Ontological Layer: Mathematical Constraints
Ohm's Law & Circuit Relations
The Syntax of Network Behavior
The Rules of the Grid
Physics provides the components; mathematics dictates how they interact. This territory establishes the fundamental rules of electronic networks—how voltage, current, and resistance constrain each other, how sources deliver power, and how intersection points on a graph determine the operational state of a device.
VOLTAGE +
CURRENT →
V = IR →
V-I CURVES →
LOAD LINE →
Q-POINT →
SOURCES →
NETWORKS →
MAX POWER
The 11 Mathematical Nodes
Vertical Ontology: From Formula to System Response
NODE 01
Ohm's Law
V
I
R
- The V-I-R Constraint
- Proportionality & Limits
- Resistance as V/I Ratio
- V-I Relations in Devices
Ohmic vs Non-Ohmic
- Linear vs Nonlinear Relations
- Ohmic Behavior (Constant R)
- Non-Ohmic Behavior (Diodes, Transistors)
- V-I Characteristics Curves
Static & Dynamic Resistance
- Static Resistance (R = V/I)
- Dynamic Resistance (r = dV/dI)
- Secant vs Tangent Interpretation
- Small-Signal Modeling Basis
Load Line & Q-Point
- DC Load Line Concept
- Circuit Constraint Intersections
- Operating Point (Q-Point)
- Bridge to Transistor Biasing
Voltage & Current Sources
V
V
- Ideal Voltage & Current Sources
- Practical Sources & Internal Resistance
- Source-Load Relationships
- Terminal Voltage Variations
Source Transformation
↔
- Thevenin ↔ Norton Equivalence
- Voltage Source + Series R
- Current Source + Parallel R
- Circuit Simplification Techniques
Network Connections
- Series & Parallel Topologies
- Series-Parallel Networks
- Equivalent Circuit Reduction
- Network Behavior Analysis
Division Rules
- Voltage Division (Series R)
- Current Division (Parallel R)
- Proportional Branching
- Analyzing Resistor Networks
Maximum Power Transfer
- Power Delivered to Load
- Condition for Maximum Power
- Impedance Matching Concept
- Efficiency vs Maximum Transfer
Open & Short Circuits
- Open-Circuit Condition (I = 0)
- Short-Circuit Condition (V = 0)
- Extreme States of Resistance
- Reference Cases for Analysis
Polarity & Conventions
+
-
- Polarity & Sign Convention
- Passive Sign Convention
- Reference Directions
- Circuit Constraints & Consistency
SIMULATION RUNNING