# Network Topologies and Signal Concepts

## Network Topologies

### Star Topology

All devices are connected to a central hub or router. This central node acts as a communication point for all other nodes.

- Typically, the central node is a hub or switch.
- Allows for quick communication between all nodes.
- If the central node fails, the entire network is disconnected.

### Extended Star Topology

Used when more connections are needed than a single star topology can provide.

- Similar to the star topology, but each node connected to the central node can also act as the center of another star.
- Shorter cabling and limits the number of devices connected to any single central node.
- Hierarchical structure.

### Tree Topology

Similar to the extended star topology but with a central node acting as a backbone.

- Has a backbone link node, usually a hub or switch, from which other nodes branch out.
- The link is a trunk cable with layers of branching, and information flow is hierarchical.
- A host server is typically connected to the other end of the backbone link.

### Full Mesh Topology

Each node is directly connected to all other nodes.

- If one link fails, information can still travel through other links.
- Allows for multiple routes for information to circulate.
- Only practical for a small number of nodes due to the high number of connections required.

### Irregular Topology

No clear pattern of links and nodes.

- Often found in networks that are in the early stages of development or poorly planned.

## Network Classification by Scale

### Local Area Network (LAN)

Private networks within a building or a limited area, typically a few kilometers in size.

- Commonly used to connect personal computers and workstations in offices and factories to share resources like printers and scanners.
- Restricted in size, leading to predictable transmission times and simplified network administration.
- Operate at speeds up to 1 Gbps with low latency and few errors.
- Star and tree topologies are commonly used.

### Metropolitan Area Network (MAN)

A larger version of a LAN, typically covering a city or metropolitan area.

- Can connect multiple offices or a whole city and can be private or public.
- Maximum range of a few tens of kilometers and operates at speeds around 10 Gbps.

### Wide Area Network (WAN)

Extends over a large geographical area, such as a country or continent.

- Can span hundreds of kilometers and operate at speeds close to 1 Tbps.

## UD2. Media: Concepts and Requirements

### Mathematical Concepts

#### Superposition Principle

The effect caused by multiple signals is equal to the sum of the effects of each signal individually:

f(x + y) = f(x) + f(y)

#### Fourier Analysis

Any continuous and differentiable function can be broken down into a sum of simpler terms, represented as a series. This series is infinite if the function is periodic and becomes an integral if the function is not. Each term in the series is a sine signal.

### Sine Signals

Sine functions have the following mathematical notation:

f(t) = a_{m} * sin(ωt + θ)

- t: independent variable, represents time (seconds).
- ω: angular frequency (radians/second).
- θ: represents the phase shift (degrees or radians).
- a
_{m}: maximum signal amplitude. - F = ω / 2π: frequency (Hertz).
- T = 2π / ω: period (seconds).

Remember that the sine signal is periodic with a period of 2π radians.

**Example:**

If f (frequency) = 50 Hz, then:

- ω = 2πf = 2π * 50 = 100π ≈ 314.16 rad/sec
- T = 1/f = 1/50 = 0.02 seconds