the need to create a mid-supply virtual reference to handle AC signals.
Design with a Single Supply
With a single supply, for example between 0 V and a positive voltage, the inverting circuit requires a virtual ground. In practice, the non-inverting terminal is not connected to GND, but to an intermediate reference. The input signal must be properly coupled and biased so that it swings around this reference.
Conceptual example with single supply: Power supply: Vcc = 9 V GND = 0 V Virtual reference: Vref = Vcc / 2 = 4.5 V Non-inverting terminal: connected to Vref, not to GND Input: AC-coupled through a capacitor if it comes from a source centered at 0 V Output: centered around Vref, not around 0 V Note: The TL072 and RC4558 are not modern rail-to-rail op amps. With low single-supply voltages, the input range and output swing must be checked carefully.
The main challenge with a single supply is preventing the input or output from leaving the valid operating range of the op amp. Many classic op amps do not work well with signals very close to the supply rails, so sufficient headroom is required.
Input Bias Current Compensation
In a real circuit, the op amp inputs draw small currents. These currents, flowing through the resistors connected to the inputs, create voltage drops that can appear as output offset. To reduce this effect, a resistor is often placed between the non-inverting terminal and ground, or between the non-inverting terminal and the virtual ground, with a value equal to the parallel combination of Rin and Rf.
Compensation resistor on the non-inverting terminal: Rb = Rin || Rf Where: Rb = resistor between the non-inverting input and the reference Rin = input resistor Rf = feedback resistor Formula: Rb = (Rin * Rf) / (Rin + Rf) Example: Rin = 10 kOhm Rf = 47 kOhm Rb = (10 kOhm * 47 kOhm) / (10 kOhm + 47 kOhm) Rb = approximately 8.25 kOhm Possible standard value: 8.2 kOhm
This technique is more important with bipolar-input op amps, such as the RC4558, than with FET-input op amps such as the TL072. However, even with FET-input op amps, proper balancing can be useful, especially in precision circuits.
Frequency Response and Gain-Bandwidth Product
The ideal gain calculated from the resistor ratio does not remain valid at every frequency. Every op amp has a limited bandwidth. The most commonly used parameter for an initial estimate is the gain-bandwidth product, often indicated as GBW.
Simplified estimate of the closed-loop bandwidth: Approximate usable bandwidth = GBW / |Av| Theoretical example: GBW = 3 MHz |Av| = 10 Approximate bandwidth = 3 MHz / 10 = 300 kHz Note: This is a first-order estimate. Actual stability also depends on phase shift, load, parasitic capacitances, layout, and circuit configuration.
In audio circuits, the required bandwidth is relatively limited, but sufficient margin is still needed to avoid phase shift, high-frequency distortion, and instability. In measurement circuits or pulse-signal applications, bandwidth and slew rate become much more critical.
Slew Rate and Large-Signal Distortion
Slew rate indicates the maximum speed at which the output voltage of the op amp can change. Even if the frequency gain appears sufficient, a large and fast signal may require an output voltage rate of change greater than the op amp can provide, resulting in distortion.
Useful relationship for a sinusoidal signal: Required SR = 2 * pi * f * Vp Where: Required SR = minimum slew rate f = signal frequency Vp = peak output voltage Example: f = 20 kHz Vp = 5 V Required SR = 2 * pi * 20000 * 5 Required SR = 628318 V/s Required SR = approximately 0.628 V/us Comparison: an op amp with a slew rate of 1.7 V/us can theoretically handle this case with some margin; an op amp with a slew rate of 13 V/us provides much greater margin.
For moderate-level audio signals, the RC4558 can be sufficient, but the TL072 provides greater dynamic margin in terms of slew rate. This can be useful in stages with high gain, large signals, or impulsive content.
Noise in the Inverting Configuration
The total noise of an inverting stage depends on the op amp’s own noise, the thermal noise of the resistors, and the selected gain. High-value resistors generate more thermal noise and make the inverting node more sensitive to interference and parasitic capacitance.
