Example Data Table
| Feedback | G | H (β) | Loop Gain (G·H) | Closed-loop Gain (Acl) |
|---|---|---|---|---|
| Negative | 100,000 | 0.01 | 1,000.0000 | 99.9001 |
| Negative | 50,000 | 0.02 | 1,000.0000 | 49.9500 |
| Negative | 2,000 | 0.1 | 200.0000 | 9.9502 |
| Positive | 100 | 0.005 | 0.5000 | 200.0000 |
| Positive | 20 | 0.04 | 0.8000 | 100.0000 |
Formula Used
For a basic feedback system with open-loop gain G and feedback factor H:
- Negative feedback: Acl = G / (1 + G·H)
- Positive feedback: Acl = G / (1 − G·H)
The loop gain is L = G·H. Sensitivity is computed as:
- S = 1 / (1 + L) for negative feedback
- S = 1 / (1 − L) for positive feedback
How to Use This Calculator
- Select a mode: compute Acl, solve G, or solve H.
- Choose negative or positive feedback for the correct denominator.
- Enter your known values in linear units, not dB.
- Press Calculate to show results above the form.
- Use CSV or PDF to export a compact calculation report.
FAQs
1) What is closed-loop gain?
It is the gain of a system after feedback is applied. It is often more stable and predictable than open-loop gain, especially with negative feedback.
2) What does the feedback factor H (β) represent?
H is the fraction of the output fed back to the input summing node. It is usually dimensionless and comes from your feedback network or sensor scaling.
3) Why do negative and positive feedback use different formulas?
The sign of feedback changes how the loop gain affects the denominator. Negative feedback adds stability via 1 + G·H, while positive feedback can reduce the denominator and cause runaway near 1 − G·H = 0.
4) When should I use dB display?
Use dB when comparing gains across wide ranges or frequency response plots. This calculator uses 20·log10(|gain|) for amplitude gains.
5) What does “near-singularity” mean here?
It warns that the denominator is close to zero, so small input changes can cause huge output swings. This is especially important with positive feedback where instability is common.
6) Can this be used for amplifiers and control loops?
Yes. It matches the common block-diagram model for linear feedback systems. For real designs, also consider phase margin, bandwidth limits, and nonlinearity.
7) How accurate are the results if G varies?
With strong negative feedback (large G·H), closed-loop gain becomes less sensitive to G changes. The sensitivity value in the results shows that reduction.
8) What inputs should be linear rather than in dB?
Enter G, H, and target Acl as linear ratios. If you only have dB values, convert them to linear before using this calculator.