Inverting Amplifier Circuit Diagram: Av = -Rf/Rin, Virtual Ground & Op-Amp Design
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An inverting amplifier is an op-amp circuit where the input signal is applied to the inverting (−) terminal through a resistor Rin, the non-inverting (+) terminal is grounded, and feedback is provided by resistor Rf from output to the inverting input. The voltage gain is Av = −Rf/Rin — negative because the output is 180° out of phase with the input. This is one of the two fundamental op-amp amplifier configurations and is widely used in signal processing, audio, and instrumentation.
The inverting amplifier exploits the ideal op-amp's two key properties: virtually infinite open-loop gain and virtually infinite input impedance. These properties create the 'virtual ground' at the inverting input — a concept central to all inverting op-amp circuits.
**Virtual Ground Concept**
Because the non-inverting input (+) is tied to ground (0V) and the op-amp has enormous open-loop gain, the feedback forces the inverting input (−) to remain at approximately 0V as well. This virtual ground does not mean the inverting pin is connected to ground — it means the op-amp's output adjusts to keep the differential input voltage near zero. This is the foundation of inverting amplifier analysis.
**Deriving the Gain Formula**
With the inverting input at virtual ground (0V): - Current through Rin: I = Vin / Rin (since V− ≈ 0V) - Because the op-amp input draws no current (infinite impedance), all of I flows through Rf - Voltage at output: Vout = −I × Rf = −(Vin / Rin) × Rf - Gain: Av = Vout / Vin = −Rf / Rin
The negative sign indicates phase inversion: a positive input gives a negative output.
**Input Impedance**
The input impedance of an inverting amplifier is Zin = Rin (not the op-amp's intrinsic impedance). This is because the virtual ground at V− means the input 'sees' only Rin to a virtual 0V node. Keep Rin large enough (typically ≥ 1 kΩ) to avoid loading the source.
**Output Impedance**
With negative feedback, the output impedance is very low — ideally 0Ω, practically a few ohms. The op-amp can typically source or sink 5–25 mA depending on the device.
**Bandwidth Consideration: Gain-Bandwidth Product**
Real op-amps have a Gain-Bandwidth Product (GBW) specification. The bandwidth of an inverting amplifier is:
BW = GBW / |Av| = GBW × Rin / Rf
For an LM741 (GBW ≈ 1 MHz) with Av = −10: BW = 1 MHz / 10 = 100 kHz. For a TL071 (GBW ≈ 3 MHz) with Av = −10: BW = 300 kHz.
For audio applications requiring 20 kHz bandwidth at gain of 10, a GBW of ≥ 200 kHz is needed.
**Common Op-Amps for Inverting Amplifiers**
- LM741: Classic general-purpose bipolar op-amp, GBW 1 MHz, requires ±15V supply - LM358: Dual op-amp, single or dual supply, GBW 1 MHz - TL071/TL081: JFET input, very low input bias current, GBW 3 MHz - NE5534: Low-noise audio op-amp, GBW 10 MHz - LM324: Quad op-amp, single supply operation
**Gain Setting Resistor Values**
Practical resistor values should be in the range 1 kΩ to 1 MΩ. Too small (< 1 kΩ) can overload the source or the op-amp output. Too large (> 1 MΩ) makes the circuit susceptible to bias current errors and parasitic capacitance effects.
For a unity-gain inverting amplifier (Av = −1): Rin = Rf (equal resistors). To minimise offset due to bias current, add a compensation resistor R_comp = Rin || Rf at the non-inverting (+) input to ground.
**Summing Amplifier Extension**
The inverting amplifier extends naturally to a summing amplifier: multiple input resistors (R1, R2, R3...) connect to the same virtual-ground inverting node. Output = −Rf × (V1/R1 + V2/R2 + V3/R3...). This is used in audio mixers and D/A converters.
Build and simulate your inverting amplifier circuit diagram in the free circuitdiagrammaker.com editor. Place an op-amp symbol, connect Rin from input to V−, Rf from V− to output, and tie V+ to ground. Adjust resistor values to set gain and observe the output phase inversion.
How to wire inverting amplifier circuit diagram
- Choose op-amp and supply voltage Select an op-amp based on GBW, supply voltage, and input impedance requirements. LM741 works at ±15V; TL071 offers lower noise and higher GBW at ±15V; LM358 operates from single 3V to 32V supply.
- Calculate resistor values Decide on required gain |Av|. Choose Rin (e.g. 10 kΩ), then compute Rf = |Av| × Rin. For Av = −20 with Rin = 10 kΩ: Rf = 200 kΩ. Use standard E24 or E96 resistor values closest to calculated values.
- Connect op-amp supply pins Connect V+ supply (pin 7 on LM741/TL071) to positive rail (e.g. +15V) and V− supply (pin 4) to negative rail (−15V) or GND for single-supply. Add 100nF decoupling capacitors on each supply pin to ground.
- Wire input resistor Rin Connect one end of Rin to the input signal source. Connect the other end to the inverting input (pin 2 on LM741) of the op-amp.
- Wire feedback resistor Rf Connect Rf between the op-amp output (pin 6) and the inverting input (pin 2). This completes the negative feedback loop.
- Ground the non-inverting input Connect the non-inverting input (pin 3 on LM741) to ground through the compensation resistor R_comp = Rin||Rf. This minimises output offset caused by op-amp input bias currents.
