Effects of Negative Feedback on Amplifiers

May 30, 2024

Review flashcards

Lecture Notes: Effects of Negative Feedback on Amplifiers

Properties of Negative Feedback

  • Bandwidth Extension
  • Increase in Input Resistance
  • Decrease in Output Resistance

Bandwidth Extension

Key Concepts

  • Bandwidth = Difference between lower cutoff frequency (fL) and upper cutoff frequency (fU).
  • Negative feedback increases bandwidth.

Frequency Response Diagrams

  • Without feedback: Lower cutoff frequency (fL) and upper cutoff frequency (fU).
  • With feedback: Lower cutoff frequency (fL') and upper cutoff frequency (fU').
  • Negative feedback decreases fL and increases fU.

Steps to Prove Bandwidth Extension

Lower Cutoff Frequency

  1. Gain at low frequency without feedback: AL = AM / (1 - j(fL/f)).
    • AM = Mid-band gain.
    • fVL = Lower cutoff frequency without feedback.
  2. Gain with feedback: ALF = AL / (1 + ALβ).
    • Substitute AL value: ALF = AM / (1 - j(fL/f)) / (1 + (AM / (1 - j(fL/f)) * β)).
  3. Simplify: ALF = AMF / (1 - j(fL'/f)).
    • AMF = Gain with feedback (AM / (1 + AMβ)).
    • fL' = fL / (1 + AMβ).
  4. Conclusion: Lower cutoff frequency decreases with feedback.

Upper Cutoff Frequency

  1. Gain at high frequency without feedback: AU = AM / (1 + j(f/fU)).
  2. Gain with feedback: AUF = AU / (1 + AUβ).
    • Substitute AU value: AUF = AMF / (1 + j(f/fU')).
    • fU' = fU * (1 + AMβ).
  3. Conclusion: Upper cutoff frequency increases with feedback.
  • Overall Bandwidth Conclusion: Bandwidth increases due to the extension of fL and fU by the factor (1 + AMβ).

Increase in Input Resistance

Key Concepts

  • High input resistance reduces loading effect.

Steps to Prove Increased Input Resistance

  1. Consider feedback amplifier model with input resistance RI and feedback voltage VF.
  2. Input impedance with feedback: RIF = VS / II.
    • Substitute VI = VS - VF;
    • VS = VI + VF = VI + βVO.
    • VO = A * VI.
  3. Simplify: RIF = RI * (1 + Aβ).
  • Conclusion: Input impedance increases by the factor (1 + Aβ).

Decrease in Output Resistance

Key Concepts

  • Low output resistance avoids loading effect on subsequent stages.

Steps to Prove Decreased Output Resistance

  1. Consider small signal model with output resistance RO and current IO.
  2. Voltage drop: IORO = VO - AVI.
  3. Assume no input signal (VS = 0), the feedback voltage acts alone: VI = -VF.
    • Substitute: IORO = VO(1 + Aβ).
  4. Simplify: ROF = RO / (1 + Aβ).
  • Conclusion: Output resistance decreases by the factor (1 + Aβ).