Ideal Op-Amp

The ideal op-amp is a theoretical model of the operational amplifier that simplifies circuit analysis by assuming perfect electrical characteristics. While no real device is truly ideal, this model gives results that are close enough for most practical designs and is the foundation for analyzing all op-amp based circuits in analog electronics courses and GATE examinations.

Core Concept: The Ideal Op-Amp Model

An operational amplifier is a high-gain differential amplifier. In the ideal model, the open-loop voltage gain Av is assumed to be infinite. This means even a tiny differential voltage between the inverting and non-inverting inputs would produce an infinitely large output, which is why op-amps are almost never used in open-loop configurations in linear circuits. Negative feedback is applied to control the gain to a finite, predictable value.

The input impedance is assumed to be infinite, which means no current flows into either input terminal. This is an extremely useful assumption because it allows you to analyze the circuit around the op-amp without worrying about loading at the input. In reality, the input impedance of a JFET-input op-amp can be in the range of teraohms, making this assumption practically valid.

The output impedance is assumed to be zero. This means the op-amp can drive any load without a drop in output voltage. In practice, real op-amps have output impedances of 50 to 200 ohms, but with feedback this is reduced by the loop gain, making it appear nearly zero to the load.

Mathematical Expression: Virtual Short Principle

The most powerful consequence of infinite open-loop gain in a negative feedback circuit is the virtual short circuit principle. If the output is finite and the gain is infinite, then the differential input (V+ minus V-) must approach zero. This does not mean V+ and V- are physically connected, but that the circuit forces them to be equal through feedback. This is called a virtual short.

Combined with the zero input current rule, two golden rules emerge for ideal op-amp analysis. First, no current flows into either input terminal (Iin = 0). Second, when negative feedback is applied, V+ equals V-. These two rules allow almost any op-amp circuit to be analyzed using basic Kirchhoff's laws without solving complex differential equations.

For a general negative feedback configuration, the closed-loop gain is ACL = Aol / (1 + Aol * beta), where beta is the feedback fraction. As Aol approaches infinity, ACL approaches 1/beta. This means the closed-loop gain depends only on the feedback network (typically passive resistors), not on the op-amp gain itself, making designs extremely stable and reproducible.

Practical Understanding: Why the Ideal Model Works

Modern op-amps like the LM741 or TL071 have open-loop gains of 100 dB (100,000) or more at DC. At signal frequencies, gain falls with frequency, but within the operating bandwidth, the ideal model remains valid. The infinite bandwidth assumption breaks down at higher frequencies where the gain-bandwidth product (GBW) limits performance.

The ideal model is used to find the gain, input impedance, and output voltage of circuits involving inverting amplifiers, non-inverting amplifiers, summing amplifiers, integrators, and differentiators. Every such circuit analysis begins by applying the two golden rules derived from the ideal model.

Given:
An op-amp in negative feedback with open-loop gain Aol = 200,000
Feedback fraction beta = 0.1 (set by resistors R1 and R2)

Why this formula applies:
Closed-loop gain formula applies to any inverting or non-inverting configuration.

Formula:
ACL = Aol / (1 + Aol * beta)

Substitution:
ACL = 200000 / (1 + 200000 * 0.1)

Calculation:
ACL = 200000 / (1 + 20000)
ACL = 200000 / 20001
ACL ≈ 9.9995

Final Answer:
ACL ≈ 10 (= 1/beta = 1/0.1)
The gain is set almost entirely by the feedback network, not by Aol.

Exam Tip: In GATE, always apply the two golden rules first: Iin = 0 and V+ = V- (in negative feedback). If the feedback is positive, these rules do NOT apply. Confusing feedback polarity is a common source of errors in op-amp circuit analysis questions.

Quick Revision

• Ideal op-amp: Aol = infinity, Rin = infinity, Rout = 0, BW = infinity, offset = 0.
• Golden Rule 1: No current enters either input terminal (I+ = I- = 0).
• Golden Rule 2: With negative feedback, V+ = V- (virtual short circuit principle).
• Closed-loop gain: ACL = Aol / (1 + Aol*beta) ≈ 1/beta when Aol is very large.
• Virtual short does NOT mean the terminals are physically connected. No current flows through the virtual short.
• GATE trap: Virtual short applies ONLY in negative feedback. For positive feedback or open loop, V+ is NOT equal to V-.
• All ideal op-amp circuit analysis (inverting, non-inverting, integrator, summing amplifier) uses these two rules as the starting point.