Building an Inverting Amplifier with Operational Amplifiers

An inverting amplifier is an op-amp circuit that amplifies an input signal and inverts its polarity — a positive input produces a negative output and vice versa. Built with just two resistors and an op-amp, it produces a closed-loop gain of −R_f / R_in, where R_f is the feedback resistor and R_in is the input resistor. The inverting amplifier is one of the most widely used analog circuits, appearing in audio equipment, sensor interfaces, signal processing systems, and instrumentation.

Introduction: The Workhorse of Analog Design

If you were to survey the analog circuits in a typical piece of electronic equipment — a mixing console, a medical instrument, a radio receiver, an industrial sensor interface — you would find one circuit configuration appearing more frequently than almost any other: the inverting amplifier.

Its dominance is well-earned. The inverting amplifier is simple to design, easy to analyze, predictable in behavior, and remarkably versatile. With just two resistors and an op-amp, you can set any gain from less than one (attenuation) to thousands, with accuracy limited only by the precision of your resistors. The virtual ground at the inverting input provides a stable, low-impedance summing point that enables multi-channel mixing, current-to-voltage conversion, and mathematical signal operations. And the circuit’s behavior is so well-defined by the external components that you can swap one op-amp for another without recalculating anything, as long as the replacement meets the basic gain-bandwidth and offset requirements.

This article is a complete, practical guide to designing and building inverting amplifier circuits. We begin with the circuit’s operating principle and gain formula — familiar from the ideal op-amp analysis — but quickly move into the practical details that determine whether a real circuit works correctly: how to choose resistor values, how bandwidth limits affect high-gain designs, how to minimize DC offset errors, how to handle single-supply operation, how to compensate for input bias current, and how to lay out the circuit on a breadboard or PCB for stable, low-noise performance.

By the end, you’ll have worked through multiple complete design examples spanning audio preamplification, sensor signal conditioning, and current measurement, with component choices justified by real specifications rather than assumed away by the ideal model.

Circuit Topology: Understanding the Inverting Configuration

The inverting amplifier circuit consists of three elements:

• The op-amp itself
• R_in — the input resistor, connecting the signal source to the inverting input (V−)
• R_f — the feedback resistor, connecting the output back to the inverting input (V−)

The non-inverting input (V+) connects to ground (for dual-supply circuits) or to a mid-supply reference voltage (for single-supply circuits).

Why the Inverting Input?

Both inputs of the op-amp can receive signals, but the inverting amplifier specifically applies the input signal to the V− (inverting) input through R_in, while feeding the output back to the same V− input through R_f.

This creates negative feedback: if the output increases, the fed-back voltage at V− increases, which acts to reduce the output. The system stabilizes with V− equal to V+ (virtual short), and the gain is determined by the R_f / R_in ratio.

If you accidentally connect the feedback to V+ instead of V−, you create positive feedback — the circuit latches to one supply rail and stays there. This is a common wiring mistake on breadboards. Always verify: R_f connects from output to V−.

The Virtual Ground: Key to Understanding the Circuit

When V+ is connected to ground (0V), the virtual short condition (V− = V+) means V− = 0V as well. This is called a virtual ground — the inverting input is held at 0V by the feedback mechanism, even though it is not physically connected to ground.

The virtual ground is not a real ground — it cannot sink or source current from external connections. It is purely a consequence of the op-amp’s feedback action. But for circuit analysis purposes, it behaves like a ground: any resistor connected to the V− node sees a 0V reference at that node.

This virtual ground has important practical consequences:

The input impedance of the inverting amplifier is R_in — not the op-amp’s actual input impedance. Because V− is held at virtual ground by feedback, the source “sees” R_in connected from the signal node to (virtual) ground. The signal drives current through R_in; that current flows through R_f to the output. The op-amp’s own input impedance (megohms to teraohms) doesn’t matter — it’s masked by the virtual ground behavior.