In low-noise audio circuits, it is advisable to avoid excessively high resistor values, use a careful layout, keep the inverting-node trace short, use clean power supplies, and place bypass capacitors close to the IC supply pins.
Practical noise guidelines: - avoid an excessively high Rf if it is not necessary; - avoid an excessively high Rin with weak sources; - use low-noise resistors with suitable tolerance; - keep the inverting node short; - separate power grounds from signal grounds; - filter and decouple the power supplies properly; - check both voltage noise and current noise of the op amp.
Stability and Parasitic Capacitance
The inverting node is a sensitive point. Parasitic capacitances caused by long PCB traces, breadboards, cables, or instrument inputs can introduce unwanted poles and reduce phase margin. In real circuits, especially with high resistor values or fast op amps, it can be useful to place a small capacitor in parallel with the feedback resistor.
Simplified compensation with capacitor Cf: Rf in parallel with Cf Effect: - reduces gain at high frequencies; - limits high-frequency noise; - improves stability in the presence of parasitic capacitance; - turns the stage into an inverting low-pass filter. Approximate cutoff frequency: fc = 1 / (2 * pi * Rf * Cf) Example: Rf = 100 kOhm Cf = 47 pF fc = 1 / (2 * pi * 100000 * 47e-12) fc = approximately 33.9 kHz
The addition of Cf should not be arbitrary: if the circuit must operate across the audio band, a cutoff frequency that is too low will attenuate the high frequencies. If, however, the circuit is a preamplifier or measurement stage, it can be a useful solution to reduce noise and oscillations.
Practical Example: Inverting Audio Summing Amplifier with TL072
One of the most interesting applications of the inverting configuration is the summing amplifier. Each input is connected to the inverting node through its own resistor. The contribution of each channel depends on the ratio between the feedback resistor and the input resistor of that specific channel.
3-input audio summing amplifier with TL072: Goal: mix three audio signals with equal weighting Components: R1 = 22 kOhm for input 1 R2 = 22 kOhm for input 2 R3 = 22 kOhm for input 3 Rf = 22 kOhm Op amp = TL072 Formula: Vout = -Rf * (Vin1/R1 + Vin2/R2 + Vin3/R3) With R1 = R2 = R3 = Rf: Vout = -(Vin1 + Vin2 + Vin3) Practical note: if the three signals can add up to a high level, the output may saturate. In a real mixer, it is often necessary to attenuate each input or reduce Rf.
Practical Example: Inverting Attenuator with RC4558
The inverting configuration is not always used for amplification. If Rf is lower than Rin, the circuit attenuates the signal and inverts it. This solution is useful when a signal needs to be reduced while maintaining a defined input impedance.
Inverting attenuator with RC4558: Goal: reduce the signal to approximately one fifth Components: Rin = 47 kOhm Rf = 10 kOhm Op amp = RC4558 Calculation: Av = -Rf / Rin Av = -10 kOhm / 47 kOhm Av = approximately -0.213 Possible use: level matching between an audio stage with a high output level and a more sensitive following stage.
Practical Example: Inverting Low-Pass Filter
By adding a capacitor in parallel with Rf, an inverting low-pass filter is obtained. At low frequencies, the capacitor has high impedance and the circuit behaves like a normal inverting amplifier. At high frequencies, the capacitor reduces the impedance of the feedback branch and therefore reduces the gain.
Inverting low-pass filter: Components: Rin = 10 kOhm Rf = 100 kOhm Cf = 1 nF Low-frequency gain: Av = -Rf / Rin Av = -100 kOhm / 10 kOhm Av = -10 Cutoff frequency: fc = 1 / (2 * pi * Rf * Cf) fc = 1 / (2 * pi * 100000 * 1e-9) fc = approximately 1.59 kHz Applications: - bandwidth limitation; - high-frequency noise reduction; - audio filters; - conditioning of slow signals.
