# FIT5083 Network Infrastructure Formula
###### tags: `2020S1`
> You may like this [website](https://www.wolframalpha.com)
## Basic Wave
`T= 1/f`
## Nyquist Bit Rate
> The Nyquist bit rate formula is use to calculate the theoretical maximum bit rate.
> Nyquist Bandwidth: Given an error-free medium of bandwidth B, the highest signal rate the can be carried is ___.

For binary signals (**two** voltage levels)
`C = 2B`
For multilevel signaling
`C = 2Blog_2(M)`
`M = number of discrete signal or voltage levels.`
## Signal-to-Noise Ratio
> Ratio of the power in a signal to the power contained in the noise that is present at a particular point in the transmission.
> A high SNR means a high-quality signal, lower number of required intermediate repeaters.
>
`(SNR)_db = 10log(signal power/noise power)`
## Shannon Capacity for noisy channel
> Represents theoretical maximum that can be achieved for a noisy channel, we can use Shannon capacity.
> Shannon Capacity uses **SNR**, not ~~(SNR)_db~~
>
`Capacity = bandwidth * log_2(1+SNR)`
`C = Blog_2(1+SNR)`

## Effective Area and Antenna Gain

## Antenna Gain

G = 4πAe / λ^2 , λ = c/f

G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light (3*10^8 m/s)
λ = carrier wavelength

## Line-of-Sight Equations

d = 3.57(√Kh_1 + √Kh_2)

h_1 = height of antenna one
h_2 = height of antenna two
K = adjustment factor to account for refraction, rule of thumb K = 4/3 = 1.3

## Free space loss equation

Pt/Pr = (4πd)^2 / λ^2 , λ = c/f

Pt = siangl power at the transmitting antnna
Pr = siangl power at the receiving antnna
λ = carrier wavelength (m)
f = carrier frequency
d = propagatin distance between antennas (m)
c = speed of light (3*10^8 m/s)

Pt/Pr = (4πd)^2 / GrGtλ^2 = (λd)^2 / ArAt, λ = c/f

Gt = gain of the transmitting antenna
Gr = gain of the receiving antenna
At = effective area of the transmitting antenna
Ar = effective area of the receiving antenna

## Thermal Noise
> Amount of thermal noise to be found in a bandwidth B=1Hz in any device or conductor is:
>

N_0 = kT (W/Hz)

N_0 =  noise power density in watts per 1Hz of bandwidth
k = Boltzmann's constant = 1.3803 * 10^-23 J/K
T = temperature, in kelvins (absolute temperature)

## Learning Decibels (dB)
### Basics
`1 W = 1000 mW = 1000000 (10^6) μW = 0.001 kW`

dB value = 10log(Po/Pi)

Pi = input power
Po = output power

### dBm and dBW

Value (dBm) = 10log(P/(1mW))
Value (dBW) = 10log(P/(1W))

### dBi and dBd
> dBi is used to quantify the gain of an antenna. It stands for dB above (or below) an isotropic.
> dBd
### EIRP
> Effective Isotropically Radiated Power
>

EIRP(dBW) = Pt + L + antenna gain

Pt: Output power of the transmitter in dBm or dBW
L: line loss in dB
antenna gain: dB

## Pulse Code Modulation

SNR_db = 20log(2^n) + 1.76dB = 6.02n + 1.76dB

## Traffic Intensity

A = λh

λ = mean rate of calls attempted per unit time
h = mean holding time per successful call
A = average number of calls arriving during average holding period, for normalized λ. Measured in dimension-less unit "Erlang"