Discuss the properties and applications of operational amplifiers (op-amps) in electronic circuits.

1. High Gain: Op-amps have a very high voltage gain, typically in the range of tens of thousands to hundreds of thousands, making them suitable for amplification tasks.

2. Differential Inputs: Op-amps have two inputs: inverting (-) and non-inverting (+). The output voltage is proportional to the difference between these inputs.

3. High Input Impedance: Op-amps have high input impedance, meaning they draw very little current from the input sources, making them ideal for interfacing with high-impedance sensors and other circuits.

4. Low Output Impedance: The output impedance of an op-amp is very low, allowing it to drive other circuits or loads with minimal signal loss.

5. Ideal Model: In theoretical discussions, op-amps are often considered ideal, which means they have infinite open-loop gain, infinite input impedance, zero output impedance, and zero offset voltage. In practice, real-world op-amps deviate from this ideal behavior, but many of their properties are still close to the theoretical model.

6. Common Operating Modes:

Inverting Amplifier: The output is the inverted and amplified version of the input signal.

Non-Inverting Amplifier: The output is the amplified version of the input signal with the same polarity.

Differential Amplifier: The output is proportional to the difference between two input signals.

Summing Amplifier: The output is the weighted sum of multiple input signals.

Integrator: The output is the integration of the input signal with respect to time.

Differentiator: The output is the differentiation of the input signal with respect to time.

7. Feedback Configurations: Op-amps often use feedback to control their behavior and tailor their performance for specific applications. Feedback can be negative or positive, influencing the gain, stability, and linearity of the op-amp.

Applications:

1. Signal Amplification: Op-amps are extensively used for amplifying weak signals from sensors, microphones, or other low-level sources before processing or further use.

2. Active Filters: Op-amps are used in active filter circuits like low-pass, high-pass, band-pass, and notch filters to process signals and eliminate unwanted frequencies.

3. Instrumentation Amplifiers: These specialized op-amp configurations provide high common-mode rejection and are commonly used in precision measurement and sensor applications.

4. Voltage Regulators: Op-amps can be part of voltage regulator circuits, providing stable output voltage in power supply applications.

5. Oscillators: Op-amps are used in oscillator circuits to generate waveforms at specific frequencies.

6. Comparators: Op-amps can be used as comparators to compare two voltage levels and produce a digital output based on their relationship.