Operational Amplifier Configurations

Why This Matters

Operational amplifiers are the workhorses of analog circuit design, and understanding their configurations is essential for analyzing and designing real-world systems. You're being tested not just on recognizing circuit topologies, but on understanding why each configuration behaves the way it does: how negative feedback shapes gain, bandwidth, and impedance, and how component placement determines whether a circuit amplifies, integrates, or compares signals.

These configurations demonstrate core principles you'll encounter throughout your circuits coursework: negative feedback, virtual ground, input/output impedance, and signal processing. When you see an op-amp circuit on an exam, your approach should be:

1. Identify the feedback path (negative or positive? resistive or reactive?)
2. Determine the transfer function using ideal op-amp assumptions
3. Predict the output behavior for a given input

Don't just memorize the gain formulas. Understand what makes each configuration unique and when you'd choose one over another.

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Basic Gain Configurations

These foundational circuits use resistive feedback to set predictable voltage gain. The key principle: negative feedback forces the op-amp to adjust its output so that the voltage difference between its two input terminals is driven to zero. This is the virtual short condition, and it's the starting point for analyzing every linear op-amp circuit.

Inverting Amplifier

The input signal connects through $R_{in}$ to the inverting ($-$) terminal, while the non-inverting ($+$) terminal is grounded. The feedback resistor $R_f$ connects from the output back to the inverting terminal.

• Gain: $A_v = -\frac{R_f}{R_{in}}$. The negative sign means a 180° phase inversion between input and output.
• Virtual ground at the inverting input means the voltage at that node sits at approximately 0 V. Because of this, the input impedance seen by the source equals $R_{in}$, which can load high-impedance sources.
• Feedback resistor $R_f$ directly controls gain magnitude. Larger $R_f$ means higher gain.

Non-Inverting Amplifier

The input signal connects directly to the non-inverting ($+$) terminal. $R_{in}$ connects from the inverting terminal to ground, and $R_f$ connects from the output to the inverting terminal.

• Gain: $A_v = 1 + \frac{R_f}{R_{in}}$. The output stays in phase with the input, and gain is always $\geq 1$.
• High input impedance (ideally infinite) because the signal feeds directly into the op-amp's non-inverting input. This prevents loading the source.
• This configuration is ideal when you need gain and you can't afford to draw significant current from the source.

Voltage Follower (Unity Gain Buffer)

A special case of the non-inverting amplifier where $R_f = 0$ and $R_{in} \to \infty$ (the output connects directly to the inverting input with no resistor divider).

• Gain equals exactly 1 ($A_v = 1$). Output voltage tracks input voltage precisely.
• Extremely high input impedance and low output impedance make it perfect for impedance matching between circuit stages.
• 100% negative feedback provides maximum bandwidth and stability. You're trading all gain for the best possible buffering performance.

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Signal Combining Configurations

These circuits process multiple inputs or extract specific signal components. The underlying principle is superposition: each input contributes independently to the output based on its associated resistor network.

Summing Amplifier

This is an extension of the inverting amplifier with multiple input resistors feeding into the same inverting node. Each input has its own resistor ($R_1, R_2, R_3, \ldots$), and they all connect to the virtual ground point.

• Output: $V_{out} = -R_f \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right)$. This is a weighted, inverted sum of all inputs.
• Resistor ratios determine weighting for each input channel. If all input resistors are equal, you get a simple sum. Unequal resistors let you weight certain inputs more heavily, which is how audio mixers adjust channel levels.
• Virtual ground isolates inputs from each other. Changing one input voltage doesn't affect the current flowing from the others.

Differential Amplifier

This single op-amp circuit has one input applied through a resistor to the inverting terminal and another input applied through a resistor to the non-inverting terminal (with a resistor to ground on that side as well).

• Amplifies only the difference between two inputs: $V_{out} = \frac{R_f}{R_{in}}(V_2 - V_1)$, but only when the resistor ratios are properly matched ($\frac{R_f}{R_{in}}$ must be the same on both sides).
• Common-mode rejection ratio (CMRR) measures how well the circuit rejects signals that appear identically on both inputs (like 60 Hz power line noise). Higher CMRR means better noise rejection.
• Resistor matching is critical. Even a 1% mismatch between resistors can significantly degrade CMRR and introduce measurement errors. This is the main practical limitation of the single op-amp differential amplifier.

