System Feedback Loop Gain Calculator

Calculate open-loop gain, closed-loop gain (with feedback), loop gain, and gain margin for negative and positive feedback systems.

Forward Path Gain (A) — dimensionless

Feedback Factor (β) — dimensionless (0 to 1 for typical systems)

Feedback Type

Results will appear here.

Loop Gain: T = A · β

Closed-Loop Gain (Negative Feedback): A_cl = A / (1 + Aβ)

Closed-Loop Gain (Positive Feedback): A_cl = A / (1 − Aβ)

Gain (dB): G_dB = 20 · log₁₀(|G|)

Gain Margin (dB): GM = −20 · log₁₀(|Aβ|) [negative feedback]

Sensitivity: S = 1 / (1 + Aβ) [negative feedback]

Desensitivity Factor: D = 1 + Aβ [negative feedback]

Single-loop, single-input single-output (SISO) feedback system.
A and β are real, frequency-independent (DC or mid-band) values.
Negative feedback: error signal = input − feedback signal.
Positive feedback: error signal = input + feedback signal.
Gain margin calculation assumes phase crossover occurs at 180° (standard Bode criterion); for full stability analysis, phase margin and Nyquist plot are required.
Positive feedback systems with Aβ ≥ 1 are inherently unstable (used intentionally in oscillators and Schmitt triggers).
Reference: Sedra & Smith, Microelectronic Circuits, 7th ed., Ch. 10; Ogata, Modern Control Engineering, 5th ed., Ch. 7.

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