Feedback & Stability
Negative feedback is the most powerful and most controversial tool in amplifier design. It trades gain for linearity, lowers output impedance, and extends bandwidth — but demands careful attention to stability. Explore the theory and the trade-offs interactively.
What Is Feedback?
A portion of the output signal is returned to the input. The direction determines everything.
Every amplifier has imperfections: nonlinearity, noise, output impedance that varies with frequency. Feedback is the deliberate practice of taking a fraction of the output and combining it with the input to correct these errors. In negative feedback (NFB), the returned signal opposes the input, reducing gain but also reducing distortion, noise, and impedance irregularities by the same factor.
Positive feedback adds to the input, increasing gain until the circuit oscillates — useful in oscillators but catastrophic in amplifiers. The entire art of amplifier feedback design is ensuring that negative feedback stays negative across all frequencies.
- • Reduces gain by factor 1+Aβ
- • Reduces distortion by same factor
- • Lowers output impedance
- • Extends bandwidth
- • Desensitizes to component drift
- • Increases gain toward infinity
- • Used in oscillators, flip-flops
- • Causes motorboating, squealing
- • Result of excessive NFB + phase shift
- • The enemy of amplifier stability
Local vs Global Feedback
Feedback can be applied within a single stage or around the entire amplifier.
Local feedback operates within a single gain stage. The most common form is the unbypassed cathode resistor: signal current flowing through Rk creates a voltage that opposes the grid drive. Plate-to-grid feedback (a resistor from plate to grid) is another form. Local feedback is inherently stable because it involves only one stage of phase shift.
Global feedback takes a sample from the output transformer secondary and returns it to an early stage — typically the input cathode or a dedicated summing point. It corrects errors in every stage at once, including the output transformer, but introduces multiple poles of phase shift that can cause instability.
- • Always stable (single pole)
- • Linearizes one stage at a time
- • Does not correct OPT distortion
- • Forms: unbypassed Rk, plate-to-grid
- • Corrects entire signal chain incl. OPT
- • Greatest distortion & impedance reduction
- • Multi-pole — stability is critical
- • Typical: 6–20 dB in hi-fi amps
NFB Gain & Distortion
Explore how feedback fraction trades gain for linearity.
Impedance & Damping Factor
NFB transforms pentode-like output impedance toward triode-like values.
A tube amplifier's output impedance determines how well it controls the loudspeaker. High output impedance (typical of pentode stages) means the speaker's own resonances are poorly damped. Negative feedback reduces output impedance by the same 1+Aβ factor, dramatically improving the damping factor.
Bandwidth & Stability
Feedback extends bandwidth but introduces the risk of oscillation.
The gain-bandwidth product is approximately constant: as feedback reduces gain, the bandwidth expands proportionally. But every stage adds phase shift at high frequencies. When the total phase shift reaches 180° while loop gain is still above unity, the negative feedback becomes positive and the amplifier oscillates.
The phase margin is the safety buffer: how far the phase is from −180° at the frequency where loop gain crosses 0 dB. A phase margin above 45° is considered stable; below 30° you'll hear ringing on transients. Below 0° — oscillation.
Stability Compensation
Practical methods to keep your feedback loop stable.
The goal of compensation is to ensure adequate phase margin at all frequencies. In tube amplifiers, the output transformer is usually the dominant source of high-frequency phase shift. Several proven techniques exist:
A series R-C across the output transformer secondary. Tames the inductive rise in impedance at HF and prevents the transformer resonance from adding excess phase shift.
A small capacitor (10–100 pF) from the plate of a gain stage to its grid. Multiplied by the stage gain (Miller effect), it creates a dominant pole that rolls off the loop gain before other poles add dangerous phase shift.
A resistor in series with the feedback path, bypassed by a small capacitor. Adds a phase lead at high frequencies to compensate for the lag introduced by the amplifier poles. Common in Williamson-type circuits.
A small capacitor at the feedback summing point to ground. Rolls off the feedback signal at HF, reducing loop gain before problematic phase shifts accumulate. Simple but effective.
- • Low-quality output transformers with poor HF response and unpredictable phase behavior
- • Single-ended triode amps that already have low distortion and output impedance
- • When you cannot square-wave test and verify stability into reactive loads
- • Guitar amplifiers where distortion character is part of the desired tone
The Great Debate
Zero feedback vs deep NFB: two valid approaches to amplifier design.
Few topics in audio generate more passionate disagreement than negative feedback. The debate has raged since the 1950s and shows no sign of settling. Both sides have legitimate technical and subjective arguments.
- • Measurably lower THD and IMD
- • Lower output impedance, better speaker control
- • Flatter frequency response
- • Reduced sensitivity to tube aging and drift
- • Proven in countless classic hi-fi designs
- • The science is unambiguous: NFB reduces all forms of distortion
- • NFB can convert benign low-order harmonics into higher-order ones
- • Transient response: no ringing, no overshoot
- • Stability guaranteed regardless of load impedance
- • Simpler circuit, fewer failure modes
- • High Zout can be a feature: speaker damping preference
- • Many listeners prefer the subjective sound
The pragmatic view: Neither approach is universally superior. A well-designed amplifier with moderate NFB (6–12 dB) and proper compensation can outperform a zero-feedback design on the test bench. But a poorly stabilized high-NFB amplifier can sound worse than a simple zero-feedback SET, because transient intermodulation distortion (TIM) and ringing artifacts are more objectionable than gentle harmonic distortion. The quality of your output transformer matters more than the amount of feedback you use.
Key Equations
The essential formulas for feedback analysis, all in one place.
Test Your Knowledge
Validate your understanding of feedback and stability before moving on.
What does negative feedback do to distortion?