link characteristics and performance · telecommunications satellite communications link...

Telecommunications Satellite Communications

Link Characteristics and Performance

Courseware Sample 86312-F0

Order no.: 86312-10 First Edition Revision level: 07/2015

By the staff of Festo Didactic

© Festo Didactic Ltée/Ltd, Quebec, Canada 2014 Internet: www.festo-didactic.com e-mail: [email protected]

Printed in Canada All rights reserved ISBN 978-2-89640-419-3 (Printed version) ISBN 978-2-89747-103-3 (CD-ROM) Legal Deposit – Bibliothèque et Archives nationales du Québec, 2014 Legal Deposit – Library and Archives Canada, 2014

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The purchaser shall be entitled to use the work to train his/her staff at the purchaser's site/location and shall also be entitled to use parts of the copyright material as the basis for the production of his/her own training documentation for the training of his/her staff at the purchaser's site/location with acknowledgement of source and to make copies for this purpose. In the case of schools/technical colleges, training centers, and universities, the right of use shall also include use by school and college students and trainees at the purchaser's site/location for teaching purposes.

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© Festo Didactic 86312-10 III

Safety and Common Symbols

The following safety and common symbols may be used in this manual and on the equipment:

Symbol Description

DANGER indicates a hazard with a high level of risk which, if not avoided, will result in death or serious injury.

WARNING indicates a hazard with a medium level of risk which, if not avoided, could result in death or serious injury.

CAUTION indicates a hazard with a low level of risk which, if not avoided, could result in minor or moderate injury.

CAUTION used without the Caution, risk of danger sign , indicates a hazard with a potentially hazardous situation which, if not avoided, may result in property damage.

Caution, risk of electric shock

Caution, hot surface

Caution, risk of danger

Caution, lifting hazard

Caution, hand entanglement hazard

Notice, non-ionizing radiation

Direct current

Alternating current

Both direct and alternating current

Three-phase alternating current

Earth (ground) terminal

Safety and Common Symbols

IV © Festo Didactic 86312-10

Symbol Description

Protective conductor terminal

Frame or chassis terminal

Equipotentiality

On (supply)

Off (supply)

Equipment protected throughout by double insulation or reinforced insulation

In position of a bi-stable push control

Out position of a bi-stable push control

© Festo Didactic 86312-10 V

Table of Contents

Preface .................................................................................................................. XI

About This Manual .............................................................................................. XIII

To the Instructor .................................................................................................. XV

List of Equipment Required ............................................................................... XVII

Introduction Characterizing a Communications Link ..................................... 1

DISCUSSION OF FUNDAMENTALS ....................................................... 1Communications inks ............................................................... 1Measurements and sources of error ........................................ 1

Instrument uncertainties ............................................................. 2Measurement inaccuracies ......................................................... 2Environmental factors ................................................................. 2

Exercise 1 Power Gain and Antenna Parameters ........................................ 3

DISCUSSION ..................................................................................... 3Power gain ............................................................................... 3Antennas .................................................................................. 5

Field regions ............................................................................... 8Solid angles ................................................................................ 8Radiation intensity .................................................................... 10

Directive gain and directivity .................................................. 11Power density and the inverse-square law ............................ 12Radiation pattern and beamwidth .......................................... 14

Beam solid angle ...................................................................... 19Shortcut for calculating the beam solid angle ........................... 20

Efficiency ................................................................................ 20Effective aperture ................................................................... 21Antenna gain .......................................................................... 22

Gain of a pyramidal horn antenna ............................................ 23Electrical size ........................................................................... 25Gain of a parabolic antenna ..................................................... 26Shortcut for calculating the gain of a dish antenna from the frequency and the diameter ...................................................... 26The relationship between gain and beamwidth ........................ 28Shortcut for calculating the beamwidth of a dish antenna ........ 28Shortcut for calculating the gain of a dish antenna from the beamwidth ................................................................................ 28General rules for aperture antennas ......................................... 28Measuring antenna gain ........................................................... 29

Polarization ............................................................................ 29The Satellite Communications Training System .................... 30

Horn antenna polarization ........................................................ 30Frequencies used in the system ............................................... 32Power Sensors ......................................................................... 32Power measurements ............................................................... 33

Table of Contents

VI © Festo Didactic 86312-10

PROCEDURE ................................................................................... 34System startup ....................................................................... 34

Connection Diagrams ............................................................... 35Power gain ............................................................................. 36

Aligning the antennas ............................................................... 38Feed-line loss ........................................................................... 39Gain of the repeater .................................................................. 44Gain of Down Converter 2 ........................................................ 49

