What are the key characteristics of an ideal operational amplifier (op-amp)?

Infinite open-loop gain (AOL): The ideal op-amp has an infinite gain, meaning it can amplify signals of any magnitude without saturation. In practical terms, a very high gain is desirable.

Infinite input impedance: The ideal op-amp has infinite input impedance, meaning it does not draw any current from the input signal source. This ensures that the input signal is not affected or loaded down by the op-amp's input circuitry.

Zero output impedance: The ideal op-amp has zero output impedance, meaning it can drive any load without being affected by the load impedance. In practice, low output impedance is desired to minimize signal degradation.

Infinite bandwidth: The ideal op-amp has infinite bandwidth, enabling it to amplify signals of any frequency without distortion. In real-world op-amps, bandwidth is limited, and the amplifier's performance may degrade at higher frequencies.

Zero input offset voltage: In an ideal op-amp, the voltage difference between its two inputs (non-inverting and inverting) would be exactly zero when the op-amp is in a balanced state. In reality, op-amps have a small input offset voltage that can cause errors in precision applications.

Infinite common-mode rejection ratio (CMRR): The ideal op-amp rejects any signal that is common to both inputs (common-mode signal) perfectly, focusing only on amplifying the differential input (the difference between the two inputs). In practical op-amps, the CMRR is high but not infinite.

Infinite slew rate: The ideal op-amp has an infinite slew rate, meaning it can change its output voltage instantaneously in response to a change in the input signal. In real op-amps, a finite slew rate can lead to signal distortion at high frequencies.

Zero noise: The ideal op-amp would not add any noise to the input signal. In reality, op-amps have noise contributions from various sources, and low-noise designs are desired for sensitive applications.

Infinite supply voltage range: The ideal op-amp can operate with both positive and negative supply voltages of infinite magnitude. In practice, op-amps have specified supply voltage ranges.

Infinite common-mode input voltage range: The ideal op-amp can handle any common-mode input voltage without issues. Real op-amps have a limited common-mode input voltage range.

While no op-amp can achieve all these characteristics perfectly, modern op-amps are designed to come as close as possible to these ideal attributes to ensure reliable and accurate signal amplification and processing in various electronic circuits and applications.