Multiple inputs don’t interact — because each input resistor connects to the same virtual ground node, changing one input voltage doesn’t affect the voltage at that node (it stays at 0V). Multiple inputs can be summed without loading each other, which is the principle behind the summing amplifier / audio mixer.

The Gain Formula: Derivation and Implications

Deriving the Gain

Using the two golden rules of the ideal op-amp model:

Rule 1: No current into the inverting input — all current from R_in flows through R_f.

Rule 2: V− = V+ = 0V (virtual ground, since V+ is grounded).

Current through R_in (from signal source to virtual ground):

I = (V_in − 0) / R_in = V_in / R_in

I = (V_in − 0) / R_in = V_in / R_in

This same current must flow through R_f (from virtual ground to output, since no current goes into the op-amp):

I = (0 − V_out) / R_f = −V_out / R_f

I = (0 − V_out) / R_f = −V_out / R_f

Setting the two expressions equal:

V_in / R_in = −V_out / R_f
V_out = −(R_f / R_in) × V_in

V_in / R_in = −V_out / R_f
V_out = −(R_f / R_in) × V_in

Closed-loop gain:

G = V_out / V_in = −R_f / R_in

G = V_out / V_in = −R_f / R_in

Key Implications of the Formula

The gain magnitude is set by the resistor ratio. Doubling R_f doubles the gain. Halving R_in also doubles the gain. What matters is the ratio, not the absolute values — though absolute values affect input impedance, bandwidth, and noise performance.

The negative sign indicates phase inversion. A positive input voltage produces a negative output voltage. For a sinusoidal input, the output is 180° out of phase. Whether this matters depends on the application:

• In audio: Phase inversion in a single channel is generally inaudible and irrelevant
• In a cascaded amplifier chain: Two inverting stages cancel each other’s inversions (−1 × −1 = +1)
• In feedback control systems: Phase matters critically — an extra inversion can turn negative feedback into positive feedback

Gain can be less than 1 (attenuation). Setting R_f < R_in gives |G| < 1. For example, R_in = 100kΩ and R_f = 10kΩ gives G = −0.1 — the circuit attenuates the signal by 10× while inverting it. This is useful for reducing signal levels before an ADC input or between stages.

Gain of −1 (inverter/buffer): Setting R_f = R_in gives G = −1. The circuit inverts the signal with unity gain — useful for phase correction in audio chains or creating complementary signals for differential driving.

Component Selection: Resistor Values

Choosing the right resistor values is not just about setting the gain ratio. The absolute values of R_in and R_f affect input impedance, bandwidth, DC offset errors, and noise performance. There is an optimal range for most applications.

The Practical Resistor Range: 1kΩ to 1MΩ

Lower limit (~1kΩ): Very low resistor values demand high output current from the op-amp. With R_f = 1kΩ and V_out = 10V, the feedback current is 10mA — a significant fraction of a typical op-amp’s 25mA output current limit. Low resistors also increase power consumption and place thermal demands on the op-amp. Additionally, very low R_in values may overload the signal source.

Upper limit (~1MΩ): Very high resistor values amplify noise. Johnson thermal noise voltage across a resistor is:

V_noise = √(4kTRΔf)

V_noise = √(4kTRΔf)

Where k = 1.38×10⁻²³ J/K (Boltzmann’s constant), T is temperature in Kelvin, R is resistance in ohms, and Δf is the bandwidth in Hz.

For R = 1MΩ at room temperature (300K) over 20kHz audio bandwidth:

V_noise = √(4 × 1.38×10⁻²³ × 300 × 10⁶ × 20,000)
         = √(3.31×10⁻¹³) = 18.2µV RMS

V_noise = √(4 × 1.38×10⁻²³ × 300 × 10⁶ × 20,000)
         = √(3.31×10⁻¹³) = 18.2µV RMS

For R = 10kΩ:

V_noise = √(4 × 1.38×10⁻²³ × 300 × 10,000 × 20,000) = 1.82µV RMS

V_noise = √(4 × 1.38×10⁻²³ × 300 × 10,000 × 20,000) = 1.82µV RMS

High resistance means high noise. For low-noise applications (audio, precision measurement), keep resistors below 100kΩ. For general non-critical applications, up to 1MΩ is acceptable.

