Linear Circuit Analysis
1. Introduction
2. Basic Concepts
- Charge, current, and voltage
- Power and energy
- Linear circuits
- Linear components
- Nodes and loops
- Series and parallel
- R, L & C combinations
- V & I combinations
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. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
- Introduction
- Inductors and capacitors
- First-order transients
- Nodal analysis
- Mesh analysis
- Laplace transforms
- Additional techniques
12. Two-Port Networks
Appendix
LTspice
LTspice is a powerful, fast, and free SPICE (Simulation Program with Integrated Circuit Emphasis) simulator software developed by Analog Devices. It is widely used by engineers for simulating analog circuits, mixed-signal circuits, and power electronics. LTspice provides a user-friendly graphical interface for designing circuits, running simulations, and analyzing results. It supports a wide range of components, including resistors, capacitors, inductors, diodes, transistors, and operational amplifiers. Additionally, LTspice allows users to create custom components and models, making it a versatile tool for circuit design and analysis. Feel free to download and install it on your computer LTspice from here.
Users can export circuit digrams from the CircuitsU website as a netlist file (*.net) that can be opened in LTspice for further analysis and simulation. This option is currently available only for DC and AC circuits.
Syntax
LTspice is using a modified nodal analysis technique to compute the voltages and currents in the circuit numerically. To simulate a circuit the user create a netlist file that contains a list of components and their connections. Below is a description of some of the basic components that can be inncluded in a netlist file.
-
Independent voltage source
Vname N+ N- [DC value] [AC value] [transient shape] -
Independent current source
Iname N+ N- [DC value] [AC value] [transient shape]Both sources can be set can generate waveforms:
SIN(offset amplitude freq)PULSE(V1 V2 Tdelay Trise Tfall Ton Tperiod)EXP(...), PWL(...), etc.
-
Resistor
Rname N1 N2 value -
Capacitor
Cname N1 N2 value [IC=initial_voltage] -
Inductor
Lame N1 N2 value [IC=initial_current] -
Voltage-Controlled Voltage Source
Ename N+ N- NC+ NC- gain -
Voltage-Controlled Current Source
Gname N+ N- NC+ NC- transconductance -
Current-Controlled Voltage Source
Hname N+ N- Vcontrol gain -
Current-Controlled Current Source
Fname N+ N- Vcontrol gain
The ground node is denoted by 0. Since LTspice uses a modified nodal analysis technique to solve the circuit equations, it is important for the circuit to have a ground node.
Otherwise, one can get errors such Node XXX is floating or singular matrix.
The following examples illustrate how to write the netlist file for a few simple circuits.
Example 1
* Circuit with independent voltage and current sources
R1 v1 v2 20 ; 20Ω resistor from node v1 to v2
I1 v3 v1 10 ; 10A current source from node v3 to v1
R2 v1 v3 4 ; 4Ω resistor from node v1 to v3
R3 v2 0 3 ; 3Ω resistor from node v2 to 0
V1 v3 0 5 ; 5V voltage source from node v3 to 0
.op ; Compute the DC bias point
.end
Example 2
* Circuit with a current-controlled voltage source
V1 v2 v1_ 1 ; 1V voltage source from node v2 to v1_
VIx v1_ v1 DC 0 ; add dummy voltage source with 0V
H3Ix v1 0 VIx 3 ; Voltage-controlled voltage source from node v1 to 0
I1 v1 0 3 ; 3A current source from node v1 to 0
R1 v2 v3 1 ; 1Ω resistor from node v2 to v3
R2 0 v3 2 ; 2Ω resistor from node 0 to v3
.op ; Compute the DC bias point
.end
Example 3
* Circuit with voltage-controlled current source
V1 0 v1 6 ; 6V voltage source from node 0 to v1
G3Vx 0 v2 N2 N3 3 ; Voltage-controlled current source from node 0 to v2
R1 v1 v3 2 ; 2Ω resistor from node v1 to v3
R2 0 v2 20 ; 20Ω resistor from node 0 to v2
R3 0 v2 5 ; 5Ω resistor from node 0 to v2
V2 v2 v3 8 ; 8V voltage source from node v2 to v3
R4 v3 v4 10 ; 10Ω resistor from node v3 to v4
R5 v2 v5 9 ; 9Ω resistor from node v2 to v5
R6 v4 v5 10 ; 10Ω resistor from node v4 to v5
.op ; Compute the DC bias point
.end
Example 4
Consider that the current of the independent source is $$I_1(t)=9 \class{mjunit}A \cdot \cos(\omega t + 45^\circ)$$
* AC circuit simulation
R1 0 v1 3 ; 3Ω resistor from node 0 to v1
I1 v2 v1 AC 9 45 ; 9A current source from node v2 to v1
E2Vx 0 v3 v2 v1 2 ; voltage-controlled voltage source from node 0 to v3
L1 0 v4 2E-05 ; 2E-05H inductor from node 0 to v4
R2 v1 v2 20 ; 20Ω resistor from node v1 to v2
L2 v3 v4 3E-05 ; 3E-05H inductor from node v3 to v4
C1 v4 v2_C1 3E-06 ; 3E-06F capacitor from node v4 to v2_C1
VI0 v2_C1 v2 0 ; add dummy voltage source with 0 V so LTspice can compute the current going through the wire
.ac lin 100 1k 10k ; Compute the small-signal response from 1 KH to 20 kHz
.end