Intro to Operational Amplifiers (Op-Amps)
Operational amplifiers, commonly known as op-amps, are one of the most widely used building blocks in analog electronics. They can amplify weak electrical signals, perform mathematical operations such as addition and subtraction, and serve as the foundation of countless circuits, from audio amplifiers to filters and oscillators.
What is an Operational Amplifier?
An operational amplifier is an integrated circuit (IC) with two input terminals and one output:
- Non-inverting input (+): Receives the input signal that is in-phase with the output.
- Inverting input (–): Receives the input signal that is 180° out of phase with the output.
- Output: The amplified result of the input signals and feedback network.
Op-amps are called “operational” amplifiers because, in early analog computers, they were designed to perform mathematical operations like addition, subtraction, integration, and differentiation.
Ideal Op-Amp Assumptions
Before diving into real-world circuits, we first consider the ideal op-amp model. In this idealized version, several assumptions simplify analysis:
- Infinite open-loop gain (A → ∞)
- Infinite input impedance (no current flows into the inputs)
- Zero output impedance (perfect voltage source)
- Perfectly balanced inputs (the voltage difference between inputs is driven toward zero by feedback)
Although no real op-amp meets these assumptions perfectly, many modern op-amps (like the LM741, TL081, or modern rail-to-rail op-amps) come close enough that we can use the ideal model for most calculations.
The Inverting Amplifier
The inverting amplifier configuration is one of the most common uses of an op-amp. In this circuit, the input signal is applied to the inverting terminal through a resistor, while the non-inverting terminal is grounded.
Deriving the Gain Equation
- The voltage at the non-inverting input (+) is 0V (grounded).
- By the virtual short principle, the inverting input (–) is also at 0V (virtual ground).
- No current flows into the op-amp input, so the input current flows entirely through the feedback resistor.
By Ohm’s Law:
This same current flows through the feedback resistor (Rf):
Equating the two currents:
Therefore, the gain is:
The negative sign indicates that the output is inverted relative to the input.
The Non-Inverting Amplifier
The non-inverting amplifier is another essential configuration. In this setup, the input signal is applied directly to the non-inverting input (+), while the inverting input (–) receives feedback from the output through a resistor divider network.
Deriving the Gain Equation
The voltage at the inverting input is determined by the resistor divider:
Since the op-amp forces the inputs to be equal (ideal assumption):
Rearranging gives:
This equation shows that the non-inverting amplifier has a positive gain, and the output is in-phase with the input.
Practical Considerations
Real op-amps deviate from the ideal model. Some important non-ideal characteristics include:
- Finite gain: Practical op-amps have high but finite open-loop gain (e.g., 100,000).
- Input bias current: Small currents (nA to μA) flow into the input terminals.
- Input offset voltage: A small voltage difference is required to achieve a zero output.
- Slew rate: Limits how fast the output can change (important in audio and high-speed circuits).
- Bandwidth: The gain decreases at high frequencies.
Despite these limitations, op-amps remain incredibly useful and versatile in electronics design.
Applications of Op-Amps
- Audio Amplifiers: Boosting microphone or guitar signals.
- Filters: Low-pass, high-pass, and band-pass active filters.
- Summing Amplifiers: Adding multiple signals together.
- Voltage Followers: Buffer circuits providing high input impedance and low output impedance.
- Oscillators: Signal generation in waveform generators.
- Instrumentation: Precision amplifiers for sensors and measurement devices.
Practice Problems
Problem 1: In an inverting amplifier, Rin = 10kΩ and Rf = 100kΩ. What is the gain?
Problem 2: In a non-inverting amplifier, Rin = 5kΩ and Rf = 20kΩ. What is the gain?
Problem 3: If an inverting amplifier has Rin = 1kΩ and Rf = 47kΩ, and Vin = 0.2V, what is Vout?
Conclusion
Operational amplifiers are fundamental to analog electronics. By understanding their ideal behavior and how feedback shapes inverting and non-inverting amplifier circuits, you gain the tools to analyze and design a wide range of circuits. While real op-amps introduce practical limitations, the core principles remain powerful and widely applicable. Keep practicing problems, experiment in simulation tools, and apply these concepts in real circuits to deepen your knowledge.