Also: High R_f values interact with the op-amp’s input capacitance and stray PCB capacitance to create a low-pass filter in the feedback path, which can cause frequency response errors or even instability at high frequencies. A large R_f combined with even a few picofarads of stray capacitance forms an RC pole that rolls off the feedback at a lower frequency than expected.

Recommended Starting Values

Bias Current Compensation Resistor

For BJT-input op-amps (741, LM741, NE5532), input bias current flowing through R_f creates a DC offset at the output. The standard compensation technique is to add a resistor R_comp to the non-inverting input:

R_comp = R_in ∥ R_f = (R_in × R_f) / (R_in + R_f)

R_comp = R_in ∥ R_f = (R_in × R_f) / (R_in + R_f)

This makes both inputs see the same DC resistance, so the bias currents produce equal voltage drops that appear as a common-mode signal and are rejected by the differential input stage.

Example: R_in = 10kΩ, R_f = 100kΩ:

R_comp = (10,000 × 100,000) / (10,000 + 100,000) = 9,091Ω → use 9.1kΩ or 10kΩ

R_comp = (10,000 × 100,000) / (10,000 + 100,000) = 9,091Ω → use 9.1kΩ or 10kΩ

For JFET-input op-amps (TL071, TL081) with picoamp bias currents, this compensation resistor makes negligible difference and is often omitted.

Bandwidth Considerations

The gain-bandwidth product (GBW) of the op-amp limits the frequency range over which the inverting amplifier achieves its specified gain.

The Gain-Bandwidth Relationship

For a compensated op-amp, the closed-loop −3dB bandwidth is approximately:

f_−3dB ≈ GBW / |G_CL|

f_−3dB ≈ GBW / |G_CL|

Where G_CL is the closed-loop gain magnitude. Higher gain means lower bandwidth.

Example calculations (assuming TL071 with GBW = 3MHz):

For an audio amplifier (20Hz–20kHz) with gain 100, the TL071 provides 30kHz bandwidth — 1.5× the audio range. This is marginal; gain will be slightly below 100 at 20kHz. A safer choice is an op-amp with GBW ≥ 10× (desired gain × maximum frequency):

GBW_required ≥ 10 × 100 × 20,000 = 20MHz

GBW_required ≥ 10 × 100 × 20,000 = 20MHz

The NE5532 (GBW = 10MHz) or LM4562 (GBW = 55MHz) would be better choices for this application.

Non-Inverting Input Bandwidth Note

The bandwidth formula above is a simplification. The exact closed-loop bandwidth also depends on the noise gain — the gain the op-amp “sees” from its own input noise to the output. For the inverting amplifier:

Noise gain = 1 + R_f / R_in = 1 + |G_CL|

Noise gain = 1 + R_f / R_in = 1 + |G_CL|

For large gains (|G_CL| >> 1), noise gain ≈ |G_CL|, and the bandwidth formula above is accurate. For low gains (|G_CL| near 1), noise gain = 2 at gain 1, so the bandwidth is GBW/2, not GBW/1.

This is why the inverting amplifier at gain −1 has bandwidth = GBW/2, while a voltage follower (non-inverting gain of +1) has bandwidth = GBW — the noise gain of the voltage follower is 1 (no feedback resistors), while the inverting unity-gain circuit has noise gain 2.

DC Offset Analysis and Minimization

Even with the ideal resistors, a real inverting amplifier has a DC output offset caused by the op-amp’s non-ideal properties. Understanding and minimizing this offset is essential for DC-coupled precision applications.

