# 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

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.

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.

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

#### Independent Current Source

#### Dependent Voltage Source

#### Dependent Current Source

##### Voltage Controlled Voltage Source

##### Voltage Controlled Current Source

##### Current Controlled Current 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