Antenna gain .......................................................................... 50Gain of the large-aperture horn antenna at the uplink frequency .................................................................................. 51Gain of the small-aperture horn antenna versus downlink frequency .................................................................................. 54Gain of the large-aperture horn antenna versus downlink frequency .................................................................................. 58Effective aperture and efficiency ............................................... 62

Beamwidth and radiation pattern ........................................... 623 dB beamwidth ........................................................................ 64Radiation pattern ...................................................................... 65

Polarization isolation .............................................................. 69

Exercise 2 Losses, Radiated Power and Receiver Input Power ............... 71

DISCUSSION ................................................................................... 71Effective isotropic radiated power of a directional antenna ... 71Friis transmission equation .................................................... 72Free-space loss ...................................................................... 73

Notes on free-space loss .......................................................... 73Atmospheric attenuation and path loss .................................. 75Feeder loss ............................................................................ 75Pointing loss ........................................................................... 76Polarization mismatch loss .................................................... 76Receiver input power ............................................................. 77

PROCEDURE ................................................................................... 78System startup ....................................................................... 78Preliminary measurements .................................................... 79Free-space loss ...................................................................... 79

Set up for measuring free-space loss ....................................... 80Notes on measuring the transmitted and received power ......... 82Determining the effective isotropic radiated power ................... 82Measuring the receiver input power .......................................... 84Calculating the free-space loss ................................................. 86

Receiver input power ............................................................. 92Polarization mismatch loss .................................................... 94

Table of Contents

© Festo Didactic 86312-10 VII

Exercise 3 Noise and the Link Budget ...................................................... 101

DISCUSSION ................................................................................. 101Noise in communications systems ....................................... 101Thermal noise characteristics .............................................. 102

Amplitude distribution ............................................................. 103Frequency distribution ............................................................ 105

Half-power and equivalent noise bandwidths ...................... 107Additive white Gaussian noise (AWGN) .............................. 108Thermal noise power ........................................................... 109

Noise power example ............................................................. 111Signal-to-noise ratio ............................................................. 111Noise figure .......................................................................... 112

Noise figure example .............................................................. 114Noise temperature ............................................................... 117

Noise figure versus noise temperature ................................... 119Composite noise figure and noise temperature of cascaded elements .............................................................. 120

Noise figure and noise temperature example ......................... 121Noise figure and noise temperature of an attenuator or a feed line .................................................................................. 126

Antenna noise temperature .................................................. 127System noise temperature ................................................... 128

Composite temperature of the antenna and feed line ............. 130Link performance and receiver figure of merit ..................... 131Link budget ........................................................................... 132

Link budget example .............................................................. 132Analog and digital figures of merit .......................................... 135

PROCEDURE ................................................................................. 136System startup ..................................................................... 136Noise figure .......................................................................... 137

Set up for measuring noise figure ........................................... 137Measuring received carrier power and RF front end gain ....... 138Measuring the gain of the preamplifier ................................... 139Measuring the receiver output noise power ............................ 141Calculating the receiver noise figure and effective input noise temperature................................................................... 143

System noise temperature ................................................... 143Link budget ........................................................................... 145

Appendix A Glossary of New Terms ............................................................ 153

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VIII © Festo Didactic 86312-10

Appendix B Setting Up the Satellite Communications Training System . 157Set up the modules .............................................................. 158Align the antennas ............................................................... 162Connect the power supplies ................................................. 162USB connections to the Telemetry and Instrumentation Add-On ................................................................................. 163

Appendix C Care of Microwave Cables ....................................................... 165

Appendix D Using the Telemetry and Instrumentation Add-On ............... 167Virtual Instruments ............................................................... 167Data Generation/Acquisition Interface ................................. 167

Spectrum Analyzer Interface................................................... 168Digital Inputs ........................................................................... 169Digital Outputs ........................................................................ 169USB Connectors ..................................................................... 169

Virtual Instrument package .................................................. 170Using the Binary Sequence Generators .............................. 171

Symbols used in the manuals ................................................. 171Generator Settings .................................................................. 172Digital Output Settings and connections ................................. 173

Using the Waveform Generator ........................................... 175Symbol used in the manuals ................................................... 175Settings and connections ........................................................ 175

Using the Oscilloscope ........................................................ 176Symbols used in the manuals ................................................. 176Settings and connections ........................................................ 177

Using the Spectrum Analyzer .............................................. 178Symbol used in the manuals ................................................... 178Settings and connections ........................................................ 178

