closed-loop gain

The Closed-Loop Gain: Mastering Feedback in Operational Amplifiers

In the realm of electronics, operational amplifiers (op-amps) are versatile building blocks, capable of performing a wide array of functions. While their open-loop gain – the gain without any feedback – is incredibly high, it is rarely utilized directly due to its inherent instability and susceptibility to noise. Enter the concept of closed-loop gain, a fundamental aspect of op-amp circuits that introduces a controlled feedback mechanism, allowing for precise and predictable operation.

Understanding the Closed-Loop Concept

The closed-loop gain refers to the gain of an op-amp circuit where a portion of the output signal is fed back to the input, creating a feedback loop. This feedback is usually negative, meaning it opposes the input signal. By controlling the feedback loop, we can effectively regulate the overall gain of the circuit.

Why Negative Feedback is Crucial

Stability: Negative feedback reduces the overall gain of the op-amp, making it more stable and less susceptible to external noise and variations.
Precision: The closed-loop gain becomes largely independent of the open-loop gain, making it more predictable and precise.
Linearity: Negative feedback helps linearize the op-amp's output, ensuring a more accurate response to input signals.

Calculating Closed-Loop Gain

The closed-loop gain (A_cl) is typically determined by the values of the resistors in the feedback network. For a non-inverting amplifier, the closed-loop gain is given by:

A_cl = 1 + (R_f / R₁)

Where:

R_f is the feedback resistor
R₁ is the input resistor

For an inverting amplifier, the closed-loop gain is:

A_cl = - (R_f / R₁)

Benefits of Closed-Loop Operation

Flexibility: The closed-loop gain can be easily adjusted by changing the values of the feedback resistors.
Customizability: Closed-loop configurations allow for the realization of various circuit functionalities, such as amplifiers, filters, and oscillators.
Enhanced Performance: Feedback provides increased stability, accuracy, and linearity, making the op-amp circuit more robust and reliable.

Conclusion

The closed-loop gain is a critical concept in op-amp circuit design, enabling the stable and precise operation of these powerful devices. By understanding and utilizing negative feedback, we can unlock the full potential of op-amps, creating sophisticated circuits for diverse applications in electronics, instrumentation, and signal processing.

Test Your Knowledge

Closed-Loop Gain Quiz

Instructions: Choose the best answer for each question.

1. What is the primary purpose of negative feedback in an op-amp circuit?

(a) To increase the open-loop gain. (b) To make the circuit more stable and predictable. (c) To introduce noise and instability. (d) To amplify the input signal without any limitations.

Answer

(b) To make the circuit more stable and predictable.

2. Which of the following is NOT a benefit of closed-loop operation in op-amps?

(a) Flexibility in adjusting the gain. (b) Increased susceptibility to noise and variations. (c) Enhanced accuracy and linearity. (d) Customizable circuit functionalities.

Answer

(b) Increased susceptibility to noise and variations.

3. What is the closed-loop gain of a non-inverting amplifier with a feedback resistor (R_f) of 10 kΩ and an input resistor (R₁) of 1 kΩ?

(a) 10 (b) 11 (c) 1 (d) -10

Answer

(b) 11

4. In an inverting amplifier, how does the closed-loop gain relate to the values of the feedback resistor (R_f) and input resistor (R₁)?

(a) A_cl = R_f / R₁ (b) A_cl = 1 + (R_f / R₁) (c) A_cl = - (R_f / R₁) (d) A_cl = R₁ / R_f

Answer

5. Which of the following best describes the relationship between open-loop gain (A_ol) and closed-loop gain (A_cl) in a practical op-amp circuit?

(a) A_cl is directly proportional to A_ol. (b) A_cl is largely independent of A_ol. (c) A_cl is always smaller than A_ol. (d) A_cl is always larger than A_ol.

Answer

(b) A_cl is largely independent of A_ol.

Closed-Loop Gain Exercise

Task: Design a non-inverting amplifier circuit with a closed-loop gain of 5. Use standard resistor values (e.g., 1 kΩ, 2.2 kΩ, 4.7 kΩ, 10 kΩ).

Steps:

Choose a value for R₁.
Calculate the required value for R_f to achieve a gain of 5.
Select the closest standard resistor values to the calculated R_f value.

Drawing: Draw the schematic diagram of your circuit, clearly labeling the components.

Correction:

Exercice Correction

Solution:

Choose R₁: Let's choose R₁ = 1 kΩ.
Calculate R_f: A_cl = 1 + (R_f / R₁) 5 = 1 + (R_f / 1 kΩ) R_f = 4 kΩ
Select standard resistor values: The closest standard resistor value to 4 kΩ is 4.7 kΩ.

Circuit Diagram:

[Insert a schematic diagram of the non-inverting amplifier with R₁ = 1 kΩ and R_f = 4.7 kΩ]

Note: The actual closed-loop gain will be slightly higher than 5 due to using a 4.7 kΩ resistor instead of 4 kΩ.

Books

"Op Amps for Everyone" by Bruce Carter and Ron Mancini: A comprehensive and accessible guide to op-amp theory and applications, including detailed discussions on closed-loop gain and feedback.
"Microelectronic Circuits" by Sedra & Smith: A classic textbook in electronics that covers op-amp theory, feedback, and closed-loop gain in detail.
"The Art of Electronics" by Horowitz & Hill: A comprehensive reference for electronics, encompassing the fundamentals of op-amps, feedback, and closed-loop gain, as well as a wide range of circuit applications.
"Operational Amplifiers and Linear Integrated Circuits" by James Roberge: A textbook focusing on the theory and applications of op-amps, providing detailed explanations of closed-loop gain and feedback concepts.

Articles

"Understanding Operational Amplifiers (Op Amps)" by All About Circuits: An introductory article explaining the basics of op-amps, including feedback, closed-loop gain, and common applications.
"Negative Feedback in Operational Amplifiers" by Electronicshub: A detailed article discussing the theory and benefits of negative feedback in op-amp circuits, including the concept of closed-loop gain.
"Closed-Loop Gain of an Op-Amp" by Circuit Digest: A concise article focusing specifically on calculating closed-loop gain in both inverting and non-inverting op-amp configurations.

Online Resources

Khan Academy - Operational Amplifiers: A free online resource offering video lectures and practice exercises covering the fundamentals of op-amps, including feedback and closed-loop gain.
All About Circuits - Op-Amp Circuits: A website with numerous articles, tutorials, and resources related to op-amp theory and applications, including sections on feedback, closed-loop gain, and common circuit configurations.
Electronic Tutorials - Operational Amplifiers: A website offering a comprehensive collection of tutorials and articles on op-amps, covering topics such as feedback, closed-loop gain, and various circuit applications.