A circuit composed of operational amplifiers is referred to as an op-amp circuit.
These circuits come in many types and are essential for studying analog electronics and a must-master skill for electronics engineers.
A circuit composed of operational amplifiers is referred to as an
op-amp circuit.
These circuits come in many types and are essential for studying analog electronics and a must-master skill for electronics engineers.
Instead of memorizing topologies and formulas, you should understand the core principles. When analyzing op-amp circuits, temporarily ignore terms like inverting/non-inverting amplifier, adder, subtractor, differential input, and related formulas. Also ignore parameters such as input bias current, CMRR, and offset voltage—focus on the ideal op-amp.
Most op-amp problems can be solved with two core rules: Virtual Short and Virtual Open. These are fundamental in all textbooks, but mastering them requires practice.
About Virtual Short & Virtual Open
Virtual Short
The open-loop voltage gain of a general-purpose op-amp is above 80 dB, while the output voltage is limited (typically 10–14 V). The differential input voltage is less than 1 mV, so the two input terminals are nearly at the same potential, like a “false short.”
Definition: When an op-amp operates linearly, the two inputs can be treated as equal in voltage (virtual short). They must not be physically shorted.
Virtual Open
The differential input resistance of a general-purpose op-amp is above 1 MΩ. The current into the input terminals is less than 1 μA, much smaller than external circuit current. The inputs behave like an open circuit.
Definition: When an op-amp operates linearly, the two inputs can be treated as drawing zero current (virtual open). They must not be physically disconnected.
Case 1: Inverting Amplifier
Inverting op-amp circuit diagram
Analysis:
- By virtual short: Non-inverting input = 0 V → inverting input V⁻ = 0 V.
- By virtual open: No current enters the op-amp. R₁ and R₂ are in series, so currents are equal.
- I₁ = (Vi − V⁻) / R₁
- I₂ = (V⁻ − Vout) / R₂
- V⁻ = V⁺ = 0, I₁ = I₂
- Solve: Vout = −(R₂/R₁) × Vi
This is the classic inverting proportional amplifier.
Case 2: Non-Inverting Amplifier
Non-inverting op-amp circuit diagram
Analysis:
- By virtual short: Vi = V⁻
- By virtual open: No current enters the op-amp. Current through R₁ = current through R₂ = I.
- I = Vout / (R₁ + R₂)
- Vi = I × R₂
- Solve: Vout = Vi × (R₁ + R₂) / R₂
This is a non-inverting amplifier.
Case 3: Inverting Adder
Inverting adder circuit diagram
Analysis:
- By virtual short: V⁻ = V⁺ = 0
- By virtual open and Kirchhoff’s law:
(V₁ − V⁻)/R₁ + (V₂ − V⁻)/R₂ = (Vout − V⁻)/R₃
- Simplify: V₁/R₁ + V₂/R₂ = Vout/R₃
- If R₁ = R₂ = R₃: Vout = −(V₁ + V₂)
This is an inverting adder.
Simulation Examples
Simulation with R₁=R₂=R₄ → VO = V₁+V₂
Simulation with R₂=R₄, R₁=3R₂ → VO=3(V₁+V₂)
Practical Circuit (OP07C)
OP07C low-frequency noise amplifier circuit
Case 4: Non-Inverting Adder
Non-inverting adder circuit diagram
Analysis:
- By virtual open: Currents through R₁=R₂; currents through R₃=R₄.
- (V₁−V⁺)/R₁ = (V⁺−V₂)/R₂
- (Vout−V⁻)/R₃ = V⁻/R₄
- By virtual short: V⁺ = V⁻
- If R₁=R₂, R₃=R₄:
V⁺ = (V₁+V₂)/2, V⁻ = Vout/2
- Result: Vout = V₁ + V₂
Summary
All basic op-amp circuits can be analyzed using virtual short and virtual open, combined with Ohm’s Law and Kirchhoff’s Laws.
Extended Circuits
Differential Subtractor
Differential subtractor circuit
Analysis gives:
Vout = V₂ − V₁Integrator
Op-amp integrator circuit
Vout = −(1/(R₁C₁)) ∫V₁ dt
For constant DC input Vi: Vout = −Vi·t/(R₁C₁)
Integrator simulation (input square wave, output sawtooth wave)
Differentiator
Op-amp differentiator circuit
Vout = −R₂C₁ · dV₁/dt
Differential Amplifier (High CMRR)
High-CMRR differential amplifier
Gain A = 1 + 2R₁/R₂
Current-to-Voltage Converter (4–20 mA)
4–20 mA current to voltage circuit
Converts 4–20 mA to −0.88 ~ −4.4 V for ADC input.
Voltage-to-Current Converter
Voltage-to-current converter circuit
Output current through R₇ is I = Vi/R₇, suitable for driving loads.
With these methods, you can analyze nearly all op-amp circuits step by step.
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Inverting op-amp circuit diagram
Non-inverting op-amp circuit diagram
Inverting adder circuit diagram
Simulation with R₁=R₂=R₄ → VO = V₁+V₂
Simulation with R₂=R₄, R₁=3R₂ → VO=3(V₁+V₂)
OP07C low-frequency noise amplifier circuit
Non-inverting adder circuit diagram
Differential subtractor circuit
Analysis gives: Vout = V₂ − V₁
Op-amp integrator circuit
Vout = −(1/(R₁C₁)) ∫V₁ dt
For constant DC input Vi: Vout = −Vi·t/(R₁C₁)
Integrator simulation (input square wave, output sawtooth wave)
Op-amp differentiator circuit
Vout = −R₂C₁ · dV₁/dt
