An important topic in analog circuits is the operational amplifier (op amp). Op amp circuits take many forms and are a core part of analog design. Analyzing op amp behavior can be challenging without understanding the core concepts.
Virtual Short and Virtual Open
Based on practical experience, two properties are most frequently used when analyzing op amp circuits: the virtual short and the virtual open. These concepts are covered in analog electronics textbooks and are widely applied in op amp circuit analysis. Proficiency requires practice and a solid understanding of circuit fundamentals.
Virtual short: This means the noninverting and inverting inputs of the op amp can be treated as having the same voltage. They are not physically shorted, so this is called a "virtual" short.
Virtual open: The input impedance of an ideal op amp is very high, so the input currents are negligible (typically much less than 1 μA). For analysis, the input terminals can be approximated as open circuits, hence "virtual open." In other words, the currents into the noninverting and inverting inputs are approximated as zero.
When analyzing op amp circuits, apply the virtual short and virtual open assumptions together with basic circuit laws to derive input-output relationships. This approach often avoids memorizing separate formulas for inverting, noninverting, summing, or differential configurations.
Examples
1) Inverting amplifier
Using virtual short: V+ = V-. Using virtual open: input currents at the op amp terminals are zero, so the current through R1 equals the current through R2.
Since V+ = 0 (ground), V- = 0.
I1 = (Vi - V-)/R1
I2 = (V- - Vout)/R2
Setting I1 = I2 gives (Vi - V-)/R1 = (V- - Vout)/R2
With V- = 0, this simplifies to Vout = -(R2/R1) * Vi, the standard inverting amplifier gain.
2) Noninverting amplifier
From virtual short: Vi = V-. From virtual open: input currents at the op amp terminals are zero, so the current through R2 equals the current through R1.
I1 = (Vi - 0)/R2
I2 = (Vout - Vi)/R1
Equating currents: (Vi - 0)/R2 = (Vout - Vi)/R1
Solving gives Vout = Vi * (R1 + R2)/R2, the standard noninverting amplifier gain.
3) Summing (inverting) amplifier
For the inverting summing amplifier, virtual short gives V+ = V- = 0. Virtual open implies the currents into the op amp inputs are zero, so the current through R3 equals the sum of the currents through R1 and R2.
(V- - Vout)/R3 = (V1 - V-)/R1 + (V2 - V-)/R2
With V- = 0, this becomes -Vout/R3 = V1/R1 + V2/R2. If R1 = R2 = R3, then Vout = -(V1 + V2).
4) Differential amplifier (subtractor)
Using virtual short and virtual open, first compute the voltages at the inputs.
V+ = V2 * R3 / (R2 + R3)
V- = V+ = V2 * R3 / (R2 + R3)
Equating currents through R4 and R3:
(V1 - V-)/R1 = (V- - Vout)/R4
Solving yields Vout = [(R2 + R4) * R3 * V2] / [(R1 + R4) * R2] - (R4/R2) * V1.
In practical applications, if R1 = R2 and R3 = R4, the relationship simplifies to Vout = (V2 - V1) * R4 / R1. If R1 = R4, then Vout = V2 - V1.