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Time-Domain Processing Configurations

These circuits perform mathematical operations on signals over time. The key is that capacitors introduce frequency-dependent behavior. A capacitor's impedance is $Z_C = \frac{1}{j\omega C}$, so it behaves differently at different frequencies. This is what enables integration and differentiation.

Integrator

Replace the feedback resistor in an inverting amplifier with a capacitor $C$, and you get an integrator.

• Output is proportional to the time integral of the input: $V_{out} = -\frac{1}{R_{in}C} \int V_{in} \, dt$
• The capacitor in the feedback path accumulates charge over time. Apply a constant DC voltage to the input, and the output ramps linearly. Apply a square wave, and you get a triangle wave.
• DC stability problem: Any tiny DC offset at the input will cause the capacitor to charge continuously, eventually driving the output to saturation. Practical integrators include a large resistor in parallel with the feedback capacitor to provide a DC path and prevent this drift.
• The product $R_{in}C$ is the time constant of the integrator and sets the rate of integration.

Differentiator

Now swap the positions: put the capacitor in series with the input (replacing $R_{in}$) and keep a resistor $R_f$ in the feedback path.

• Output is proportional to the rate of change of the input: $V_{out} = -R_f C \frac{dV_{in}}{dt}$
• The capacitor in series with the input blocks DC and only passes current when the input voltage is changing. A linear ramp input produces a constant DC output. A square wave input produces sharp spikes at the transitions.
• High-frequency noise sensitivity is a major practical limitation. Since differentiation amplifies higher frequencies, any high-frequency noise gets boosted. Real differentiator circuits include a small resistor in series with the input capacitor to roll off gain at high frequencies.

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Specialized Signal Processing Configurations

These configurations address specific application needs like threshold detection, precision measurement, and signal conversion. Each solves a particular problem that basic amplifier configurations cannot.

Comparator

Unlike every other configuration here, the comparator uses no negative feedback. The op-amp runs in open-loop mode.

• Outputs a digital-like signal (saturates to $+V_{sat}$ or $-V_{sat}$) based on which input voltage is greater. There's no linear amplification region.
• Because the open-loop gain is enormous (typically $10^5$ or more), even a microvolt difference between the inputs drives the output to one rail or the other.
• Hysteresis can be added by connecting a resistor from the output to the non-inverting input (positive feedback). This creates two different switching thresholds (upper and lower), which prevents the output from oscillating rapidly when the input hovers near the threshold. A comparator with hysteresis is called a Schmitt trigger.

Instrumentation Amplifier

A three op-amp topology that overcomes the limitations of the single op-amp differential amplifier.

• The first stage consists of two non-inverting amplifier buffers (one for each input), which provide extremely high input impedance on both inputs. The second stage is a standard differential amplifier that subtracts the buffered signals.
• A single external resistor $R_G$ sets the gain: $A_v = 1 + \frac{2R}{R_G}$. This makes gain adjustment simple and precise without affecting CMRR.
• Superior CMRR compared to the single op-amp differential amplifier because the gain resistors in the first stage can be laser-trimmed on the IC. This makes instrumentation amplifiers essential for bridge sensors (like strain gauges) and biomedical signals (like ECG) where you need to extract microvolts from a noisy environment.

Voltage-to-Current Converter

This circuit produces an output current that's proportional to the input voltage, regardless of what load is connected.

• Load current is independent of load resistance, which is the defining feature. The feedback loop maintains a constant current by sensing the voltage across a reference resistor: $I_{out} = \frac{V_{in}}{R_{sense}}$
• Useful for driving LEDs at a consistent brightness, exciting sensor elements with a known current, and transmitting signals over long wires (4-20 mA current loops are standard in industrial systems).

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Quick Reference Table

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Self-Check Questions

1. Which two configurations both use resistive feedback but differ in input impedance characteristics? Explain why this difference matters for source loading.

2. You need to extract a small sensor signal buried in 60 Hz noise that appears equally on both signal wires. Which configuration should you choose, and what parameter determines its effectiveness?

3. Compare the integrator and differentiator: where is the capacitor placed in each, and how does this affect their frequency response?

4. An op-amp circuit has the output connected directly to the inverting input and the signal applied to the non-inverting input. What configuration is this, what is its gain, and why would you use it?

5. Why does a comparator operate differently from all other configurations on this list? What happens if you add hysteresis, and why would you want to?