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
Linear components (devices)
Table 1 shows a list of linear components (also called devices or elements) used in linear circuit analysis. All the components (and, implicitly, their current-voltage characteristics) are assumed to be ideal.
| Name/Unit | Symbol | Description |
|---|---|---|
| Resistor Ohms, $Ω$ | A resistor is a 2-terminal device that satisfies Ohm's law:$$\begin{equation}V(t)=I(t)R\end{equation}$$ where $R$ is the resistance and $V(t)$ is the voltage from the terminal where current $I(t)$ is assumed to enter the resistor to the terminal where the current is assumed to exit the resistor. In the case of DC circuits (i.e. when the voltage and current do not depend on time) the above equation is usually written as $V=IR$, where $V$ and $I$ are the DC values of the voltage and current. In the case of AC circuits (in frequency domain) the Ohm's law remains the same, but $V$ and $I$ are the complex values of the voltage and current. | |
| Capacitor Faradays, $F$ | A capacitor is a 2-terminal device in which the current and voltage satisfy the following equation $$\begin{equation}I(t)=C\dfrac{V(t)}{dt}\end{equation}$$ where $C$ is the capacitance (see figure for notations). In frequency domain (AC analysis) this equation becomes $$\begin{equation}I=\frac{V}{j{\omega}C}\end{equation}$$ where $I$ and $V$ are the complex values of the current and voltage and $\omega$ is the angular frequency of the AC signal (the above equation is equivalent to Ohm's law). | |
| Inductor Henries, $H$ | An inductor is a 2-terminal device in which the current and voltage satisfy the following equation $$\begin{equation}V(t)=L\dfrac{I(t)}{dt}\end{equation}$$ where $L$ is the inductance (see figure for notations). In frequency domain (AC analysis) this equation becomes $$\begin{equation}V=j{\omega}L I\end{equation}$$ where $I$ and $V$ are the complex values of the current and voltage and $\omega$ is the angular frequency of the AC signal (the above equation is equivalent to Ohm's law). | |
| Impedance Ohms, $Ω$ | An impedance is a 2-terminal device that is defined for the frequency domain (i.e. in AC circuits) and in which the complex current and complex voltage satisfy the following equation $$\begin{equation}V=Z I\end{equation}$$ where $Z$ is the (complex) impendace (see figure for notations). Notice that the same symbol (rectangle) is sometimes used to represent a "black" box, which is an electronic component with two terminals that can contain a combinations of resistors, inductors, capacitors, sources, etc. | |
| Voltage source (independent) Volts, $V$ | An independent voltage source is a 2-terminal device in which the voltage from the positive to the negative terminals is equal to $V$. | |
| Current source (independent) Amperes, $A$ | An independent current source is a 2-terminal device in which the current flowing in the direction of the arrow is equal to $I$. | |
| Dependent voltage source Volts, $V$ | A dependent voltage source is a 2-terminal device in which the voltage from the positive to the negative terminals is equal to the value indicated ($V_x$ in this case), which can depend on other currents and voltages in circuit. | |
| Dependent current source Amperes, $A$ | A dependent current source is a 2-terminal device in which the current flowing in the direction of the arrow is equal to the value indicated ($I_x$ in this case), which can depend on other currents and voltages in circuit. |