Using the True RMS Voltmeter / Power Meter .................... 181Symbols used in the manuals ................................................. 181Settings and connections ........................................................ 181

Using the Bit Error Ratio Tester ........................................... 182Symbol used in the manuals ................................................... 183Settings and connections ........................................................ 183

Appendix E Using Conventional Instruments ............................................ 185Instrument symbols and terms ............................................. 185Signal levels in the Satellite Communications Training System ................................................................................. 185Power Sensors ..................................................................... 187Spectrum analyzer ............................................................... 188

Table of Contents

© Festo Didactic 86312-10 IX

Appendix F Noise Measurement Using a Spectrometer ........................... 189How a spectrum analyzer works .......................................... 189Sensitivity ............................................................................. 189Detector mode...................................................................... 190Trace averaging ................................................................... 192Resolution bandwidth ........................................................... 193Corrections to the measured noise level ............................. 194

Averaging ............................................................................... 194Equivalent noise bandwidth .................................................... 195Preamplifier gain .................................................................... 195Summary ................................................................................ 195

Index of New Terms ........................................................................................... 197

Bibliography ....................................................................................................... 201

© Festo Didactic 86312-10 XI

Preface

Since the Soviet Union shocked the western world by launching the first artificial satellite, SPUTNIK I, on October 4, 1957, the science of satellites and satellite communications has undergone an amazing evolution. Today satellites play an essential role in global communications including telephony, data networking, video transporting and distribution, as well as television and radio broadcasting directly to the consumer. They fulfill critical missions for governments, the military and other organizations that require reliable communications links throughout the world, and generate billions of dollars annually in revenue for private enterprise.

Communications satellites offer several important advantages over other types of long-range communications systems: the capability of direct communication between two points on earth with only one intermediate relay (the satellite), the ability to broadcast or collect signals and data to or from any area ranging up to the entire surface of the world, and the ability to provide services to remote regions where ground-based, point-to-point communications would be impractical or impossible.

One of the greatest advantages of satellite communications systems is the ratio of capacity versus cost. Although satellites are expensive to develop, launch and maintain, their tremendous capacity makes them very attractive for many applications. INTELSAT I, launched in 1965, had a capacity of only 240 two-way telephone channels or one two-way television channel, and an annual cost of $32 500 per channel. Since then, the capacity and lifetime of communication satellites have increased tremendously resulting in a drastic reduction in the cost per channel. Communications satellites now have capacities sufficient for several hundred video channels or tens of thousands of voice or data links.

In addition to applications designed specifically for communications purposes, satellites are used extensively for navigation systems, scientific research, mapping, remote sensing, military reconnaissance, disaster detection and relief and for many other applications. All of these applications, however, require at least one communications link between the satellite and one or more earth stations.

The Satellite Communications Training System is a state-of-the-art training system for the field of satellite communications. Specifically designed for hands-on training, the system covers modern satellite communication technologies including analog and digital modulation. It is designed to use realistic satellite uplink and downlink frequencies at safe power levels and to reflect the standards commonly used in modern satellite communications systems.

The Orbit Simulator provides interactive visualization of satellite orbital mechanics and coverage, and the theory behind antenna alignment with geostationary satellites. The optional Dish Antenna and Accessories provides hands-on experience in aligning a typical antenna with real geostationary satellites.

Preface

XII © Festo Didactic 86312-10

We invite readers of this manual to send us their tips, feedback, and suggestions for improving the book.

Please send these to [email protected].

The authors and Festo Didactic look forward to your comments.

© Festo Didactic 86312-10 XIII

About This Manual

Manual Objective

When you have completed this manual, you will be familiar with the main concepts and parameters that characterize microwave links and link performance. These concepts and parameters apply to both terrestrial and satellite RF links.

You will be familiar with the parameters that characterize antennas and with the different losses in a microwave link. You will also be familiar with the origins and characteristics of noise and with the noise parameters used to characterize components and systems.

Finally, you will be familiar with the analysis of an RF link known as a link budget, a mathematical model of the link that predicts its performance.

a The objective of this manual is to demonstrate the concepts that determine link performance and not to make precise measurements, since precise measurements require specialized equipment and ideal conditions. b Many calculations will be required as you carry out the exercise procedures. Although tables are provided to facilitate these calculations, you are encouraged to use a spreadsheet program or a mathematics application such as Matlab or Scilab for these calculations.

Description

This Student Manual is divided into several units each of which covers one topic. Each unit begins with an Introduction presenting important background information. Following this are a number of exercises designed to present the subject matter in convenient instructional segments. In each exercise, principles and concepts are presented first followed by a step-by-step, hands-on procedure to complete the learning process.