Sources of Output Offset Voltage

1. Input offset voltage (V_OS):

The op-amp’s internal offset voltage appears as an equivalent input error, amplified by the noise gain:

V_out_offset (from V_OS) = V_OS × (1 + R_f / R_in)

V_out_offset (from V_OS) = V_OS × (1 + R_f / R_in)

For a 741 (V_OS = 2mV typical) at gain 100 (R_in = 1kΩ, R_f = 100kΩ):

V_out_offset = 2mV × (1 + 100) = 202mV

V_out_offset = 2mV × (1 + 100) = 202mV

2. Input bias current through R_f:

Even with the compensation resistor R_comp on the non-inverting input, residual offset arises from the difference in bias currents between the two inputs (the input offset current I_OS):

V_out_offset (from I_OS) = I_OS × R_f

V_out_offset (from I_OS) = I_OS × R_f

For a 741 (I_OS = 20nA typical) with R_f = 100kΩ:

V_out_offset = 20nA × 100,000 = 2mV (referred to output)

V_out_offset = 20nA × 100,000 = 2mV (referred to output)

3. Combined output offset:

The total DC output offset is approximately:

V_out_total ≈ V_OS × (1 + R_f/R_in) + I_OS × R_f

V_out_total ≈ V_OS × (1 + R_f/R_in) + I_OS × R_f

For the gain-100 example with 741:

V_out_total ≈ 202mV + 2mV = ~204mV

V_out_total ≈ 202mV + 2mV = ~204mV

This is far too large for precision work. Solutions:

Solution 1: Use a precision op-amp. OP07 has V_OS_max = 75µV and I_OS_max = 3.5nA:

V_out_total ≈ 75µV × 101 + 3.5nA × 100kΩ = 7.6mV + 0.35mV ≈ 8mV

V_out_total ≈ 75µV × 101 + 3.5nA × 100kΩ = 7.6mV + 0.35mV ≈ 8mV

Much better — 25× improvement.

Solution 2: Use offset null adjustment. Most op-amps have null pins (pins 1 and 5 on the 741). A 10kΩ potentiometer between these pins with the wiper to V− allows trimming V_out to exactly 0V. This compensates V_OS at a specific temperature but doesn’t eliminate drift.

Solution 3: AC coupling. If DC accuracy is unimportant (audio, high-frequency signals), place a coupling capacitor in series with R_in. The capacitor blocks DC, so offset doesn’t accumulate through amplification stages.

Single-Supply Operation

Many modern systems operate from a single positive supply (5V, 3.3V) rather than dual ±15V supplies. Operating an inverting amplifier from a single supply requires modifications to handle the shifted operating point.

The Problem with Single Supply

With a single supply (e.g., 0V to 5V), the “ground” reference is at 0V — the negative rail. A traditional inverting amplifier with V+ connected to ground cannot produce negative output voltages. If the input signal is an AC signal centered on 0V, the output would swing both positive and negative — but the negative excursion would hit the supply rail (0V) and clip.

The Solution: Virtual Mid-Supply Reference

Create a mid-supply reference voltage (V_ref = VCC/2) and connect V+ to this reference instead of to ground:

V_ref = VCC / 2 = 2.5V (for 5V supply)

V_ref = VCC / 2 = 2.5V (for 5V supply)

Create V_ref with a voltage divider: two equal resistors (10kΩ each) from VCC to GND, with a bypass capacitor (10µF) from V_ref to GND to reduce AC impedance at the reference node.

Now the virtual ground at V− is at 2.5V (not 0V), and the output swings around 2.5V instead of 0V. The signal can swing from nearly 0V to nearly 5V (for a traditional op-amp) or from 0V to 5V (for a rail-to-rail output op-amp).

The modified gain formula:

With V+ = V_ref (not 0V):

V_out = V_ref − (R_f / R_in) × (V_in − V_ref)

V_out = V_ref − (R_f / R_in) × (V_in − V_ref)

For V_in centered on V_ref (which it should be in a properly designed single-supply circuit):

V_out_AC = −(R_f / R_in) × V_in_AC

V_out_AC = −(R_f / R_in) × V_in_AC

The AC gain formula is unchanged. The only difference is that all voltages are offset by V_ref.

