Workbench / Output Stage

Feedback & Damping

Global NFB, output impedance and damping factor.

Open-Loop Amplifier

Open-loop gain A

Input to speaker terminals

Open-loop output Z

Open-loop low −3 dB

Open-loop high −3 dB

Feedback Network

Feedback resistor Rf

Cathode resistor Rk

Speaker load

Global feedback loop

Feedback amount

8.5 dB

Closed-loop gain

30.00×

29.5 dB

Output Z

1.500 Ω

open loop 4 Ω

Damping factor

5.3

open loop 2.0

Open loopClosed loop

Engineering Notes

How it works

Negative feedback samples the output, scales it down by the feedback fraction β, and subtracts it from the input. In a typical valve amp, a resistor Rf runs from the speaker terminal back to the unbypassed cathode resistor Rk of an early stage:

β = Rk / (Rk + Rf) Loop gain = A·β Feedback = 20·log₁₀(1 + A·β) dB

Every quantity that feedback improves is improved by the same factor (1 + Aβ):

A_cl = A/(1+Aβ) Zout_cl = Zout/(1+Aβ) f_low/(1+Aβ) · f_high×(1+Aβ)

Damping factor is the speaker impedance divided by the amplifier's output impedance. A high damping factor gives the amplifier tight control over cone motion (especially bass resonance). Feedback-less SET triode amps have DF ≈ 2–5; pentode push-pull amps with 20 dB of feedback reach 15–30; solid-state amps exceed 100.

Guitar amps like the Vox AC30 and many Marshalls trade feedback for "looseness" and raw gain, a deliberate tonal choice. The simple single-pole model used here ignores the extra transformer poles that limit how much feedback can be applied safely.

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