# Understanding Link Budgets and Balancing SNR Ratios

October 14, 2019

One of the last steps in the design of an automobile—especially with those eye-catching cars that resemble sleek jets--involves a performance team.  After the design has become almost fully engineered, the performance team uses computer software to fine tune the design for factors such as differential torque bias, aerodynamics, and tire characteristics.

Along with working with the software, the performance team also tests different components to achieve the highest efficiency while withstanding stress. After working with those and other factors, the performance team refers their information to the design team for the final finishing touches to the automobile.

When we work with transmitters and receivers, we want to achieve the best performance. To accomplish our performance objectives, we use a link budget to illustrate gains and losses throughout the entire system—from transmitter, through free spaces, cables, waveguides, and other examples of the medium, to the receiver. The link budget serves as a tool for predicting performance and for recognizing if the system provides acceptable performance.

## Link Budget Fundamentals Are Fun

Building a link budget begins with the fundamentals. Let’s consider the power at the receiver (Prx) and the power at the transmitter (Ptx) minus any loss (LO) that occurs as the signal travels through the medium.  In equation form, this occurs as:

Ptx – LO = Prx.

Now, let’s build the equation out a little more by adding the transmit antenna (Gt) and receive antenna gains (Gr).

Ptx + Gt + Rt – LO = Prx

Gain represents all positive values while losses represent all negative values. Losses occur within antenna cabling and connectors at the transmitter and receiver or as propagation losses within the medium.  When working with free spaces as a medium, loss increases with distance and frequency. Along with equaling the difference between the gains and losses, the link margin also shows how the amount of received power exceeds the receiver sensitivity.

## There’s Much to Gain Here

When we think of gain, we turn to a famously dimensionless unit called the Bel. A Bel expresses ratios and gains on a log scale. The term decibel (db) represents 1/10 of a Bel and represents a relative number of the amount of increase or decrease in signal.  Work with telecommunications requires another method of measuring power since we work with absolute power. For those networks—regardless of whether we work with radio frequencies or microwave frequencies, we reference the power ratio in decibels to one milliwatt or Decimal Milliwatts (dBm) to measure absolute power and to define signal strength.

Let’s break this down even more. The dBm defines the amount of power that an antenna can produce. When we think about decibels and Decimal Milliwatts, we need to remember that both represent logarithmic values. Because a logarithm equals the power that we raise a number to attain some other number, the measurement of power magnitude changes. In terms of a link budget, the transmitted power and received power measure as dBm while the gains and losses measure as decibels.

Going back to our statement about link margins, a large amount of received power—when compared to the sensitivity of the receiver—allows the system to send data with less errors and satisfies the link budget.

Every antenna adds gain to the telecommunications system. Rather than simply looking at antenna gain in terms of decibels, we consider the Effective Isotropic Radiated Power (EIRP).

The EIRP equals the amount of transmission power fed to an isotropic antenna plus the antenna gain and allows us to compare the different characteristics of antennas. Looking at this a bit differently, the EIRP tells us about the amount of power radiated from an antenna needed to produce the equivalent power density of an antenna radiating in a specific direction.

When we consider power at the receiver, we know that a minimum required level of power at the receiver translates to a minimum required service quality. The link budget allows us to think in terms of range, energy, and cost.  If we want to spend more to decrease channel loss, we extend range. Boosting transmission power leads to a greater need for energy. The need for more sensitivity adds costs.

To achieve this balance, we establish a target carrier-to-noise ratio (C/N) at the receiver input. For telecommunications systems, the antenna can pick up noise. Thermal noise can also subtract from the output signal.

## It’s Noisy in Here! Noise in Link Budgets

Another part of the link budget is the power of noise generated by the atmospheric and man-made sources picked up by the antenna, the circuitry within the receiver, and other sources such as waveguides, amplifiers, and mixers. For just a moment, let’s focus on those last items.

Any object that experiences an increase in temperature generates thermal noise (NO). We can view noise as an additive function with each source of noise adding to the first noise source.

Follow signal best practices like avoiding the crossing of analog and digital signals

As we consider the impact of noise, we must also remember that bandwidth affects the capacity of any communications. The combination of RF power and bandwidth serve as the upper limits of the link between the transmitter and the receiver. Every bit of information moving across the telecommunications system requires energy (Eb). Moving to the link budget, we not only look at the amount of RF power but also the available bandwidth. A third function—signal reliability—becomes apparent through the Bit Error Rate (BER).

The performance of any telecommunication depends on the achievable signal-to-noise ratio (SNR) at the receiver.  The signal-to-noise ratio represents the strength of the signal compared to noise interference. A SNR higher than 1:1 or greater than 0 dB indicates that the system has more desired signal than unwanted noise. In other words, we need a signal-to-noise ratio that allows the receiver to achieve signal reliability when measured against the bit error rate. In the form of an equation, the SNR appears as a function of the energy per bit of information, the amount of thermal noise in 1Hz of bandwidth, the system data rate (R), and the system bandwidth (BT):

(Eb / NO) x (R/BT) = SNR in decibels.

Dividing the Energy per Bit by the amount of thermal noise gives us the noise power density. Attaining that number allows us to compare the bit error rate performance for different digital modulation schemes.

As you work with your transmitter/receiver design, you will find that the bit error rate for the system goes to an unacceptable high level below a specific SNR. That level determines the lowest acceptable performance of the system.

Another ratio allows us to analyze whether noise will cover the carrier and render the system useless. The carrier-to-noise ratio (C/N) equals the ratio of the relative power level to the noise level in the bandwidth of the system.

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