Feedback System Solver Calculator

Calculator Inputs

Use this solver for scalar linear feedback models. It handles negative and positive feedback, missing-variable solving, and output estimation.

Solve Mode

Choose what the solver should determine.

Feedback Type

Negative uses 1 + GH. Positive uses 1 - GH.

Reference Input R

Used for output plots and Y calculations.

Open-Loop Gain G

Required for full analysis, output, and H solving.

Feedback Factor H

Required for full analysis, output, and G solving.

Target Closed-Loop Gain T

Needed when solving G or H from a target.

Open-Loop Bandwidth

Optional single-pole estimate for closed-loop bandwidth.

Graph Samples

Higher values create smoother lines.

Plotly Graph

The graph compares open-loop output and closed-loop output versus reference input. It helps visualize the effect of feedback on amplification.

Example Data Table

Case	Feedback Type	G	H	R	Computed T	Output Y
Amplifier with moderate negative feedback	Negative	10	0.10	2	5	10
Strong stabilizing loop	Negative	25	0.20	1.5	4.1667	6.25
Positive feedback near critical level	Positive	8	0.10	1	40	40

Formula Used

Negative feedback closed-loop gain: T = G / (1 + GH)

Positive feedback closed-loop gain: T = G / (1 - GH)

Output: Y = T × R

Error ratio: E / R = 1 / (1 ± GH)

Sensitivity: S = 1 / (1 ± GH)

Bandwidth estimate: BW_CL ≈ BW_OL × |1 ± GH|

The symbol ± follows the loop sign. Use plus for negative feedback and minus for positive feedback. These formulas fit scalar linear feedback models and simplified single-pole bandwidth estimation.

How to Use This Calculator

Select the solving mode that matches your problem.
Choose negative or positive feedback.
Enter the known values for G, H, R, and optional bandwidth.
Enter a target closed-loop gain only when solving G or H.
Click Solve Feedback System.
Review the result table shown below the header and above the form.
Study the graph to compare open-loop and closed-loop behavior.
Export the result as CSV or PDF when needed.

Frequently Asked Questions

1. What does this feedback solver calculate?

It calculates closed-loop gain, output, loop gain, return difference, error ratio, sensitivity, desensitivity, and an optional closed-loop bandwidth estimate.

2. What is the difference between negative and positive feedback?

Negative feedback uses 1 + GH and usually improves robustness. Positive feedback uses 1 - GH and can sharply increase gain, but it may also cause instability.

3. When should I use full analysis mode?

Use full analysis when you already know G and H and want a complete set of metrics, including output, sensitivity, and return difference.

4. Can this page solve for missing open-loop gain?

Yes. Choose the mode for solving open-loop gain, then enter feedback factor and target closed-loop gain. The page will calculate the needed G value.

5. Can it solve for feedback factor too?

Yes. Select the feedback-factor solving mode, provide open-loop gain and target closed-loop gain, and the solver returns H with the related loop metrics.

6. Is the bandwidth estimate exact?

No. It is a simplified estimate based on a basic single-pole approximation. Real systems may require transfer-function poles, zeros, and frequency response analysis.

7. Why does the solver warn about instability?

The warning appears when the return difference approaches zero or turns negative. That means the loop becomes extremely sensitive or mathematically undefined.

8. What does the graph represent?

The graph plots output versus reference input. One trace uses open-loop gain. The other uses closed-loop gain, showing how feedback changes amplification.