# Link Budgets

## Introduction

A link budget is the accounting of all of the gains and losses from the transmitter, through the medium (free space, cable, waveguide, fiber, etc.) to the receiver in a telecommunication system. It accounts for the attenuation of the transmitted signal due to propagation, as well as the loss introduced by components of the transmission system such as connectors, splitters, and cable loss. Additional gains and losses from the use of antennas are also accounted for in the link budget.

Link budgets are often used to predict and model the performance of a communications system, such as a satellite link, prior to its construction.

Within that goal, a designer will create a link budget to achieve some specified performance criteria, with examples include:

- PHY data rate (PHY is the physical layer in the OSI Model)
- Receiver Noise Figure and Receive Antenna Gain
- Transmit Power and Transmit Antenna Gain
- EIRP (Equivalent Isotropically Radiated Power) or G/T (Antenna Gain to noise Temperature)

### What about a gain lineup?

This contrasts with a gain lineup, which is the accounting of all of the gains and losses inside a system (or partition of a system). A gain lineup generally doesn't include free space path loss nor wireless losses.

For example, a gain lineup for a satellite transponder would include the gains and losses of the transponder itself, but not the losses from the propagation through free space.

## Friis Transmission Equation

$P_r = P_t + G_t + G_r + 20 \log_{10} \left( \frac{\lambda}{4 \pi d} \right)$where:

- $P_r$ = received power (dBm)
- $P_t$ = transmitted power (dBm)
- $G_t$ = gain of transmitting antenna (dBi)
- $G_r$ = gain of receiving antenna (dBi)
- $λ$ = wavelength of signal (m)
- $d$ = distance between antennas (m)

## Free Space Path Loss

### Influence of distance and frequency

In free space the intensity of electromagnetic radiation decreases with distance by the inverse square law, because the same amount of power spreads over an surface area proportional to the square of distance from the source.

The free-space loss increases with the distance between the antennas and decreases with the wavelength of the radio waves due to these factors:[6]

**Intensity**( I ) – the power density of the radio waves decreases with the square of distance from the transmitting antenna due to spreading of the electromagnetic energy in space according to the inverse square law[1]**Antenna capture area**( $A_{eff}$) – the amount of power the receiving antenna captures from the radiation field is proportional to a factor called the*antenna aperture*or antenna capture area, which increases with the square of wavelength.[1] Since this factor is not related to the radio wave path but comes from the receiving antenna, the term "free-space path loss" is a little misleading.**Directivity of receiving antenna**- while the above formulas are correct, the presence of Directivities Dt and Dr builds the wrong intuition in the FSPL Friis transmission formula. The formula seems to say that "free space path loss" increases with frequency in vacuum, which is misleading. The frequency dependence of path loss does not come from free space propagation, but rather from receiving antenna capture area frequency dependence. As frequency increases, the directivity of an antenna of a given physical size will increase. In order to keep receiver antenna directivity constant in the formula, the antenna size must be reduced, and a smaller size antenna results in less power being received as it is able to capture less power with a smaller area. In other words, the path loss increases with frequency because the antenna size is reduced to keep directivity constant in the formula, and has nothing to do with propagation in vacuum.**Directivity of transmitting antenna**- the directivity of transmitting antenna does not have the same role as directivity of receiving antenna. The difference is that the receiving antenna is receiving the power from free space, and hence captures less power as it becomes smaller. The transmitting antenna does not transmit less power as it becomes smaller (for example half wave dipole), because it is receiving its RF power from a generator or source, and if the source is 1 Watt or Pt, the antenna will transmit all of it (assuming ideal efficiency and VSWR for simplicity).

## Signal to Noise Ratio

The signal-to-noise ratio (SNR) is the ratio of the power of a signal (meaningful information) to the power of the noise (unwanted signal).

The SNR is usually measured in decibels (dB). If the incoming signal strength in microvolts is $V_s$ and the noise level, also in microvolts, is $V_n$, then the signal-to-noise ratio, $S/N$, in decibels is given by: $20 \log_{10} (V_s/V_n)$

Expressed in terms of power, the signal-to-noise ratio is: $10 \log_{10} (P_s/P_n)$.

## Noise

To be continued...