Each exercise contains:

A clearly defined Exercise Objective

A Discussion Outline listing the main points presented in the Discussion

A Discussion of the theory involved

A Procedure Outline listing the main sections in the Procedure

A step-by-step Procedure in which the student observes and measures the important phenomena, including questions to help in understanding the important principles.

A Conclusion

Review Questions

a In this manual, all New Terms are defined in the Glossary of New Terms. In addition, an Index of New Terms is provided at the end of the manual.

About This Manual

XIV © Festo Didactic 86312-10

Prerequisite

As a prerequisite to this course, you should have performed the exercises in the manual Principles of Satellite Communications, part number 86311-00. This manual contains many tips on using the Satellite Communications Training System and the optional Telemetry and Instrumentation Add-On. Most of these tips are not repeated in the present manual.

Systems of units

Units are expressed using the SI system of units.

Safety considerations

Safety symbols that may be used in this manual and on the equipment are listed in the Safety Symbols table at the beginning of the manual.

Safety procedures related to the tasks that you will be asked to perform are indicated in each exercise.

Make sure that you are wearing appropriate protective equipment when performing the tasks. You should never perform a task if you have any reason to think that a manipulation could be dangerous for you or your teammates.

When studying communications systems, it is very important to develop good safety habits. Although microwaves are invisible, they can be dangerous at high levels or for long exposure times. The most important safety rule when working with microwave equipment is to avoid exposure to dangerous radiation levels.

The radiation levels in the Satellite Communications Training System are too low to be dangerous. The highest power level in the system is at the RF OUTPUT of the Earth Station Transmitter and is typically 5 dBm (approximately 3.2 mW) at 11 GHz. The maximum power density that can be produced by the Satellite Communications Training System using the supplied equipment is approximately 0.13 mW/cm2, well below all Canadian, American, and European standards for both microwave exposed workers and the general public.

c For more detailed information, refer to Safety with RF fields in Exercise 1-1 of the manual Principles of Satellite Communications, part number 86311-00.

© Festo Didactic 86312-10 XV

To the Instructor

You will find in this Instructor Guide all the elements included in the Student Manual together with the answers to all questions, results of measurements, graphs, explanations, suggestions, and, in some cases, instructions to help you guide the students through their learning process. All the information that applies to you is placed between markers and appears in red.

Accuracy of measurements

The numerical results of the hands-on exercises may differ from one student to another. For this reason, the results and answers given in this manual should be considered as a guide. Students who correctly performed the exercises should expect to demonstrate the principles involved and make observations and measurements similar to those given as answers.

Sample Exercise

Extracted from

the Student Manual

and the Instructor Guide

© Festo Didactic 86312-10 101

When you have completed this exercise, you will be familiar with noise in communications systems and with the characteristics of noise. You will also be familiar with various parameters concerning noise and how they are calculated. You will see how a link budget is calculated to include all the gains, losses and noise in the system.

The Discussion of this exercise covers the following points:

Noise in communications systems Thermal noise characteristics

Amplitude distribution. Frequency distribution. Half-power and equivalent noise bandwidths Additive white Gaussian noise (AWGN) Thermal noise power

Noise power example. Signal-to-noise ratio Noise figure

Noise figure example. Noise temperature

Noise figure versus noise temperature. Composite noise figure and noise temperature of cascaded elements

Noise figure and noise temperature example. Noise figure and noise temperature of an attenuator or a feed line.

Antenna noise temperature System noise temperature

Composite temperature of the antenna and feed line. Link performance and receiver figure of merit Link budget

Link budget example. Analog and digital figures of merit.

Noise in communications systems

Unwanted electrical signals are present in every electrical system. These unwanted signals are referred to as noise.

Noise arises from a variety of sources. Man-made sources of noise include carriers from transmitters other than those you wish to receive. This noise is referred to as interference. Natural sources of noise include the atmosphere, the sun, and the ground around a receiving antenna.

Noise limits the performance of a communications system because it tends to mask the desired signal. In an analog system, noise reduces the quality of the receiver output signal. In a digital system, noise limits the ability of the demodulator to make correct symbol decisions, which leads to errors in the received bits. For this reason, the ratio of signal power to noise power (or a

Noise and the Link Budget

Exercise 3

EXERCISE OBJECTIVE

DISCUSSION OUTLINE

DISCUSSION

Exercise 3 – Noise and the Link Budget Discussion

102 © Festo Didactic 86312-10

similar measurement) is an important factor in evaluating the performance of a communications link.

