Feedback

Feedback returns part of the output to the input. Learn negative vs positive feedback, the closed-loop gain formula A/(1 + Aβ), loop gain, desensitivity, bandwidth extension, impedance changes, the four feedback topologies, and stability (Barkhausen, phase margin).

Harold Black's 1927 invention of negative feedback made telephone amplifiers stable. Today feedback is everywhere: op-amp circuits, voltage regulators, PLLs, motor control. Positive feedback, on the other hand, creates oscillators and latches.

An analogy

Negative feedback is like driving while watching the road: small deviations are corrected continuously. Positive feedback is like a microphone near its speaker — the squeal grows on its own.

Negative vs positive

Negative feedback subtracts the fed-back signal: gain drops, but becomes accurate, linear and wide-band. Positive feedback adds: gain rises, leading to oscillation or bistable (snap-action) behaviour like Schmitt triggers.

Benefits of negative feedback

Stable gain set by passive parts (1/β), reduced distortion by 1 + Aβ, extended bandwidth, and controllable input/output impedance.

Topologies

Series–shunt (voltage amplifier: raises Z_in, lowers Z_out), shunt–series (current amplifier), series–series (transconductance), shunt–shunt (transimpedance — photodiode amplifiers).

Stability

If loop phase reaches −180° while |Aβ| ≥ 1, negative feedback becomes positive and the circuit oscillates. Phase margin ≥ 45–60° gives stable, well-damped response. Compensation capacitors add a dominant pole.

Formulas

• Closed-loop gain: A_f = A / (1 + Aβ) ≈ 1/β (Aβ ≫ 1)
• Desensitivity: dA_f/A_f = (1/(1 + Aβ)) × dA/A
• Bandwidth extension: BW_f = BW (1 + Aβ)
• Barkhausen (oscillation): Aβ = 1 ∠ 0° (or 360°)

Worked example: Gain accuracy

Given: A = 100 000, β = 0.01

Find: A_f.

• A_f = 100 000/(1 + 1000) = 99.90

Answer: 99.90 (ideal 100)

Worked example: Desensitivity

Given: A falls 50 % to 50 000

Find: New A_f.

• A_f = 50 000/(1 + 500) = 99.80

Answer: Only 0.1 % change for a 50 % change in A

Common mistakes

• Wrong: Assuming more feedback is always stable. — Right: Check phase margin; heavy feedback can oscillate.
• Wrong: Forgetting feedback changes impedances. — Right: Topology determines Z_in/Z_out.

Applications

• Precision amplifiers: Gain set by resistor ratios.
• Regulators: Error amplifiers hold output voltage constant.
• Oscillators: Positive feedback at one frequency.

Key takeaways

• A_f = A/(1 + Aβ) ≈ 1/β.
• Negative feedback: accuracy, linearity, bandwidth.
• Positive feedback: oscillators, latches.
• Keep phase margin ≥ 45°.

Going further

• Nyquist criterion: Encirclement test for stability.
• Compensation: Dominant-pole and lead networks.
• Loop-gain measurement: Middlebrook injection method.