Op-Amp Selection for Single Supply

Not all op-amps work well from a single supply. Key requirements:

Input common-mode range: Must include the mid-supply voltage V_ref. Standard op-amps (741, TL071) require inputs to stay 1–2V away from each supply rail — for a 5V supply, inputs must stay between ~1V and ~4V. A mid-supply input of 2.5V satisfies this. Rail-to-rail input op-amps allow inputs all the way to the supply rails.

Output swing: Standard op-amps can only swing their output to within ~1–2V of each supply rail. From a 5V supply, the output might only reach 1V to 4V — a 3V range. Rail-to-rail output op-amps (MCP6002, LMV321) can swing to within millivolts of both rails, providing the full 5V range.

Supply voltage: The op-amp must operate at the single supply voltage. The LM358 works from 3V to 32V. The MCP6002 works from 1.8V to 5.5V. The TL071 requires at least ±5V (10V total) — unsuitable for single 5V supply.

Complete Design Examples

Design Example 1: Audio Preamplifier (Gain = −20, Dual Supply)

Application: Amplify a microphone or instrument signal from ~50mV peak to ~1V peak for driving an ADC or further processing. Dual ±12V supply available. No phase inversion concern (audio).

Specifications:

• Gain: −20 (26dB)
• Frequency range: 20Hz – 20kHz
• Low noise
• DC-coupled (or use input coupling capacitor for AC signals)

Op-amp selection: NE5532 — low noise (5nV/√Hz), GBW = 10MHz, suitable for ±12V supply, good audio performance.

Bandwidth verification:

f_−3dB = GBW / |G_CL| = 10MHz / 20 = 500kHz >> 20kHz ✓

f_−3dB = GBW / |G_CL| = 10MHz / 20 = 500kHz >> 20kHz ✓

Resistor selection: Choose R_in = 10kΩ (good input impedance, reasonable noise). R_f = 20 × R_in = 20 × 10kΩ = 200kΩ.

Prefer keeping R_f ≤ 100kΩ for noise. So instead: R_in = 5.1kΩ (standard E24 value), R_f = 100kΩ. Actual gain = 100k / 5.1k = 19.6 ≈ 20 ✓ (−0.2% error from target)

Bias compensation:

R_comp = R_in ∥ R_f = (5100 × 100,000) / (5100 + 100,000) = 4,851Ω → use 4.7kΩ

R_comp = R_in ∥ R_f = (5100 × 100,000) / (5100 + 100,000) = 4,851Ω → use 4.7kΩ

Input coupling: Place 1µF film capacitor in series with R_in to block DC from the signal source. The capacitor and R_in form a high-pass filter:

f_high_pass = 1 / (2π × R_in × C) = 1 / (2π × 5100 × 1×10⁻⁶) = 31.2Hz

f_high_pass = 1 / (2π × R_in × C) = 1 / (2π × 5100 × 1×10⁻⁶) = 31.2Hz

Slightly above 20Hz — acceptable for audio. Use 2.2µF for f = 14Hz, below the audio band.

Full component list:

• NE5532 op-amp (DIP-8)
• R_in = 5.1kΩ, 1% metal film
• R_f = 100kΩ, 1% metal film
• R_comp = 4.7kΩ, 1% metal film (to V+ input, other end to GND)
• C_in = 2.2µF film capacitor (series with R_in for AC coupling)
• C_bypass = 100nF ceramic × 2 (one per supply pin to GND, as close to IC as possible)
• C_bulk = 10µF electrolytic × 2 (one per supply rail to GND, nearby)
• ±12V regulated dual supply

Circuit connections (pin numbering for NE5532 in 8-pin DIP):

