| Supplemental
Notes |
Topics
|
|
1.
Voltage, Current and Resistance
(14 pages)
|
| Typical
electric energy sources |
|
ideal
independent voltage source |
|
ideal
independent current source |
| Voltage
waveforms |
| What
is voltage? |
| What
is current? |
| Circuit
elements |
|
passive
(e.g. resistors, inductors, capacitors) |
|
active
(e.g. transistors and diodes) |
|
functional
blocks (e.g. amplifiers, logic gates, power supplies) |
| Resistance
and Ohm's Law |
|
what
is a resistor? |
|
resistance
and resistivity |
|
practical
resistors in circuits |
|
|
2.
Ohm's Law, Power Energy, and KVL
(11 pages)
|
| Ohm's
Law |
|
voltage
/ current behavior for a resistor |
| Power
dissipated by a resistor |
| Resistor
connected to an a.c. current source |
|
waveforms
for voltage, power, energy |
| Kirchhoff's
Voltage Law (KVL) |
|
several
examples with voltage sources and resistors |
|
|
3.
Resistors in Series and Parallel; Voltage and Current Division; Nodal
Analysis of Circuits
(14 pages)
|
| Resistors
in series |
| Resistors
in parallel |
| Conductance:
the reciprocal of resistance |
| Voltage
division |
| Current
division |
| Resistive
ladder network |
| Circuit
analysis techniques |
|
Kirchhoff's
Voltage Law (KVL) |
|
Kirchhoff's
Current Law (KCL) |
|
Nodal
analysis (based on KCL) |
|
Mesh
analysis (based on KVL) |
| Solving
simultaneous equations using matrix methods and Cramer's Rule |
|
|
4.
Mesh Analysis of Circuits; Superposition
(14 pages)
|
| Mesh
analysis of circuits |
|
examples |
| Principle
of Superposition |
|
examples |
|
|
5.
Superposition; Thevin and Norton Equivalent Circuits
(18 pages)
|
| Principle
of Superposition (cont.) |
|
examples,
independent voltage or current sources |
|
examples,
dependent sources |
| Thevenin
and Norton Equivalent Circuits |
|
examples |
|
|
6.
Applications of Thevenin's and Norton's Equivalent Circuits; Maximum Power
Transfer
(15 pages)
|
| Applications
of Thevenin's and Norton's Equivalent Circuits |
|
example,
graphical solution |
|
example
for a non-linear load (p-n diode) |
| Maximum
Power Transfer Theorem |
|
proof;
why is it important? |
|
example |
|
|
7.
Review of Matrices
(9 pages)
|
| Definition
of a matrix; matrix multiplication |
|
example |
| Additional
matrix definitions |
|
diagonal
matrix |
|
identity
matrix |
|
transpose
matrix |
|
determinant
of a square matrix |
|
matrix
co-factor |
|
adjoint
of a square matrix |
|
inverse
of a square matrix |
| Cramer's
Rule |
|
example |
|
| 8.
Solving 2nd-order homogeneous
ordinary differential equations (13 pages) |
| 2nd-order
homogeneous differential equation |
|
solutions
of exponential form |
|
characteristic
equation with two roots s1, s2 |
|
three
cases: overdamped, underdamped, critically damped |
| Example
for overdamped case |
| Example
for underdamped case |
| Example
for critically damped case |
|
| 9.
Complex numbers -
a quick primer |
| Supplemental
Notes on Complex Numbers |
|
Rectangular,
polar forms of complex numbers |
|
Euler's
Identity; Complex conjugate |
|
Arithmetic
operations, with examples: addition, subtraction, multiplication,
division |
|
Some
useful identities |
|
Integer
power of a complex number |
|
Roots
of a complex number |
|
Sines
and Cosines in terms of complex exponentials |
|