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, including:

• 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)

Generally speaking, you are solving for one or several of the above variables, given the others. For example, you may be given a transmit power, and you need to solve for the antenna gain to achieve a certain EIRP.

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 or 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.

The link budget may just use a single number for the satellite's transmit gain.

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)

The logarithmic form turns the equation into a ledger: gains add, while path and implementation losses subtract. The moving trace below follows that accounting from left to right.

The dB ledger

Follow one signal from the transmitter to the receiver; every gain lifts it and every loss drops it.

Pr -79.0 dBm

Transmit power30.0 dBmTX antenna gain18 dBiDistance50 kmFrequency6.0 GHzSystem loss-3.0 dBRX antenna gain18 dBi

Free Space Path Loss

Influence of distance and frequency

In free space, the intensity of electromagnetic radiation decreases with distance according to the inverse-square law. The same transmitted power spreads over a spherical area proportional to the square of distance.

Spreading versus capture

Separate the geometry of the wave from the frequency-dependent assumptions about the receive antenna.

Pr -82.0 dBm

Hold constant

12 dBi gain0.60 m aperture

Distance50 kmFrequency6.0 GHz

Free-space loss

142.0 dB

With gain held fixed, doubling distance or frequency adds about 6 dB.

Receive antenna

12.0 dBi

Physical capture area shrinks as frequency rises.

Effective aperture

31.5 cm²

Frequency effect vs 1 GHz: -15.6 dB.

The explorer separates two effects that are easy to conflate:

• Geometric spreading: power density falls as $1/d^2$, regardless of frequency in a vacuum.
• Receive capture area: for a fixed-gain antenna, effective aperture is proportional to $λ^2$, so it shrinks as frequency rises.
• Fixed physical aperture: holding antenna size constant instead makes receive gain rise with frequency. In the ideal Friis model, that gain offsets the frequency term in free-space path loss.

At a distant receiver, a small patch of each spherical front is approximately planar. RFD 0009 uses that far-field approximation to show how arrival angle becomes a relative phase delay across an array.

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: $10 \log_{10} (P_s/P_n)$.

At room temperature, a common receiver input-noise estimate is:

$$N \approx -174\ \mathrm{dBm/Hz} + 10 \log_{10}(B) + NF$$

where $B$ is the receiver noise bandwidth in hertz and $NF$ is the receiver noise figure in decibels. The available link margin is the measured SNR minus the SNR required by the waveform and receiver.

Can the receiver hear it?

Move the signal and noise terms independently, then compare the available SNR with the demodulator requirement.

closes +17.0 dB

Received signal-82.0 dBmNoise bandwidth1.00 MHzReceiver noise figure5.0 dBRequired SNR10.0 dB

Noise floor

-109.0 dBm

−174 dBm/Hz + bandwidth + receiver noise figure

Available SNR

27.0 dB

Received signal power minus the integrated noise floor

Link margin

+17.0 dB

Positive margin: the signal clears the requirement.

Noise

Noise Factor (F) is a common metric of a network or device, which is defined as the ratio of the signal-to-noise power ratio at the input to the signal-to-noise power ratio at the output.

Thus the noise factor of a network describes the degradation in signal-to-noise ratio as the signal passes through the network or device.

Noise Figure (NF) is the noise factor ratio in units of decibels (dB), which is $10 \log_{10} (SNR_i/SNR_o)$ or $10 \log_{10} (F)$.

External References

• OSI Model
• Antenna Gain to Noise Temperature
• inverse-square law