ALLPCB
Overview
An op amp circuit is any circuit that uses an operational amplifier (op amp). These circuits are a core part of analog electronics and are essential knowledge for electronic engineers and embedded developers. Rather than memorizing many specific input-output formulas, the correct approach is to understand the underlying principles so you can analyze variant circuits.
Key approximations: virtual short and virtual open
When analyzing op amp circuits in their linear region, two commonly used idealized properties simplify analysis:
- Virtual short: Because an op amp has a very high open-loop voltage gain and a limited output swing, the differential input voltage is typically very small. For analysis it is often accurate to treat the inverting and non-inverting inputs as being at the same potential (V+ = V-). This is called the virtual short. Note this is not an actual short circuit.
- Virtual open (virtual open-circuit): Because an op amp has a very large input resistance, the input currents are negligible. For circuit analysis the op amp inputs can usually be treated as open circuits (no input current). This is called the virtual open. Note this is not an actual open circuit.
Case 1: Inverting amplifier
Using the virtual short and virtual open approximations, consider an inverting amplifier with input resistor R1 and feedback resistor R2. The inverting input is at virtual ground (V- = V+ = 0). No current enters the op amp input, so the current through R1 equals the current through R2:
I1 = (Vi - V-)/R1, I2 = (V- - Vout)/R2, V- = 0, I1 = I2
Solving gives:
Vout = -(R2 / R1) * Vi
Case 2: Non-inverting amplifier
For the non-inverting configuration where the input is applied to the non-inverting input and a resistor divider R1 and R2 provides feedback to the inverting input, virtual short gives Vi = V- = V+. The currents through R1 and R2 are equal (no input current):
I = Vout / (R1 + R2), Vi = I * R2
Thus the closed-loop gain is:
Vout = Vi * (R1 + R2) / R2 = Vi * (1 + R1 / R2)
Case 3: Inverting summing amplifier
With the non-inverting input grounded (V+ = 0), and input resistors R1 and R2 connecting sources V1 and V2 to the inverting node, KCL at the summing node (virtual ground) gives:
V1 / R1 + V2 / R2 + Vout / R3 = 0
So the output is:
Vout = -R3 * (V1 / R1 + V2 / R2)
For R1 = R2 = R3, this becomes Vout = -(V1 + V2), a classic inverting summing amplifier.
Summing amplifier with input averaging
A variant includes balancing resistors so the circuit produces a non-inverted sum. With appropriate resistor choices and using virtual short and virtual open, one can derive:
If R1 = R2 and R3 = R4 then V+ = (V1 + V2)/2 and V- = Vout/2. Enforcing V+ = V- yields Vout = V1 + V2.
Subtractor (differential) circuit
For a differential subtractor built from an op amp and four resistors, virtual open gives equal currents through paired resistors and virtual short gives V+ = V-. If R1 = R2 and R3 = R4, the result is:
Vout = V2 - V1
Integrator
An inverting integrator uses a resistor R1 at the input and a capacitor C1 in the feedback path. Virtual short sets the summing node voltage, and virtual open means input current equals capacitor current. The output is:
Vout = - (1 / (R1 * C1)) * ∫ V1 dt
For a constant input V1 = U, this yields Vout = -U * t / (R1 * C1), a ramp whose slope is proportional to U.
Differentiator
An inverting differentiator swaps the resistor and capacitor: the input is applied through a capacitor C1 and the feedback path uses resistor R2. With virtual short and virtual open:
i = C1 * dV1/dt => Vout = -i * R2 = -R2 * C1 * dV1/dt
For a step input, the output is a pulse opposite in polarity to the input change.
Differential amplifier with adjustable gain
A more complex differential amplifier can be built using cascaded resistor networks and buffer stages. Using virtual short and virtual open and assuming certain resistor equalities (for example R6 = R7 and R4 = R5), it can be shown that the output takes the form:
Vout = (Vy - Vx) * (R1 + R2 + R3) / R2
where the factor (R1 + R2 + R3) / R2 sets the differential gain.
4–20 mA current-to-voltage conversion and scaling
A common front-end for controllers converts a 4–20 mA loop current to a voltage via a shunt resistor. For example, a 100 Ω shunt produces 0.4–2.0 V for 4–20 mA. Using an op amp-based scaling stage and virtual open/short analysis, the output can be related to the shunt voltage. With R3 = R2 and R4 = R5, one obtains:
Vout = - (0.4 to 2.0) * (R4 / R2)
For R4 / R2 = 22k / 10k = 2.2, this yields Vout = -0.88 to -4.4 V, suitable for subsequent ADC input after level shifting if needed.
Current output via transistor in the feedback path
If the feedback path includes a transistor emitter junction in series with resistors, the same virtual short and virtual open principles apply. With appropriate resistor ratios (for example R2 = R6, R4 = R5) the op amp forces the voltage across a resistor R7 to follow the input Vi, producing a feedback-controlled current I = Vi / R7. If the load RL is much less than about 100 kΩ, the load current approximately equals I.
Conclusion
Across these examples, the same basic tools—virtual short, virtual open, Ohm's law, and Kirchhoff's laws—allow straightforward analysis of most op amp circuits. Mastering these approximations makes it possible to analyze and design a wide variety of op amp topologies.
