Feedback Amplifiers

Why it matters

Feedback amplifiers are essential in electronic systems for improving performance characteristics such as gain stability, bandwidth, and distortion reduction. They are widely used in applications like audio amplifiers, control systems, and communication devices, where precise signal amplification is crucial.

Key ideas

• Feedback Concept: Feedback involves taking a portion of the output signal and returning it to the input. This can be done in two ways: positive feedback (regenerative) and negative feedback (degenerative).
• Types of Feedback: There are four basic types of feedback topologies based on the input and output connections:
  1. Voltage Series Feedback (Series-Shunt)
  2. Voltage Shunt Feedback (Shunt-Shunt)
  3. Current Series Feedback (Series-Series)
  4. Current Shunt Feedback (Shunt-Series)
• Effects of Negative Feedback:
  • Gain Desensitization: Reduces the sensitivity of the amplifier gain to component variations.
  • Bandwidth Extension: Often increases bandwidth for a dominant-pole amplifier; it is not universal for arbitrary multipole systems.
  • Distortion Reduction: Minimizes nonlinear distortion.
  • Noise: Suppression depends on where noise enters the loop. Input-referred noise and noise from the feedback network are not generally eliminated.
• Feedback Factor (β): The fraction of the output signal that is fed back to the input.
• Loop Gain (Aβ): Product of the amplifier gain (A) and the feedback factor (β). It determines the stability and performance of the feedback system.

Formulas

The gain relation is for a stable negative-feedback voltage amplifier with compatible signal definitions. The bandwidth formula assumes a single-pole low-pass open-loop response and frequency-independent feedback, with A denoting DC gain.

• Closed-loop gain for negative feedback: A_f = A / (1 + Aβ)
  • A_f: Closed-loop gain (unitless)
  • A: Open-loop gain (unitless)
  • β: Feedback factor (unitless)
• Bandwidth with feedback: BW_f = BW * (1 + Aβ)
  • BW_f: Bandwidth with feedback (Hz)
  • BW: Original bandwidth without feedback (Hz)

Worked example

Given: An amplifier with an open-loop gain A = 1000, feedback factor β = 0.01, and original bandwidth BW = 20 kHz.

1. Calculate the closed-loop gain:

   • Formula: A_f = A / (1 + Aβ)
   • Calculation: A_f = 1000 / (1 + 1000 * 0.01)
   • A_f = 1000 / 11
   • A_f ≈ 90.91

2. Calculate the bandwidth with feedback:

   • Formula: BW_f = BW * (1 + Aβ)
   • Calculation: BW_f = 20,000 * (1 + 1000 * 0.01)
   • BW_f = 20,000 * 11
   • BW_f = 220,000 Hz

Final Answer: The closed-loop gain is 90.91 (unitless) and the bandwidth with feedback is 220,000 Hz.

Common mistakes

• Confusing positive and negative feedback, leading to incorrect stability analysis.
• Miscalculating the feedback factor (β), which affects the loop gain and overall performance.
• Ignoring the effect of feedback on bandwidth and distortion.

For GATE EC

Questions on feedback amplifiers often involve calculating closed-loop gain, bandwidth, and stability analysis. Practice problems that require understanding the impact of different feedback topologies and calculating loop gain.

Quick check

1. What is the primary purpose of negative feedback in amplifiers?
2. Name the four basic types of feedback topologies.
3. How does negative feedback affect the bandwidth of an amplifier?

Answers: 1. To improve stability and reduce distortion. 2. Voltage Series, Voltage Shunt, Current Series, Current Shunt. 3. It increases bandwidth under the stated dominant-pole assumptions; stability must be checked.