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 job is to identify the feedback path, determine the transfer function, and predict the output behavior. 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 is that negative feedback forces the op-amp to adjust its output to minimize the voltage difference between its input terminals.

Inverting Amplifier

• Gain is $A_v = -\frac{R_f}{R_{in}}$—the negative sign indicates a 180° phase inversion between input and output
• Virtual ground at the inverting input means the input impedance 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

• Gain is $A_v = 1 + \frac{R_f}{R_{in}}$—output stays in phase with input, and gain is always ≥ 1
• High input impedance (ideally infinite) prevents loading the source signal
• Signal connects directly to non-inverting terminal, making this ideal when source loading is a concern

Voltage Follower (Unity Gain Buffer)

• 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 stages
• 100% negative feedback (output connected directly to inverting input) provides maximum bandwidth and stability

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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

• Output is $V_{out} = -R_f \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right)$—a weighted sum of all inputs
• Resistor ratios determine weighting for each input channel, enabling audio mixing and signal combining
• Virtual ground isolates inputs from each other, preventing interaction between signal sources

Differential Amplifier

• Amplifies only the difference between two inputs: $V_{out} = \frac{R_f}{R_{in}}(V_2 - V_1)$ when resistors are matched
• Common-mode rejection ratio (CMRR) measures how well the circuit rejects noise present on both inputs
• Resistor matching is critical—mismatched resistors degrade CMRR and introduce errors

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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—impedance varies with signal frequency, enabling integration and differentiation.

Integrator

• Output is proportional to the time integral of the input: $V_{out} = -\frac{1}{R_{in}C} \int V_{in} \, dt$
• Capacitor in the feedback path accumulates charge over time, converting voltage to a ramp or area-under-curve representation
• DC stability requires a large parallel resistor across the capacitor to prevent output saturation from input offset

Differentiator

• Output is proportional to the rate of change of input: $V_{out} = -R_f C \frac{dV_{in}}{dt}$
• Capacitor in series with input blocks DC and responds only to changing signals
• High-frequency noise sensitivity is a major limitation—practical circuits include a series resistor to limit bandwidth

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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

• Outputs a digital-like signal (high or low) based on which input voltage is greater—no linear amplification region
• No negative feedback means the op-amp operates in open-loop, switching rapidly between saturation states
• Hysteresis (positive feedback) can be added via a resistor to the non-inverting input to prevent oscillation near the threshold

Instrumentation Amplifier

• Three op-amp topology provides differential amplification with extremely high input impedance on both inputs
• Single resistor sets gain—typically $A_v = 1 + \frac{2R}{R_G}$, making adjustment simple and precise
• Superior CMRR compared to single op-amp differential amplifier; essential for bridge sensors and biomedical signals

Voltage-to-Current Converter

• Produces output current proportional to input voltage—load current is independent of load resistance
• Feedback maintains constant current by sensing voltage across a reference resistor: $I_{out} = \frac{V_{in}}{R_{sense}}$
• Useful for driving LEDs, sensors, and transmission lines where current control matters more than voltage

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

4. An FRQ shows an op-amp circuit with the output connected directly to the inverting input and the signal applied to the non-inverting input. What configuration is this, and what is its gain?

5. Why does a comparator operate differently from all other configurations on this list? What would happen if you accidentally used a standard op-amp configuration when you needed comparator behavior?