Beginning Circuit Analysis Course Material Outline

What needs to happen?

Need to answer: Theory: What is it? How does it work? Practice: Homework problems Possible permutations

Circuits 1 Outline

Units and Scales

TODO: Dimensional Analysis

International System of Units (SI)

def: seven basic units upon which all others are based

Units

Base Quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin k
amount of substance mole mol
luminous intensity candela cd

Prefixes

Factor Name Symbol
femto f 10^-15
pico p 10^-12
nano n 10^-9
micro μ 10^-6
milli m 10^-3
centi c 10^-2
kilo k 10^3
mega M 10^6
giga G 10^9
tera T 10^12

Charge, Current, Voltage, Power

TODO: Nomenclature Disambiguation

  • Describe the difference between unit, dimension, and symbol in terms of dimensional analysis.

Charge

def: A physical property of matter that causes it to experience a force when placed in an electromagnetic field.

unit: Coulombs dimension: C symbol: Q or q

One Coulomb is the magnitude of charge of $ 6.242*10^18 * electrons or protons.

$$ 1C = 1A*s = 1F*V $$

Current

def: The flow of electrical charge (understood as the movement of electrons).

unit: Ampere dimension: A symbol: I or i

$$ 1A = 1C / s $$ (as above)

NOTE: *amp-hours* is another way to write the amount of charge a battery has. Just do a little algebra and see.

Voltage

def: the electric potential energy between two points per unit electric charge.

unit: Volt dimension: V symbol: V or v

$$ V = \frac{ N * M}{C} = \frac{ kg * m^2 }{ A *s^3 } $$

Power

def: Literally power is change in energy over change in time, in this instance it is the rate at which electrical energy is transferred by a circuit.

unit: Watts dimension: W symbol: P

$$ P = V * I = \frac{V^2}{R} = I^2 * R $$

Peak Power: the rate of energy flow a) at its peak, or b) over the time of discharge (ex, a PWM signal).

TODO: Resistance

Passive Sign Convention

def: an arbitrary and universally accepted method of labeling potential and current in an electrical circuit.

Reference Directions For Current, Voltage, and Power

passive sign convention reference directions

The reference directions are given for a passive device that is assumed to be ‘consuming’ or ‘dissipating’ power. In this instance $p=v*i$ and $r=v/i$. For those signs, current flows from the positive terminal of the device to the negative terminal and potential is higher on the positive side.

passive sign convention, load directions

For a device that is a load charge moves through an e-field gradient from a higher energy state, positive, to a lower energy state, negative.

passive sign convention, load directions

For a device that is a ‘source’ the charge is forced in the opposite direction, against the e-field gradient. The signs in this case are opposite: $p=-v*i$ and $r=-v/i$.

Source Power Resistance
load p > 0 r > 0
source p < 0 r < 0

Ohm’s Law

$$ V = I * R $$

Sources, Nodes, Paths, Loops, and Branches

Sources

These sources are considered “ideal” and are labeled as such. More realistic representations will follow.

Independent Voltage Source

ideal voltage source

Independent Current Source

ideal current source

Dependent Voltage Source

ideal dependent voltage source

Dependent Current Source

ideal dependent current source

Voltage Controlled Voltage Source

voltage controlled voltage source

Voltage Controlled Current Source

voltage controlled current source

Current Controlled Current Source

current controlled current source

Current Controlled Voltage Source

current controlled voltage source

Branches

def: any single element withing a circuit

  • add some examples from homeworks…

Nodes

def: Nodes connect branches (elements) together.

  • add some examples from homeworks…

Paths

def: any combination of elements, nodes, and branches

  • add some examples from homeworks…

Loops

def: any closed path in a circuit

  • add some examples from homeworks…

Kirchoff’s Laws

Kirchoff’s Voltage Law

Kirchoff’s Current Law

Series and Parallel

Resistors in Parallel

Resistors in Series

Sources in Series

Sources in Parallel

Voltage and Current Division

Nodal Voltage Analysis

Mesh Current Analysis

Linearity and Superposition

Source Transformations

Equivalent Circuits

Thevenin Equivalent

Norton Equivalents

Operational Amplifiers

Ideal Op-Amps

Non-Ideal Op-Amps

Inverting Amplifier

Non-Inverting Amplifier

Voltage Follower (Buffer)

Summing Amplifier

Difference Amplifier

Common Mode Rejection

Input Offset Voltage

Slew Rate

Capacitors

  • symbol
  • current > voltage relationship
  • integral voltage > current relationship
  • energy storage
  • in series and parallel
  • characteristics of an ideal capacitor

Inductors

  • symbol
  • voltage > current relationship
  • integral current-voltage relationship
  • energy storage
  • in series and parallel
  • characteristics of an ideal inductor

Inductor and Capacitor Combinations

Complex Numbers

Sinusoids

Phasor Circuits