Much of the potential noise in a communication system can be reduced or eliminated by careful design. However, there is one natural source of noise that can never be eliminated. This is called thermal noise, Johnson noise, or Johnson-Nyquist noise and is caused by the random, thermal agitation of an extremely large number of charged carriers (electrons) in electrical conductors.

Not all random noise in a system is thermal noise. Shot noise, for example arises from the quantized nature of current flow. This and other random phenomena produce noise whose characteristics are similar to thermal noise. The combined effect of all these random phenomena is often treated as if it were all caused by thermal noise.

Thermal noise characteristics

Figure 43 shows an example of thermal noise as it could be displayed on an oscilloscope.

Figure 43. Noise trace (time-domain representation) of 1 V rms thermal noise.

Because thermal noise is a random process, its instantaneous value (voltage or current) is constantly changing and it is impossible to predict what the value will be at a given time. Nonetheless, several properties of the noise are stable over time and these can be used to characterize the noise.

Amplitude distribution

From one instant to the next, the amplitude of unfiltered thermal noise may change very little or it may swing widely from one extreme value to another. These values can be analyzed statistically. If the noise is sampled (that is, the instantaneous noise amplitude is measured at regular intervals) and the observed range of amplitudes is divided into small ranges, it is possible to

4

3

2

1

0

1

2

3

4

John Bertrand Johnson was a Swedish-born American electrical engineer and physicist. Johnson first measured thermal noise at Bell Telephone Laboratories in 1926. He concluded that thermal noise is intrinsic to all electrical components, even in the absence of an applied voltage.

Harry Nyquist, another Swedish-born American electrical engineer, also worked as Bell Labs. In 1927, Nyquist provided a mathematical explanation of thermal noise.

Time

Am

plitu

de (V

)



determine how many samples fall within each of the ranges. The results can be plotted as a histogram. This histogram gives an idea of the statistical distribution of different amplitudes in the noise.

Figure 44 shows the same noise trace as Figure 43 but rotated 90°. The sampled amplitudes are shown as dots. The vertical lines divide the possible amplitudes into a number of equally-spaced ranges. The histogram below the trace shows the relative number samples that fall within each amplitude range.

Figure 44. Noise trace and amplitude histogram of 1 V rms thermal noise.

Amplitude

Amplitudes ranges

Num

ber o

f sam

ples

Time



Although this histogram was generated from a small number of samples, it reveals some important characteristics of thermal noise. Amplitudes near 0 V occur more frequently than amplitudes with a large positive or negative voltage. We can say that small amplitudes are more probable than large amplitudes. In addition the histogram seems to be relatively symmetrical and is centered on 0 V.

If an extremely large number of samples are taken of the noise, and if the amplitude interval of the histogram is made extremely small, the histogram tends toward a continuous curve called the probability density function. In the case of thermal noise, the probability density function has the familiar bell-curve shape of the Gaussian, or normal, probability density function shown in Figure 45. Thermal noise results from contributions of an almost infinite number of independent sources. For this reason, it can be described as a Gaussian random process.

Figure 45. Gaussian (normal) probability density function ( , ).

In theory, the domain of a probability density function ranges from to . However, the function approaches zero for values far from the mean value.

The probability density function shows the relative likelihood for a random variable, such as a voltage, to take on a given value. The probability that the variable will fall within a particular range is given by the area under the density function between the limits of the specified range. For example, in Figure 45, the probability that a single voltage sample will fall between -1 V and +1 V is equal to the area under the curve between -1 and +1. In Figure 45, this area is approximately 0.68. Since the probability that any value will lie somewhere under the curve is 1.0 (100%), the total area under the curve is equal to one.

Frequency distribution

Johnson showed that thermal noise power is constant throughout the frequency spectrum. For this reason, thermal noise is referred to as white noise. Just as white light contains equal amounts of all frequencies within the visible band of electromagnetic radiation, white noise contains equal amounts of all frequencies. More precisely, thermal noise contains an equal amount of noise power per unit bandwidth at all frequencies from dc to about 1000 GHz. For this reason, it’s power spectrum can be represented as a straight, horizontal line, as shown in Figure 46a extending from 0 Hz to a very high frequency.

The standard deviation indicates how much the values deviate from the mean value. For thermal noise, the standard devia-tion is equal to the rms value. Figure 45 represents the amplitude distribution of a 1 V rms noise signal with no dc offset, as shown in Figure 43 and Figure 44.

