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Feedback concept and square wave oscillator

Short answer

Feedback returns part of output to input; negative feedback (opposite phase) reduces gain and improves stability via Af=A/(1+Aβ), while positive feedback (in phase) increases gain and causes oscillation when Aβ=1. The square wave oscillator uses an op-amp comparator with positive feedback and RC charging; capacitor voltage ramps between ±βVsat, output toggles, generating a square wave with f≈1/(2.2RC) for R1=R2.

Explain the concept of feedback theory. Describe the working principle of square wave oscillator circuit using op-amp.

Feedback theory

Feedback means returning a part of the output signal to the input. Let the amplifier gain be A and the feedback fraction be β.

  • Feedback signal = β Vo, and the input to the amplifier is Vi' = Vs ± β Vo.
  • Negative feedback (feedback opposes the input): Af = A/(1 + Aβ). The gain falls, but stability improves, distortion and noise are reduced, and the bandwidth increases.
  • Positive feedback (feedback adds to the input): Af = A/(1 − Aβ). The gain increases; when Aβ = 1, Af = ∞ and the circuit gives an output without any input, i.e. it oscillates.

Oscillators use positive feedback and need |Aβ| = 1 with a 0° or 360° loop phase shift (Barkhausen criteria).

Square wave oscillator using op-amp

          +----------[ R ]-----------+
          |                          |
          |         |\               |
          +---------|- \             |
          |         |   >------------+----o Vo
         === C   +--|+ /             |
          |      |  |/               |
         GND     +-------[ R2 ]------+
                 |
               [ R1 ]
                 |
                GND

The op-amp works as a comparator. The resistors R2 and R1 supply positive feedback, with β = R1/(R1 + R2). R and C set the timing.

  1. Output at +Vsat: the non-inverting input is at +βVsat, and C charges through R.
  2. When Vc > +βVsat, the output switches to −Vsat and the threshold changes to −βVsat.
  3. C now discharges and charges negatively. When Vc < −βVsat, the output switches back to +Vsat.
  4. This repeats, giving a symmetrical square wave.

T = 2RC ln[(1 + β)/(1 − β)]. With R1 = R2, T ≈ 2.2 RC.

✓ Answer checked by Claude Opus 5.5 (high effort)

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