Understanding Ideal Op-amp Input Impedance

The question asks about the input impedance of an ideal operational amplifier, commonly known as an ideal Op-amp.

An ideal Op-amp is a theoretical model used to simplify the analysis of circuits containing Op-amps. It possesses several key characteristics that simplify calculations and provide a benchmark for real-world Op-amps. One of the most significant characteristics of an ideal Op-amp is its input impedance.

Ideal Op-amp Characteristics

An ideal Op-amp is assumed to have the following properties:

• Infinite input impedance
• Zero output impedance
• Infinite open-loop voltage gain
• Infinite bandwidth
• Zero input offset voltage
• Zero input bias current
• Infinite slew rate

Focus on Input Impedance

The input impedance of a circuit is the opposition it presents to current when a voltage is applied across its input terminals. For an amplifier, high input impedance is generally desirable because it means the amplifier draws very little current from the source signal. This prevents loading of the source, ensuring that the voltage signal from the source is not significantly reduced when connected to the amplifier's input.

In the case of an ideal Op-amp, the input impedance is assumed to be infinite. This means that absolutely no current flows into or out of the input terminals (the non-inverting input (+) and the inverting input (-)). Mathematically, this is represented as a resistance of infinity between the two input terminals and between each input terminal and ground.

Analyzing the Options

Let's look at the given options for the input impedance of an ideal Op-amp:

1. 100 \(\Omega\): A finite value like 100 \(\Omega\) would mean the Op-amp draws a measurable current from the source, which is not a characteristic of an ideal Op-amp.
2. Infinite: This aligns with the theoretical definition of an ideal Op-amp, where no current flows into the input terminals due to infinite opposition to current flow.
3. Unity: Unity is a value of 1. Input impedance is measured in ohms (\(\Omega\)). An input impedance of 1 \(\Omega\) is a very low value, meaning it would heavily load the source. This is the opposite of an ideal Op-amp's characteristic.
4. Zero: A zero input impedance would mean the input terminals are like a short circuit, drawing infinite current from the source, which is also the opposite of an ideal Op-amp's characteristic.

Based on the definition and characteristics of an ideal Op-amp, its input impedance is considered to be infinite.

Conclusion on Ideal Op-amp Input Impedance

For an ideal Op-amp, the assumption of infinite input impedance is crucial for simplifying circuit analysis, particularly when applying concepts like the virtual short-circuit at the input terminals in negative feedback configurations. This characteristic implies that no current flows into the input pins, only through the feedback network connected around the Op-amp.

Revision Table: Key Ideal Op-amp Properties

Additional Information on Op-amp Characteristics

While ideal Op-amps are theoretical, real Op-amps are designed to approximate these ideal characteristics as closely as possible. Understanding the ideal properties helps predict the behavior of real Op-amps in many common circuit configurations.

For example, real Op-amps have very high input impedance (often in the range of Megaohms or even Teraohms for FET-input Op-amps), but it is not truly infinite. They have low but non-zero output impedance, high but finite open-loop gain, and limited bandwidth.

The assumption of infinite input impedance in ideal Op-amp analysis simplifies problems considerably. When solving Op-amp circuits, assuming infinite input impedance means you can treat the current into the '+' and '-' terminals as zero, which is a fundamental step in applying circuit analysis techniques like nodal analysis.