Ontological Layer: Closed-Loop Control

Feedback

Self-Correction & Gain Stabilization

The Cycle of Correction

An open-loop amplifier is blind to its own errors; its gain fluctuates wildly with temperature and manufacturing tolerances. By deliberately returning a fraction of the output to oppose the input, a system sacrifices raw amplification for stability, broader bandwidth, and reduced distortion. This is the transition from a dumb amplifier to a controlled system.

OUTPUT → SAMPLE → FEEDBACK NETWORK (β) → RETURN → MIX / OPPOSE → ERROR REDUCTION → STABLE GAIN → CLOSED LOOP

The 12 Closed-Loop Nodes

Ontological Mapping: Nodes 01 - 97

GROUP 01-10

Concept & Structure

01 The Feedback Concept
02 Open-Loop vs Closed-Loop
08 Forward Path Gain (A)
10 Feedback Factor (β)

GROUP 11-14

Positive vs Negative

11 Positive (Regenerative) Feedback
12 Negative (Degenerative) Feedback
Stability vs Instability
Error Correction Principle

GROUP 15-25

The Four Topologies

21 Voltage-Series (Series-Shunt)
22 Voltage-Shunt (Shunt-Shunt)
23 Current-Series (Series-Series)
24 Current-Shunt (Shunt-Series)

GROUP 26-31

The Feedback Equation

Af =

1 + Aβ

27 Closed-Loop Gain (Af)
30 Loop Gain (Aβ)
31 The General Feedback Equation
Return Ratio Concepts

GROUP 32-35

Gain Stabilization

32 Gain Desensitivity
33 Gain Stabilization Factor
35 Parameter Variation Immunity
Trading Gain for Predictability

GROUP 36-38, 45

Performance Upgrade

36 Distortion Reduction
37 Noise Reduction (Internal)
38 Bandwidth Extension
45 Constant Gain-Bandwidth Product

GROUP 39-41

Impedance Modification

39 Input Resistance Modification
40 Output Resistance Modification
Dependence on Mixing/Sampling Type
Creating Ideal Buffer Amplifiers

GROUP 55-61

Transistor Feedback

56 Emitter Degeneration (Current-Series)
58 Collector Feedback (Voltage-Shunt)
Source & Drain Feedback
Practical Circuit Implementation

GROUP 46-51

Stability Limits

46 Stability & 47 Oscillation Risk
48 Nyquist Criterion Concepts
50 Phase Margin (PM)
51 Gain Margin (GM)

GROUP 52-54

Frequency Compensation

52 Compensation Techniques
53 Dominant-Pole Addition
Moving Poles to Ensure Phase Margin
Sacrificing Bandwidth for Stability

GROUP 62-66

Op-Amp Feedback

                        Vout = - (Rf/Rin) Vin
                    

62 Feedback in Operational Amplifiers
Virtual Ground Concept via Feedback
Voltage/Current Converters
Precision Mathematical Operations

FINAL PROTOCOL

12 — Feedback Design Laboratory

Af = A / (1 + Aβ)

Rif = Ri * (1 + Aβ)

BWf = BW * (1 + Aβ)

[72] NETWORK DESIGN [74] SENSITIVITY ANALYSIS [78] STABILITY CHECK [94] NUMERICAL CALCS [91] MEASUREMENT

Executing the engineering trade-offs. Calculating the exact desensitivity multiplier (1+Aβ), determining the modified input/output impedances for specific topologies, and ensuring the phase margin prevents catastrophic oscillation.

SIMULATION RUNNING