Closed-Loop Gain As Function Of Ideal Value Calculator

Formula Used:

\[ A_{cl} = \frac{1}{\beta} \times \frac{1}{1 + \frac{1}{A\beta}} \]

Closed-Loop Gain (A_cl):

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1. What is Closed-Loop Gain?

Closed-Loop Gain is the gain that results when negative feedback is applied to "tame" the open-loop gain in operational amplifier circuits and other feedback systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A_{cl} = \frac{1}{\beta} \times \frac{1}{1 + \frac{1}{A\beta}} \]

Where:

\( A_{cl} \) — Closed-Loop Gain
\( \beta \) — Feedback Factor
\( A\beta \) — Loop Gain

Explanation: This formula calculates the actual closed-loop gain considering both the ideal gain (1/β) and the effect of finite loop gain.

3. Importance of Closed-Loop Gain Calculation

Details: Accurate closed-loop gain calculation is crucial for designing stable feedback systems, predicting amplifier performance, and ensuring proper circuit operation in various electronic applications.

4. Using the Calculator

Tips: Enter the feedback factor (β) and loop gain (Aβ) values. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between closed-loop gain and ideal gain?
A: The closed-loop gain approaches the ideal gain (1/β) as the loop gain becomes very large. For finite loop gains, the actual closed-loop gain is slightly less than the ideal value.

Q2: How does feedback factor affect closed-loop gain?
A: The feedback factor directly determines the ideal gain value. A larger feedback factor results in lower closed-loop gain and better stability.

Q3: What is the significance of loop gain in this calculation?
A: Loop gain determines how closely the actual closed-loop gain approaches the ideal value. Higher loop gain means better approximation to the ideal gain.

Q4: When is this formula particularly important?
A: This formula is essential when designing precision amplifiers or when working with systems where the loop gain is not extremely large compared to the desired closed-loop gain.

Q5: Can this formula be used for all types of feedback systems?
A: This formula applies to negative feedback systems where the feedback network is linear and the amplifier operates within its linear region.