• Pin 1 (output 1) → R_f → also to pin 2
• Pin 2 (inverting input 1) → R_f and R_in junction
• Pin 3 (non-inverting input 1) → R_comp → GND
• Pin 4 (V−) → −12V supply
• Pin 8 (V+) → +12V supply
• C_in in series: Signal source → C_in → R_in → pin 2
• Output taken from pin 1

Design Example 2: Gain-100 Sensor Amplifier with Offset Correction (Dual Supply)

Application: Amplify a bridge sensor output of ±5mV full scale to ±500mV for ADC input. Precision required: output error < 5mV. Dual ±5V supply.

Specifications:

• Gain: −100 (40dB)
• Full-scale input: ±5mV → Full-scale output: ±500mV
• Output offset error: < 5mV (referred to output) = < 50µV (referred to input)
• Frequency range: DC to 1kHz

Op-amp selection: OP07CP — V_OS_max = 75µV, I_B_max = 4nA, GBW = 0.6MHz.

Bandwidth verification:

f_−3dB = 0.6MHz / 100 = 6kHz >> 1kHz ✓

f_−3dB = 0.6MHz / 100 = 6kHz >> 1kHz ✓

Offset verification (worst case):

V_out_error = V_OS × (1 + R_f/R_in) + I_OS × R_f

V_out_error = V_OS × (1 + R_f/R_in) + I_OS × R_f

Choose R_in = 1kΩ, R_f = 100kΩ:

V_out_error = 75µV × 101 + (4nA − 2nA) × 100kΩ
            = 7.575mV + 0.2mV = 7.8mV

V_out_error = 75µV × 101 + (4nA − 2nA) × 100kΩ
            = 7.575mV + 0.2mV = 7.8mV

This exceeds the 5mV spec. Options:

1. Use the OP07’s offset null pins to trim V_OS to near zero
2. Choose a lower-offset op-amp (AD8628: V_OS = 5µV max → V_out_error = 0.5mV + negligible I_OS term = 0.55mV ✓)

Going with AD8628 (auto-zero, V_OS = 5µV max, I_B = 200pA):

R_comp = 1kΩ ∥ 100kΩ ≈ 990Ω → use 1kΩ

R_comp = 1kΩ ∥ 100kΩ ≈ 990Ω → use 1kΩ

Offset error:

V_out_error = 5µV × 101 + ~0 (I_OS negligible) = 0.505mV ✓

V_out_error = 5µV × 101 + ~0 (I_OS negligible) = 0.505mV ✓

Well within 5mV spec.

Full component list:

• AD8628 (or AD8628ARZ for SMD)
• R_in = 1kΩ, 0.1% metal foil resistor (for gain accuracy)
• R_f = 100kΩ, 0.1% metal foil resistor
• R_comp = 1kΩ, 0.1% (to V+, other end to GND)
• C_bypass = 100nF ceramic on each supply pin
• C_bulk = 10µF on each supply rail

Design Example 3: Current-to-Voltage Converter (Transimpedance Amplifier)

A special case of the inverting amplifier where R_in = 0 (effectively) — the input is a current source directly into the virtual ground node.

Application: Convert photodiode current (0 to 10µA) to a voltage (0 to 1V) for ADC reading.

The transimpedance amplifier (TIA):

Connect the photodiode directly between the op-amp’s inverting input and ground (or reverse-biased). The photodiode current I_in flows directly into the virtual ground node. Since no current flows into the op-amp input (Golden Rule 1), all of I_in flows through R_f:

V_out = −I_in × R_f

V_out = −I_in × R_f

The “gain” is in V/A (transimpedance), not V/V.

For 10µA full scale → 1V output:

R_f = V_out / I_in = 1V / 10µA = 100kΩ

R_f = V_out / I_in = 1V / 10µA = 100kΩ

Op-amp selection: JFET input essential (TL071, OPA128) — photodiode current is tiny (microamps), and BJT bias current (nanoamps) would introduce significant error. TL071: I_B = 30pA → output error = 30pA × 100kΩ = 3µV. Negligible.

