Understanding Negative Feedback in Amplifier Circuits

An amplifier circuit is designed to increase the power or amplitude of a signal. The amount by which an amplifier increases the signal is called its gain. Gain can be expressed as the ratio of the output signal to the input signal.

Negative feedback is a technique used in amplifier circuits where a portion of the output signal is fed back to the input terminal. In negative feedback, the fed-back signal is subtracted from or is in opposition to the original input signal. This creates a feedback loop that significantly alters the characteristics of the amplifier circuit.

How Negative Feedback Affects Amplifier Gain

When negative feedback is applied to an amplifier circuit, it specifically influences the overall gain of the circuit. Let's consider the relationship between the open-loop gain (the gain without feedback) and the closed-loop gain (the gain with feedback).

The gain of an amplifier circuit with negative feedback, often called the closed-loop gain ($A_f$), is related to the open-loop gain ($A$) and the feedback fraction ($\beta$) by the formula:

$$ A_f = \frac{A}{1 + \beta A} $$

Here:

• $A_f$ is the closed-loop gain (gain with negative feedback).
• $A$ is the open-loop gain (gain without feedback).
• $\beta$ is the feedback fraction, which is the portion of the output signal fed back to the input. For negative feedback, $\beta$ is typically positive.

Since $A$ (open-loop gain) is usually very large, and $\beta$ is positive, the term $(1 + \beta A)$ in the denominator is always greater than 1. When the denominator is greater than the numerator (assuming $A$ is positive), the resulting fraction is less than 1 times the numerator. In this case, the denominator is $(1+\beta A)$ and the numerator is $A$. Therefore, the closed-loop gain $A_f$ will always be less than the open-loop gain $A$.

For example, if an amplifier has an open-loop gain ($A$) of 100 and a feedback fraction ($\beta$) of 0.1, the closed-loop gain ($A_f$) would be:

$$ A_f = \frac{100}{1 + (0.1 \times 100)} = \frac{100}{1 + 10} = \frac{100}{11} \approx 9.09 $$

As you can see, the gain has decreased from 100 to approximately 9.09 due to the negative feedback.

Effects of Negative Feedback

Applying negative feedback to an amplifier circuit has several important effects, one of which is the reduction in gain. Other effects include:

• Increased Bandwidth: The range of frequencies over which the amplifier provides useful gain increases.
• Reduced Distortion: Non-linear distortion in the output signal is decreased.
• Improved Stability: The amplifier is less likely to oscillate.
• Modified Input and Output Impedances: Negative feedback changes the effective input and output resistances of the circuit depending on the type of feedback configuration used.

While negative feedback reduces the gain, this trade-off is often acceptable because the benefits in terms of stability, bandwidth, and distortion reduction are highly desirable in many applications.

Conclusion on Amplifier Gain with Negative Feedback

In summary, the application of negative feedback in an amplifier circuit results in a significant reduction in the overall voltage or current gain compared to the open-loop gain. The feedback signal opposes the input signal, effectively decreasing the net input signal the amplifier processes, leading to a lower output signal level for the same original input, hence lower gain.

Revision Table: Amplifier Feedback Concepts

Additional Information on Amplifier Feedback

Feedback is a fundamental concept in control systems and electronics. In amplifier circuits, feedback is used to modify performance characteristics. Negative feedback is widely used because its benefits often outweigh the disadvantage of reduced gain. This reduction in gain can often be compensated by using a multi-stage amplifier or increasing the open-loop gain, provided stability is maintained.

The amount of gain reduction is determined by the feedback fraction ($\beta$). A larger $\beta$ means more feedback, leading to lower closed-loop gain but generally greater improvements in other characteristics. In the formula $A_f = \frac{A}{1 + \beta A}$, if $\beta A \gg 1$, then $A_f \approx \frac{A}{\beta A} = \frac{1}{\beta}$. This shows that when the open-loop gain is very high, the closed-loop gain becomes largely independent of the amplifier's internal gain variations and is primarily determined by the feedback network, which can be made very stable and precise.