An ideal op amp is a theoretical model of an operational amplifier with perfect electrical characteristics: infinite gain, infinite input impedance, and zero output impedance. It doesn’t exist in the real world, but it’s the foundation for analyzing and designing nearly every op amp circuit. By assuming these perfect properties, you can predict how a circuit will behave using simple algebra instead of complex equations.
The Core Assumptions
An operational amplifier takes two input voltages, compares them, and outputs an amplified version of the difference. The ideal model simplifies this by pushing every parameter to its theoretical extreme. There are four key assumptions:
- Infinite open-loop gain. The amplifier multiplies the voltage difference between its inputs by an infinitely large factor. In practice, this means even a tiny difference at the inputs would drive the output to its maximum, which is why op amps almost always use feedback to control their behavior.
- Infinite input impedance. No current flows into either input terminal. The inputs behave like perfect voltmeters, sensing voltage without disturbing the circuit they’re connected to.
- Zero output impedance. The output behaves like a perfect voltage source, delivering whatever current the load demands without any voltage drop inside the amplifier.
- Infinite bandwidth. The amplifier responds equally well to signals of any frequency, from DC to infinitely fast oscillations.
A few additional ideal properties round out the model: infinite common-mode rejection (meaning the amplifier perfectly ignores any signal that appears equally on both inputs), zero input offset voltage (the output sits at exactly zero when both inputs are at the same voltage), and zero noise.
The Two Golden Rules
When you combine the ideal assumptions with negative feedback (connecting the output back to the inverting input), two powerful simplifications emerge. These are often called the “golden rules” of op amp analysis, and they let you solve circuits quickly.
Rule 1: No current flows into either input. This follows directly from the infinite input impedance. Any current in the circuit must flow through external resistors, not into the op amp itself.
Rule 2: The two input terminals sit at the same voltage. This one is less obvious. Because the gain is infinite, the amplifier only needs an infinitely small voltage difference between its inputs to produce a finite output. In any circuit with negative feedback, the amplifier adjusts its output until the two inputs match. This condition is called a “virtual short.” The inputs behave as though they’re connected, but no current actually flows between them.
When the non-inverting input (the “+” terminal) is connected to ground, the virtual short means the inverting input also sits at zero volts. This special case is called a “virtual ground,” and it’s central to analyzing inverting amplifier circuits.
How It Simplifies Circuit Analysis
The golden rules turn what would be a difficult differential equation into basic algebra. Consider the two most common op amp configurations.
In an inverting amplifier, the input signal connects to the inverting terminal through a resistor, and a feedback resistor connects the output back to that same terminal. Applying the golden rules, the voltage gain works out to the negative ratio of the feedback resistor to the input resistor. If the feedback resistor is 10 kΩ and the input resistor is 1 kΩ, the gain is -10. The negative sign means the output is flipped in polarity relative to the input.
In a non-inverting amplifier, the input signal connects directly to the non-inverting terminal. The gain equals one plus the ratio of the feedback resistor to the ground-connected resistor. With the same 10 kΩ and 1 kΩ resistors, you get a gain of +11. The output stays in phase with the input.
Notice that in both cases, the gain depends only on the external resistors, not on any property of the amplifier itself. That’s the real power of the ideal model: it shows that a well-designed op amp circuit’s behavior is set entirely by the components you choose.
How Real Op Amps Compare
No physical device achieves the ideal, but modern op amps come remarkably close for many applications. Here’s how typical real-world specs stack up against the ideal values.
Open-loop gain in the ideal model is infinite. A classic general-purpose chip like the LM741 has a gain of about 200,000, and many modern op amps exceed 1,000,000. That’s large enough that most circuits behave almost exactly as the ideal model predicts.
Input impedance is ideally infinite. The LM741’s minimum input impedance is 2 MΩ, which is considered low by modern standards. Many op amps built with different transistor technologies have input impedances above 1 GΩ, meaning the current flowing into the inputs is negligibly small for most purposes.
Bandwidth is ideally infinite. The LM741 has a gain-bandwidth product of about 1 MHz, which means its gain drops as frequency increases. That’s slow by today’s standards. Faster op amps are available with gain-bandwidth products exceeding 1 GHz, but no real amplifier maintains its gain at all frequencies.
Input offset voltage is ideally zero. In practice, a small voltage imbalance between the inputs causes the output to drift from zero even when it shouldn’t. General-purpose precision op amps typically have offsets between 50 and 500 microvolts. The best auto-zero (chopper-stabilized) designs achieve less than 1 microvolt. Untrimmed CMOS op amps can be much worse, ranging from 5,000 to 50,000 microvolts.
Where the Ideal Model Breaks Down
The ideal model is excellent for first-pass design, but it fails to capture several real-world effects that matter in practice.
The most obvious limitation is output saturation. The ideal model implies the output can swing to any voltage, but a real op amp is powered by supply rails (for example, +15 V and -15 V), and its output cannot exceed those voltages. Even in “rail-to-rail” designs, the output typically can’t reach within about 0.2 V of the supply voltage because the internal transistors need a small voltage headroom to stay in their active operating region. Once the output hits this limit, the amplifier saturates, the golden rules no longer apply, and the circuit stops behaving linearly.
Finite gain also matters when you need high precision. If the open-loop gain is 200,000 and you’re designing a circuit with a gain of 1,000, the actual gain will be slightly less than the ideal formula predicts. For low-gain circuits, this error is negligible, but it becomes significant when pushing for accuracy.
Finite bandwidth means the gain rolls off at higher frequencies. A circuit that amplifies audio signals perfectly may struggle with radio-frequency signals if the op amp’s gain-bandwidth product isn’t high enough.
Common-mode rejection, while very high in real op amps (typically 70 to 120 dB at low frequencies), is not infinite. Signals that appear on both inputs simultaneously won’t be perfectly cancelled, which can introduce errors in precision measurement circuits.
Why the Ideal Model Still Matters
Engineers don’t use the ideal op amp model because they think it’s accurate in every detail. They use it because it captures the essential behavior of a feedback amplifier with minimal math. Once you design a circuit using ideal assumptions, you can go back and check whether real-world imperfections (offset voltage, finite bandwidth, gain error) are small enough to ignore for your application. In most cases, they are. The ideal model gives you the right answer to within a fraction of a percent for a huge range of practical circuits, which is why it remains the standard starting point in every electronics course and design workflow.