Understanding Feedback Amplifiers and Oscillation

Let's analyze the behavior of a feedback amplifier under the conditions given: the feedback voltage is in opposite phase, and the gain is less than 1. To understand if it can work as an oscillator, we need to look at the fundamental requirements for oscillation in an electronic circuit.

What is an Oscillator?

An oscillator is a circuit that produces a repetitive waveform (like a sine wave or square wave) without any external input signal. It essentially converts DC power into AC power at a specific frequency. Oscillators work based on the principle of positive feedback.

Conditions for Oscillation (Barkhausen Stability Criterion)

For sustained oscillations to occur in an amplifier with feedback, two main conditions, known as the Barkhausen criterion, must be met:

• Magnitude Condition: The magnitude of the loop gain, $\text{|A}\beta\text{|}$, must be equal to or greater than unity ($\text{|A}\beta\text{|} \ge 1$). Here, A is the gain of the amplifier and $\beta$ (beta) is the gain of the feedback network (the fraction of the output fed back to the input).
• Phase Condition: The total phase shift around the feedback loop must be zero degrees or an integer multiple of 360 degrees ($0^\circ$ or $360^\circ, 720^\circ, \dots$). This means the signal fed back to the input must be in phase with the original input signal at the oscillation frequency. This in-phase feedback is called positive feedback.

Analyzing the Given Conditions

The question provides two key pieces of information about the feedback amplifier:

1. Feedback voltage is in opposite phase: This means the feedback signal is 180 degrees out of phase with the input signal. This is the definition of negative feedback. Negative feedback reduces the effective input signal and thus the overall gain of the amplifier. It is used to improve stability, reduce distortion, and increase bandwidth.
2. The gain is less than 1: While the question doesn't specify if this is the open-loop gain (A), the closed-loop gain (with feedback), or the loop gain ($\text{A}\beta$), in the context of oscillation requirements, the loop gain is critical. If the overall gain with negative feedback is less than 1, it strongly suggests that the loop gain required for oscillation ($\text{|A}\beta\text{|} \ge 1$) is not being met, especially given the phase condition violation.

Why Oscillation Will Not Occur

Based on the Barkhausen criterion and the given conditions:

• The phase condition for oscillation requires a total loop phase shift of $0^\circ$ or $360^\circ$. This requires positive feedback. The question states the feedback voltage is in "opposite phase", which means a $180^\circ$ phase shift introduced by the feedback connection relative to positive feedback. If the amplifier contributes $180^\circ$ phase shift (as is common with common-emitter or common-source stages), positive feedback is achieved when the feedback network adds $0^\circ$ or $360^\circ$. Opposite phase feedback means the feedback network effectively adds another $180^\circ$ phase shift relative to the positive feedback case, resulting in a total loop phase shift far from the required $0^\circ$ or $360^\circ$ for oscillation. Therefore, the phase condition for oscillation is not met because the feedback is negative (opposite phase).
• The magnitude condition for oscillation requires the loop gain $\text{|A}\beta\text{|}$ to be $\ge 1$. The question states the gain is less than 1. While this might refer to closed-loop gain, if the loop gain itself is less than 1, the magnitude condition is also not met. Negative feedback inherently reduces gain, making it even harder to meet the $\text{|A}\beta\text{|} \ge 1$ requirement, especially with an initial gain less than 1 (whether open-loop or indicating a very low loop gain).

Since both the phase condition (positive feedback) and likely the magnitude condition ($\text{|A}\beta\text{|} \ge 1$) for oscillation are not met, the circuit cannot work as an oscillator.

Conclusion

An amplifier with feedback in opposite phase (negative feedback) and a gain less than 1 fundamentally lacks the necessary conditions for oscillation. Negative feedback stabilizes the amplifier and reduces gain, directly opposing the requirements for generating oscillations.

Therefore, such an amplifier will never work as an oscillator.

Revision Table: Feedback Types and Amplifier Behavior

Additional Information: Applications of Feedback

Feedback is a crucial concept in amplifier design, offering various benefits depending on whether it's positive or negative.

• Negative Feedback Applications:
  • Used extensively in linear amplifiers (like operational amplifiers) to:
  • Stabilize the amplifier gain against variations in temperature, power supply, or component aging.
  • Reduce distortion in the output signal.
  • Increase the bandwidth of the amplifier.
  • Modify input and output impedances.
• Positive Feedback Applications:
  • Used in oscillator circuits (like Wien bridge oscillators, phase-shift oscillators) to sustain oscillations.
  • Used in regenerative circuits and Schmitt triggers for hysteresis and switching behavior.
  • Can be used to increase gain, but at the cost of stability (leading to oscillation if conditions are met).

In summary, negative feedback is used for stable amplification, while positive feedback, when combined with the Barkhausen criteria, is essential for building oscillators.