In a normal distribution, approximately 68% of the values are within one standard deviation from the mean; approximately 95% of the values lie within two standard deviations; and 99.7% of the values within three standard deviations from the mean.

Value (e.g. amplitude in V)

Pro

babi

lity

dens

ity



Figure 46. Power spectrum of unfiltered and filtered white noise.

The noise power per unit bandwidth is referred to as the noise power spectral density (N-zero). Its units are W/Hz or dBm/Hz.

Although white noise contains a vast range of frequencies, harmful noise power is that which occurs in the bandwidth of the communications channel or the bandwidth of the receiver. The channel along with the receiver input stage (as well as the IF stage of a spectrum analyzer) limit the bandwidth, that is, they act as a band-pass filter.

Figure 46b shows the magnitude transfer function of an ideal band-pass filter. This ideal filter is called a brickwall filter because it allows all frequencies within its bandwidth to pass unaffected and completely blocks all other frequencies.

If white noise is applied to the input of the brickwall filter, the spectrum of the noise at the output resembles Figure 46c. This is essentially a rectangular slice of the input noise power with power spectral density within the filter bandwidth and zero elsewhere.

The symbol for noise power spectral density (N-zero) should not be confused with the symbol for output noise power (N-o).

Frequency

Frequency

Frequency

Spe

ctra

l den

sity

M

agni

tude

S

pect

ral D

ensi

ty

0

0

0

1

a) White noise spectrum

b) Brickwall band-pass filter transfer function

c) Filtered noise spectrum

0

0

0

B

B



If at the input of a network (an electrical component, circuit, or communications channel) is known, and if the network acts as an ideal (brickwall) filter with bandwidth , then the noise power at the output is simply the power spectral density multiplied by the bandwidth:

(43)

where is the output noise power is the noise power spectral density is the (ideal rectangular) bandwidth

Half-power and equivalent noise bandwidths

An ideal rectangular filter has uniform frequency response within its bandwidth and zero response outside its bandwidth, as shown in Figure 46b. Unfortunately, this ideal response is unattainable in real systems. Instead of stopping abruptly, the frequency response rolls off gradually. For this reason, many different definitions of bandwidth are used, the most common of which is the familiar half-power bandwidth or 3 dB bandwidth. This is the interval between frequencies at which the gain of the system has dropped to half power (3 dB below) the peak value.

The 3 dB bandwidth of a practical filter is shown in blue in Figure 47. Since the power is proportional to the square of the voltage, the half-power point occurs at

of the peak amplitude.

Although the 3 dB bandwidth is very useful when dealing with signals, it does not give accurate values when dealing with noise. This is due to the fact that there is no direct relationship between the amount of noise power a filter passes and its 3 dB bandwidth.

Instead, the equivalent noise bandwidth is used. This is defined as the bandwidth of a fictitious, ideal rectangular filter (brickwall filter) with the same band-center gain as the actual system, which would pass exactly as much white noise power as the actual system does. Both of these bandwidths are illustrated in Figure 47.

Figure 47. Half-power bandwidth and equivalent noise bandwidth.

00.10.20.30.40.50.60.70.80.91

1.1

Regardless of whether the device in question is a com-ponent, a cascade of com-ponents, or an entire sys-tem, we will refer to the device as a network.

The symbols , and are often used for band-width.

The equivalent noise band-width also called the noise equivalent bandwidth, the noise-power equivalent bandwidth, or simply the noise bandwidth.

Common symbols for equivalent noise bandwidth are , , and

Practical filter

Ideal Filter

3 dB (half-power) bandwidth

Equivalent noise

bandwidth

Am

plitu

de [V

]

0.707



For most analog filters and band-limited circuits, the equivalent noise bandwidth is slightly larger than the half-power bandwidth. Since a spectrum analyzer uses a narrow band-pass filter, the difference between equivalent noise bandwidth and half-power bandwidth must be taken into consideration when measuring noise power with this type of instrument.

a Since the narrow band-pass filter in a spectrum analyzer allows the instrument to resolve closely-spaced frequency components, its 3 dB bandwidth is referred to as the resolution bandwidth. The ENB of this filter may be greater than its 3 dB bandwidth. This is explained in Appendix F Noise Measurement Using a Spectrometer. It is important to read this appendix before beginning the Procedure of this exercise.

The mathematical definition of equivalent noise bandwidth is:

(44)

where is the equivalent noise bandwidth is the maximum value of the power transfer function

d is the area under the curve of the power transfer function

Additive white Gaussian noise (AWGN)

The generally accepted model for thermal noise in communication channels is described as follows:

The noise is additive. The noise adds positive and negative random values to the amplitude of the signal.