Stability consideration: Photodiodes have parasitic capacitance (C_D, typically 5–50pF). This capacitance at the virtual ground node, combined with R_f, creates a pole in the feedback loop that can cause oscillation. Solution: add a small capacitor C_f (1–10pF) in parallel with R_f to add a compensating zero:

C_f = √(C_D / (2π × GBW × R_f))

C_f = √(C_D / (2π × GBW × R_f))

For C_D = 20pF, GBW = 3MHz (TL071), R_f = 100kΩ:

C_f = √(20×10⁻¹² / (2π × 3×10⁶ × 100×10³)) = √(10.6×10⁻¹⁸) ≈ 3.3pF → use 3.3pF

C_f = √(20×10⁻¹² / (2π × 3×10⁶ × 100×10³)) = √(10.6×10⁻¹⁸) ≈ 3.3pF → use 3.3pF

This small capacitor across R_f stabilizes the transimpedance amplifier and slightly reduces high-frequency bandwidth (which is acceptable here).

Design Example 4: Single-Supply Inverting Amplifier (3.3V System)

Application: Invert and amplify an AC audio signal centered on 1.65V (VCC/2) in a 3.3V microcontroller system. Gain = −5.

Op-amp selection: MCP6002 — operates from 1.8V to 5.5V, rail-to-rail input and output, GBW = 1MHz, suitable for 3.3V single supply.

Mid-supply reference: Two 10kΩ resistors from 3.3V to GND, junction = 1.65V. Add 10µF capacitor from reference to GND (reduces AC impedance of reference).

Resistor selection: R_in = 10kΩ, R_f = 50kΩ (use 47kΩ for G = −4.7, or 51kΩ for G = −5.1). Use 47kΩ + 3.3kΩ in series = 50.3kΩ for closer to G = −5.

Bandwidth:

f_−3dB = 1MHz / 5 = 200kHz >> audio range ✓

f_−3dB = 1MHz / 5 = 200kHz >> audio range ✓

Input coupling: Series capacitor with R_in to center the signal on V_ref: C_in = 10µF (for low-frequency cutoff well below audio range):

f_high_pass = 1 / (2π × 10kΩ × 10µF) = 1.6Hz ✓

f_high_pass = 1 / (2π × 10kΩ × 10µF) = 1.6Hz ✓

Output swing: With MCP6002 (rail-to-rail output on 3.3V supply), output swings 0V to 3.3V. Peak output around 1.65V ± (5 × input_peak). For input_peak = 200mV: output swings 1.65V ± 1V = 0.65V to 2.65V. Within rail-to-rail range ✓.

Practical Circuit Layout and Construction Tips

Breadboard Construction

When building inverting amplifiers on a breadboard:

Keep connections short. Long wires act as antennas, picking up 50/60Hz hum and high-frequency interference. Route signal wires as short and direct as possible.

Place decoupling capacitors right at the power pins. The 100nF ceramic capacitors must be as close to the op-amp’s power pins as physically possible — within a centimeter ideally. On a breadboard, use small 100nF ceramics with leads bent to go directly from the VCC row to GND row adjacent to the IC.

Avoid running input and output wires parallel. Parallel wiring creates capacitive coupling between input and output — a feedback path that can cause oscillation, especially at high gains. Route the output wire away from the input side.

Secure the op-amp in a socket if available. DIY sockets prevent accidental op-amp damage and allow easy replacement for experimentation.

Verify orientation before power-up. The op-amp notch or dot marks pin 1. Double-check the datasheet pinout. An inverted op-amp usually gets very hot within seconds — immediately cut power if this happens.

PCB Layout Considerations

For permanent circuits on a PCB:

Ground plane. A continuous copper ground plane on one layer (or one side of a two-layer board) dramatically reduces noise pickup and provides a low-impedance return path. Connect all ground connections to the plane with short vias.

