System Feedback Loop Gain Calculator
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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
Negative Feedback Positive Feedback
Calculate
Results will appear here.
function sysCalc() { const A = parseFloat(document.getElementById('sys-forward-gain').value); const beta = parseFloat(document.getElementById('sys-feedback-factor').value); const fbType = document.getElementById('sys-feedback-type').value; const resultDiv = document.getElementById('sys-result');
// --- Input Validation --- if (isNaN(A) || isNaN(beta)) { resultDiv.innerHTML = '⚠ Please enter valid numbers for both Forward Path Gain and Feedback Factor.'; return; } if (A === 0) { resultDiv.innerHTML = '⚠ Forward Path Gain (A) cannot be zero.'; return; } if (beta ⚠ Feedback Factor (β) must be non-negative. Use the Feedback Type selector to choose positive or negative feedback.'; return; }
// --- Core Calculations --- // Loop Gain T = A * β (always positive magnitude; sign handled by feedback type) const loopGain = A * beta;
// Closed-Loop Gain: // Negative feedback: Acl = A / (1 + Aβ) // Positive feedback: Acl = A / (1 - Aβ) let denominator, closedLoopGain, feedbackSign; if (fbType === 'negative') { denominator = 1 + loopGain; feedbackSign = '+'; } else { denominator = 1 - loopGain; feedbackSign = '−'; }
// Check for instability (denominator = 0) if (Math.abs(denominator) ⚠ System is at the boundary of instability (1 ' + (fbType === 'negative' ? '+' : '−') + ' Aβ = 0). Closed-loop gain is undefined (→ ∞).'; return; }
closedLoopGain = A / denominator;
// Gain in dB const openLoopGain_dB = 20 * Math.log10(Math.abs(A)); const closedLoopGain_dB = 20 * Math.log10(Math.abs(closedLoopGain)); const loopGain_dB = 20 * Math.log10(Math.abs(loopGain));
// Gain Margin (only meaningful for negative feedback): // GM = 1 / |Aβ| expressed in dB → GM_dB = -20*log10(|Aβ|) // Positive GM means stable; negative means unstable. const gainMargin_dB = -loopGain_dB;
// Sensitivity (negative feedback only): S = 1 / (1 + Aβ) const sensitivity = fbType === 'negative' ? (1 / denominator) : null;
// Desensitivity factor D = 1 + Aβ (negative feedback) const desensitivity = fbType === 'negative' ? denominator : null;
// Stability assessment let stabilityNote = ''; if (fbType === 'negative') { stabilityNote = gainMargin_dB >= 0 ? '✅ System is stable (loop gain 1 — verify phase margin; system may be unstable.'; } else { if (loopGain >= 1) { stabilityNote = '⚠ Positive feedback with Aβ ≥ 1 — system is unstable (oscillatory or saturating).'; } else { stabilityNote = '✅ Positive feedback with Aβ isFinite(v) ? v.toFixed(d) : '∞'; const fmtdB = (v) => isFinite(v) ? v.toFixed(3) + ' dB' : '∞ dB';
let html = '### Results
';
const row = (label, value, note='') =>
${label}
${value}
${note ?${note}: ''};
html += row('Forward Path Gain (A)', fmt(A, 4), ''); html += row('Feedback Factor (β)', fmt(beta, 6), ''); html += row('Loop Gain (T = Aβ)', fmt(loopGain, 6), fmtdB(loopGain_dB)); html += row('Open-Loop Gain (A)', fmt(A, 4), fmtdB(openLoopGain_dB)); html += row('Closed-Loop Gain (Acl)', fmt(closedLoopGain, 6), fmtdB(closedLoopGain_dB));
if (fbType === 'negative') { html += row('Gain Margin (GM)', fmtdB(gainMargin_dB), gainMargin_dB >= 0 ? 'Stable' : 'Unstable'); html += row('Sensitivity (S = 1/(1+Aβ))', fmt(sensitivity, 6), 'Fractional change in Acl per unit change in A'); html += row('Desensitivity Factor (1+Aβ)', fmt(desensitivity, 4), 'Gain reduction factor due to feedback'); }
html += ''; html += `${stabilityNote}
`; resultDiv.innerHTML = html; }
#### Formulas
Loop Gain: T = A · β
Closed-Loop Gain (Negative Feedback): Acl = A / (1 + Aβ)
Closed-Loop Gain (Positive Feedback): Acl = A / (1 − Aβ)
Gain (dB): GdB = 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]
#### Assumptions & References
- Reference: Sedra & Smith, Microelectronic Circuits, 7th ed., Ch. 10; Ogata, Modern Control Engineering, 5th ed., Ch. 7.
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