The noise is white, that is, its power spectral density is flat. In theory, white noise has unlimited bandwidth and all frequencies are represented equally. In practice, white noise has a uniform spectral density within the bandwidth of interest.

The noise has a Gaussian, or normal probability density because it results from the agitation of a very large number of independent atomic particles. This distribution arises when a large number of independent sources contribute additively to the end result, as long as the contribution of each is small compared to the sum. With this type of distribution, instantaneous noise voltages near the mean value are more probable than voltages much higher or lower than the mean value.

This model for thermal noise is often referred to as additive white Gaussian noise (AWGN).

Transmitted signal

Channel Noise

Received Signal



Thermal noise power

As previously mentioned, all components and circuits generate thermal noise. As its name implies, the amount of thermal noise generated depends on the temperature of the device. A representation, or electrical model, of a thermal noise source is shown in Figure 48a. The source (a resistor) is shown connected to a load (the input of an amplifier).

Figure 48. Network consisting of a matched noise source and load (an amplifier).

Since the resistor has two terminals, where the current into one is identical to the current out of the other, it referred to as a one-port element.

The RMS thermal noise voltage produced by the resistor of resistance at a temperature (in kelvin) is:

(45)

where is Boltzmann’s constant

is the temperature in kelvin ( is the system equivalent noise bandwidth in Hz is the resistance in ohms.

b) Equivalent circuit

Thermal noise source

(resistance)

Matched load

(amplifier)

Noiseless resistor

Noise source with no

resistance

a) Thermal noise source and matched load



Figure 48b shows an electrically equivalent model of the circuit in Figure 48a. It consists of a noiseless resister in series with an ideal noise source which as no resistance.

Maximum power is delivered when the impedance of the source and of the load are matched (in this case, when the resistance of the load equals that of the source). The input noise voltage delivered to the impedance-matched load is one half the source noise voltage. The input noise power delivered to the amplifier, expressed in watts and in dBm, is given by:

(46)

where is Boltzmann’s constant is the temperature in K is the system equivalent noise bandwidth in Hz

a All logarithms in this manual are base 10 logarithms.

Equation (46) shows that the power delivered by a thermal noise source to the impedance-matched load depends only on the temperature and the bandwidth. It is independent of the impedance. The input noise power spectral density is therefore:

(47)

The noise power spectral density at any point in a circuit is simply the noise power contained in a bandwidth of 1 Hz. With white noise, the noise power spectral density is constant over a vast range of frequencies. The noise power at any point can be therefore determined from the noise power spectral density and the bandwidth using Equation (43).



Sometimes it is necessary to determine the noise power in some bandwidth when the noise power in a different bandwidth is known. This is easily done using Equation (48).

(48)

Expressed in dBm, this gives the very useful formula:

(49)

Noise power example

Thermal noise in a circuit with a bandwidth of has a power of . What would be the noise power if the bandwidth were reduced to ?

What in the noise power spectral density?

Signal-to-noise ratio

The signal-to-noise ratio (SNR or S/N) is a measure that compares the level of a signal to the level of background noise. It is defined as the power ratio between a signal and the background noise. It can be expressed as a ratio or in decibels.

(50)

where is the average power of the signal is the average power of the noise



Since the noise power is proportional to the bandwidth, the bandwidth is assumed to be that of the circuit, unless a different bandwidth is specified. A SNR higher than 1 (> 0 dB) indicates that there is more signal than noise.

An ideal amplifier would amplify the noise and the signal at its input equally without adding any noise of its own. The signal-to-noise ratio at the output would therefore be the same as at the input.

Unfortunately, every component and network adds some noise of its own. To characterize this added noise, it is not sufficient to compare the output noise power to the input noise power because the network may amplify or attenuate both the input noise and signal while adding noise of its own. For this reason, the noise figure is used.

Noise figure

Since a receiving system must process very weak signals in the presence of noise, it is important to be able to characterize the ability of the system to process these low-level signals. One very useful parameter is the noise figure, defined in the 1940’s by Harald T. Friis. This parameter is suitable for characterizing an entire receiving system as well as individual system components such as amplifiers and mixers. It is also used to characterize any number of components in cascade. Because the networks shown in Figure 49 have both an input and an output, they are referred to as two-port elements.

a) Two-port element

b) Cascaded two-port elements

c) Earth Station Receiver Down Converters

Figure 49. Examples of networks.

