Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Currents and voltages
- Linear circuits
- Linear components
- Loops and nodes
- Series and parallel
- R, L & C combinations
- V & I combinations
- Power and energy
3. Simple Circuits
- Ohm's law
- Kirchhoff's current law
- Kirchhoff's voltage law
- Single loop circuits
- Single node-pair circuits
- Voltage division
- Current division
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
- Superposition
- Source transformation
- The $V_{test}/I_{test}$ method
- Norton equivalent
- Thévenin equivalent
- Max power transfer
6. AC Analysis
7. Operational Amplifiers
8. Laplace Transforms
9. Time-Dependent Circuits
- Introduction
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
10. Two-port networks
Inductor Combinations
Series
If two or more inductors $L_1$, $L_2$, ... $L_n$ are connected in series they are equivalent with a inductor with $$L_{eff}=L_1+L_2+...+L_n$$ That means we can replace one of the $n$ inductors with an equivalent inductor with inductance $L_{eff}$ and replace the other inductors with short-circuits (wires).
For instance, considering the circuit in
, inductors $L_1$ and $L_2$ are connected in series. Therefore, we can keep one the inductors, say $L_1$, replace its value with $L_{eff}=L_1+L_2$, and replace inductor $L_2$ with a wire.Parallel
If two or more inductors $L_1$, $L_2$, ... $L_n$ are connected in parallel they are equivalent with a inductor with $$L_{eff}=\frac{1}{\frac{1}{L_1}+\frac{1}{L_2}+...+\frac{1}{L_n}}$$ That means we can replace one of the $n$ inductors with an equivalent inductor with inductance $L_{eff}$ and remove all the other inductors. When we have only two inductors connected in parallel, we can replace them with a single inductors with inductance $$L_{eff}=\frac{L_1 L_2}{L_1+L_2}$$
For instance, considering the circuit in
, inductors $L_3$, $L_4$, and $L_5$ are connected in parallel. Therefore, we can keep one the inductors, say $L_3$, replace its value with $L_{eff}=\frac{1}{\frac{1}{L_3}+\frac{1}{L_4}+\frac{1}{L_5}}$, and remove inductor $L_4$ from the circuit. Similarly, we could keep $L_4$ and remove $L_3$ and $L_5$, or keep $L_5$ and remove $L_3$ and $L_4$.