Main Parameters to Check in a Datasheet
When choosing an operational amplifier for an inverting configuration, it is not enough to look only at the theoretical gain. The real circuit depends on many electrical parameters. The most important ones are listed below.
Supply voltage – Check the minimum and maximum supply voltage. Some op amps work well at 5 V, while others require higher voltages. The TL072 and RC4558 are generally better suited to dual supplies or relatively high single-supply voltages compared to many modern low-voltage op amps.
Input common-mode voltage range – This is the voltage range allowed at the inputs. In an inverting configuration, it is especially important when working with single-supply operation and virtual references. If the input nodes leave the common-mode range, the output may saturate, distort, or behave non-linearly.
Output voltage swing – This indicates how close the output can get to the supply rails. A non-rail-to-rail op amp powered at ±15 V may, for example, only reach approximately ±12 V or ±13 V depending on the load. With low supply voltages, this limitation becomes very important.
Gain-bandwidth product – The gain-bandwidth product determines the available bandwidth at a given gain. As a rough approximation:
Usable bandwidth ≈ GBW / Av Example: GBW = 3 MHz Av = 10 Theoretical bandwidth ≈ 3 MHz / 10 = 300 kHz Note: theoretical bandwidth does not automatically guarantee low distortion or adequate phase margin.
Slew rate – Slew rate indicates how quickly the output voltage can change. It is essential for high-amplitude audio signals, pulse waveforms, active filters, and high-frequency signals.
Formula for a sine wave: SR_min = 2 × π × f × Vp If the required slew rate exceeds the available slew rate, the output cannot follow the signal and slew-rate distortion occurs.
Input offset voltage – This is a small equivalent differential voltage between the inputs. In an inverting amplifier, it is amplified by the noise gain of the circuit, so it is important in DC applications and precision sensor circuits.
Input bias current – This is the current required by the inputs. In a JFET op amp such as the TL072 it is very low; in a bipolar op amp such as the RC4558 it is higher. Bias currents flowing through external resistors generate voltage errors.
Voltage noise and current noise – In audio, measurement, and sensor applications, noise is a critical parameter. Total noise depends on the op amp, the resistors, the circuit bandwidth, and the source impedance.
CMRR and PSRR – CMRR indicates the ability to reject signals common to both inputs; PSRR indicates how much power-supply variations affect the output. Higher values are preferable, especially in noisy environments or with imperfectly regulated supplies.
Output current and load drive capability – Check the maximum output current and the recommended minimum load. An op amp is not always able to directly drive headphones, speakers, long cables, or capacitive loads without an additional buffer.
Unity-gain stability – If the op amp is to be used as a buffer or in low-gain configurations, the datasheet must indicate unity-gain stability or equivalent operating conditions. Otherwise, the circuit may oscillate.
Package, pinout, and power dissipation – The TL072 and RC4558 are often available as dual op amps in 8-pin packages, but the exact pinout, variant, operating temperature, power dissipation, and component availability must always be checked.
In conclusion, the inverting configuration is one of the most versatile tools in analog design with operational amplifiers. Its strength lies in its simplicity: the gain depends on the ratio between two resistors, the inverting node allows currents to be summed, and the structure can be modified to obtain filters, summing amplifiers, integrators, differentiators, and current-to-voltage converters.
Compared to the non-inverting configuration, it offers great flexibility but requires greater attention to input impedance and phase inversion. With op amps such as the TL072 and RC4558, many audio and signal-conditioning circuits can be implemented, provided that supply voltage, bandwidth, slew rate, offset, bias current, and output swing limits are respected.
During the design phase, the formula Av = -Rf/Rin is only the starting point. The real behavior depends on the datasheet, layout, load, source, type of power supply, and required bandwidth. For this reason, every design should be verified with preliminary calculations, simulation when necessary, and practical measurements on the real circuit.