- Verify gain and phase Apply a small AC signal (e.g. 100 mV, 1 kHz sine wave) from a signal generator. Measure output with an oscilloscope. Confirm |Vout| = |Av| × |Vin| and that the waveform is 180° phase-shifted (inverted).
Specifications
| Voltage gain formula | Av = -Rf / Rin |
|---|---|
| Input impedance | Zin = Rin |
| Output impedance (ideal) | ≈ 0 Ω |
| Phase shift | 180° (output inverted) |
| Bandwidth | BW = GBW / |Av| |
| LM741 GBW | 1 MHz |
| TL071 GBW | 3 MHz |
| Virtual ground node | V− ≈ 0V due to feedback |
| Unity gain (Av=-1) | Rin = Rf |
| Gain of -10 example | Rin=10kΩ, Rf=100kΩ |
| Compensation resistor | R_comp = Rin || Rf at V+ to GND |
| Practical resistor range | 1 kΩ to 1 MΩ |
Safety warnings
- Op-amp output pins must never be short-circuited directly to a power rail: most op-amps can sustain short to ground briefly but prolonged shorts destroy the output stage. Always verify no wiring error before powering up.
- When using dual-rail supplies (±15V), confirm the negative supply (V−) is connected to the correct pin — many beginners confuse V− supply with the inverting input (-). Reversing supply connections instantly destroys the IC.
Tools needed
- Op-amp IC: LM741, TL071, LM358, or NE5534 (depending on application)
- Resistors: Rin and Rf (1kΩ to 1MΩ range, 1% metal film recommended for precision gains)
- Compensation resistor R_comp = Rin || Rf
- 100nF ceramic decoupling capacitors (one per supply pin)
- Dual-rail power supply (±15V for LM741/TL071) or single supply for LM358
- Oscilloscope and signal generator for gain and phase verification
Common mistakes
- Connecting Rin to the non-inverting (+) input instead of the inverting (-) input: this creates positive feedback (comparator behaviour), not amplification. Always connect Rin to the inverting (−) pin.
- Connecting Rf from output to non-inverting (+) input: this is positive feedback, causing the op-amp to latch to the supply rail. Rf must connect output to the inverting (−) input only.
- Omitting supply decoupling capacitors: op-amps are sensitive to supply noise. Without 100nF ceramic capacitors on each supply pin, high-frequency oscillations can corrupt the output.
- Choosing resistor values too high (>1MΩ): very high impedances make the circuit susceptible to op-amp input bias current (Ib × Rf creates an offset voltage) and parasitic capacitance reduces high-frequency gain.
Troubleshooting
- Output is saturated at supply rail (stuck HIGH or LOW)
- Cause: Positive feedback (Rf connected to wrong input) or missing feedback resistor Fix: Confirm Rf is connected from output pin to the inverting (-) pin, not to (+). Remove and recheck all connections with the op-amp datasheet pinout.
- Output offset voltage too large at zero input
- Cause: Bias current mismatch between (+) and (-) inputs, or no compensation resistor Fix: Add compensation resistor R_comp = Rin||Rf at the non-inverting input. Also check that source impedance at the (-) input equals R_comp.
- Gain is lower than expected at higher frequencies
- Cause: Op-amp bandwidth limit: gain × frequency exceeds GBW Fix: Calculate required GBW = |Av| × f_max. Switch to a higher-GBW op-amp (e.g. TL071 3MHz, NE5534 10MHz) if the current op-amp cannot meet the requirement.
- Oscillation at high frequency on output
- Cause: Stray capacitance on feedback network causing phase shift, or op-amp unstable at this gain Fix: Add a small capacitor (10–100 pF) in parallel with Rf to roll off gain at high frequencies and stabilise the feedback loop.
Frequently asked questions
What is the gain formula for an inverting amplifier?
Av = -Rf/Rin. The gain magnitude is the ratio of the feedback resistor to the input resistor, and the negative sign indicates 180° phase inversion. For Rf=100kΩ and Rin=10kΩ, Av = -10.
What is virtual ground in an inverting amplifier?
Virtual ground is the condition where the inverting input (V-) of the op-amp is maintained at approximately 0V by the feedback, even though it is not directly connected to ground. This occurs because the op-amp output drives V- to match the grounded V+ terminal.
What is the input impedance of an inverting amplifier?
The input impedance is Rin — the input resistor value. Because V- is at virtual ground, the input signal sees only Rin to a 0V node. This is why Rin should be large enough not to load the source (typically ≥ 1 kΩ).
What op-amp IC is commonly used for an inverting amplifier?
Common choices include the LM741 (classic general-purpose, ±15V, GBW 1MHz), TL071 (JFET input, low noise, GBW 3MHz), LM358 (single-supply dual op-amp), and NE5534 (low-noise audio).
Why does the inverting amplifier invert the output?
The input signal is applied to the inverting (-) terminal. Negative feedback with input at this terminal causes the output to swing opposite in direction to maintain virtual ground. A rising input causes the output to fall.
What is the gain-bandwidth product and how does it affect the inverting amplifier?
GBW is a constant for a given op-amp: GBW = |Av| × Bandwidth. A higher gain means lower bandwidth. For LM741 (GBW=1MHz) at gain 10, bandwidth = 100 kHz. Choose an op-amp with GBW >> |Av| × required bandwidth.
What is the compensation resistor in an inverting amplifier?
R_comp = Rin || Rf placed from the non-inverting input to ground. It balances the impedance seen at both op-amp inputs, minimising output offset voltage caused by the op-amp's input bias current flowing through unequal source resistances.