Decoupling capacitor placement. 100nF ceramic decoupling capacitors must be adjacent to the power pins, connected directly to the ground plane with minimal trace length. Star-routing from a central ground point defeats the purpose.

Feedback resistor proximity. R_f should be close to the op-amp to minimize stray capacitance in the feedback path. Stray capacitance in parallel with R_f forms a pole that rolls off feedback at high frequencies.

Input protection. For circuits exposed to potentially overvoltage inputs (signal sources with unknown origins, long cable runs), add input protection: a series resistor (1kΩ–10kΩ) before R_in, and clamping diodes from the op-amp input to the supply rails. The series resistor limits current if the input exceeds the supply rails; the diodes clamp the voltage to safe levels.

Troubleshooting Inverting Amplifier Circuits

Problem: Output is stuck at one supply rail (saturated)

Most likely causes:

• No feedback path. Check R_f is present and connected correctly from output to V−.
• Feedback connected to wrong pin. Verify R_f goes to V− (inverting input), not V+ (non-inverting).
• V+ (non-inverting input) is floating. It must be connected — to GND for dual supply, to V_ref for single supply.
• Input signal is beyond the op-amp’s common-mode range, causing input stage malfunction.

Problem: Large DC offset at output with no input signal

• Expected for high-gain circuits with standard op-amps (V_OS × gain). Quantify and decide if it matters for your application.
• Add bias compensation resistor R_comp to the non-inverting input.
• Use a precision op-amp (OP07, AD8628) for lower V_OS.
• AC couple the input with a series capacitor if DC accuracy isn’t needed.

Problem: Output oscillates (circuit is unstable)

• R_f too large (above ~1MΩ) combined with stray capacitance creating a feedback pole — reduce R_f.
• Missing or inadequate power supply decoupling — add/move 100nF ceramics to within 5mm of power pins.
• Add a small capacitor (10–47pF) directly across R_f to reduce high-frequency loop gain.
• For transimpedance amplifiers: add C_f in parallel with R_f as calculated above.
• Long breadboard wires picking up interference and creating feedback paths — shorten all wiring.

Problem: Gain is lower than calculated

• Signal frequency too high for the op-amp’s GBW. Verify f_signal << GBW / |G_CL|.
• R_f or R_in values differ from intended — measure with multimeter.
• Output is clipping (signal amplitude too large for the supply voltage and gain combination) — reduce input amplitude or reduce gain.

Problem: Output is correct for one polarity but clips on the other

• Classic single-supply issue: virtual ground is not at exactly mid-supply. Check V_ref divider resistor values and bypass capacitor.
• Op-amp output is not rail-to-rail and cannot swing close enough to one rail. Use rail-to-rail output op-amp.

Summary

The inverting amplifier is one of the most fundamental and useful op-amp circuits. Its operation rests on the virtual ground at the inverting input — maintained by negative feedback — which forces all input current through the feedback resistor R_f to the output. The resulting gain, G = −R_f / R_in, is set with precision by the resistor ratio and is independent of the op-amp’s actual gain, as long as open-loop gain >> closed-loop gain.

Practical design requires attention beyond the gain formula. Resistor values in the 1kΩ–100kΩ range balance input impedance, noise, bandwidth, and current demands. Bias current compensation with R_comp = R_in ∥ R_f reduces DC offset in BJT-input circuits. Bandwidth must be verified against the op-amp’s gain-bandwidth product. Single-supply operation requires a mid-supply reference at V+ and AC coupling at the input. DC precision requires selecting a low-offset op-amp matched to the gain and accuracy requirements.

The four design examples — audio preamplifier (NE5532), precision sensor amplifier (AD8628), photodiode transimpedance amplifier (TL071), and single-supply microcontroller interface (MCP6002) — demonstrate how the same circuit topology adapts to radically different applications through appropriate component selection and configuration.