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
Notations
This webbook and CircuitsU use the following notations:
| $I$, $V$, $P_d$, and $P_g$ | DC currents, voltages, and powers are denoted by with capital letter |
| $I$, $V$, $P_d$, and $P_g$ | currents, voltages, and powers in the frequnecy (complex) and s-domains are denoted with capital letter* |
| $I(t)$, $V(t)$, $P_d(t)$, and $P_g(t)$ | time-dependent currents, voltages, and powers are usually shown as functions of time |
| $I(t)=I_0 \cos(\omega t+\phi)$ $V(t)=V_0\sin(\omega t+\phi)$ | AC currents AC voltages |
| $v_1$, $v_2$,... | nodal potentials (real, complex, or in the s-domain) are written in lowercases |
| $i_1$, $i_2$,... | mesh currents (real, complex, or in the s-domain) are written in lowercases |
| $v_1(t)$, $v_2(t)$,... | nodal potentials in time-domain |
| $i_1(t)$, $i_2(t)$,... | mesh currents in time-domain |
| $\textcolor{blue}{j}$ | imaginary number $j=\sqrt{-1}$ |
| $\textcolor{blue}{s}$ | complex frequency used in Laplace transforms |
*A better notation, which is often used in textbooks, is to use bold letters for complex variables ($\boldsymbol{I}$, $\boldsymbol{V}$, $\boldsymbol{P_d}$, and $\boldsymbol{P_g}$) however, due to limitations in SVG graphic fonts we are representing them with regular fonts on this website.
Subscripts
| $0$ | denotes sought variables (e.g. $V_0$, $I_0$) |
| $eff$ | effective (e.g. $R_{eff}$, $L_{eff}$,...) |
| $rms$ | root-mean square (e.g. $V_{rms}$, $I_{rms}$) |
| $d$ | dissipated (e.g. $P_d$) |
| $g$ | generated (e.g. $P_g$) |
| $N$ | Norton |
| $Th$ | Thévenin |
| $1$, $2$, ... | used for mesh currents (e.g. $i_1$, $i_2$,...), nodal potentials (e.g. $v_1$, $v_2$,...), components (e.g. $R_1$, $L_1$, $C_1$, $V_1$, $I_1$,...) |
| $x$, $y$, ... | used for control variables (e.g. $I_x$, $V_y$,...) |
Abbreviations
| AC | alternative current |
| DC | direct current |
| KCL | Kirchhoff's current law |
| KVL | Kirchhoff's voltage law |
| OpAmp | operational amplifier |
| TD | time-dependent |
Units
All variables are assumed to be expressed in the International System of Units in CircuitsU. Therefore, to simplify notations, CircuitsU will usually not write the units in mathematical expressions unless it is a final answer.
Units are written with gray characters in CircuitsU. For instance: $V_1 = 2.4 \: {\textcolor{gray}V}$, $R = \frac{2.4 \: {\textcolor{gray}V}}{1.2 \: {\textcolor{gray}A}} =2 \: {\textcolor{gray}Ω}$.