Friis defined the noise figure of a network as the degradation or decrease of the signal-to-noise ratio as the signal passes through the network:

(51)

where is the signal-to-noise ratio at the input is the signal-to-noise ratio of the output

Input Output

Input Output

OutputInput



Like gain, the noise figure can be expressed either as a unitless ratio or in decibels. When expressed as a ratio, as in Equation (51), it is sometimes referred to as the noise factor. When expressed in decibels, the noise figure is usually written as :

(52)

a In this manual, the term “noise figure” is the term generally used in phrases referring to the degradation in signal-to-noise ratio with no units being implied. Where necessary, the term “noise factor ” is used for the ratio and the term “noise figure ” is used for the value in decibels.

When the gain , the input noise power and the output noise power in decibels are known, the noise figure in decibels can be calculated directly:

(53)

The noise figure of a system does not depend on the type of modulation used. Since the noise power is proportional to the bandwidth (Equation (43)), the same bandwidth must be considered at the input and the output of the network when determining and . For this reason, the noise figure is independent of bandwidth.

The noise figure is a parameter that expresses the noisiness of a two-port network or device (that is, one with an input and an output). Since the noise figure represents a degradation, or decrease, in signal-to-noise ratio, a low noise figure is desirable. The higher the noise figure, the more noise is added by the network in consideration.



Noise figure example

Figure 50 provides an example to illustrate the use of the noise figure.

(a) At the input of an amplifier (b) At the output of an amplifier

Figure 50. Signal and noise levels as seen on a spectrum analyzer.

The signal at the input of the amplifier is at -40 dBm, 30 dB above the noise floor (-70 dBm), as displayed by a spectrum analyzer with a certain resolution bandwidth. The gain of the amplifier is 20 dB. The amplifier amplifies both the input signal and the input noise by 20 dB and adds 5 dB of noise. As a result, the signal at the output is only 25 dB above the noise floor. The noise figure of this amplifier is therefore:

Alternatively, using Equation (53):

The noise factor can be written as shown in Equation (54).

(54)

where is the gain of the network is the signal power at the input is the signal power at the output is the noise power at the input is the noise power added by the network is the noise power at the output

Frequency [GHz] Frequency [GHz]

Pow

er [d

Bm

]

Pow

er [d

Bm

]



Equation (54) shows that the noise added by the network can be considered separately from the input noise . This is illustrated in Figure 51.

Figure 51. Noise in amplifiers.

Instead of a noisy amplifier, as in Figure 51a, the amplifier can be considered to be ideal (noiseless) but with an additional, equivalent noise source at the input, as shown in Figure 51b. The two noise sources are uncorrelated and therefore simply add together. Models a and b are electrically equivalent.

Equation (55) shows the noise factor expressed using .

(55)

where is the noise power added by the network, referred to the input

( )

An ideal network that contributes no noise would have and a noise factor of 1 (a 0 dB noise figure).

Equation (54) and Equation (55) show that the noise figure is not an absolute measure of noise. Rather, it expresses the noisiness of a network relative to the input noise. The noise added by the network is fixed and does not change with

Noiseless

(b) Equivalent circuit

(a) Noisy amplifier



the input signal. As a result, when more noise is present at the input, the contribution of the added noise to the total noise is less significant.

In order to make comparisons between different devices using the noise figure, a reference value for the input noise source must be chosen. Friis suggested that the noise figure be defined for an input noise source at a standard temperature

(16.8°C or 62.3°F). The suggestion was later adopted by the IEEE as part of its standard definition of noise figure.

Equation (56) shows that the input noise spectral density from a resistance at temperature is:

(56)


To determine the output noise power under these standard conditions, a standard matched noise source (resistive load at ) is connected to the input of the network and the noise power at the output is measured.

The definition of noise factor adopted by the IEEE (Institute of Electrical and Electronics Engineers) is therefore:

(57)

where is the noise from a matched resistance at is the noise added by the network, referred to the output

By substituting for , this can be expressed as:

(58)

where is the noise power added by the network, referred to the output is the noise power added by the network, referred to the input



Since the noise figure is defined for a reference temperature of 290 K, a different value is used when the source temperature is not 290 K. This value is called the operational noise figure (or factor) or effective noise figure (or factor) and is related to the noise factor by Equation (59).

(59)

where is the operational noise factor is the source temperature is 290 K is the noise factor

Note, however, that for small deviations in source temperature, the difference between and may not be significant. For source temperatures between approximately 260 K and 330 K, the difference between and in decibels is less than 0.5 dB and it is less than 0.25 dB for source temperatures between 280 K and 300 K.

Noise temperature

Equation (46) showed that the power delivered by a thermal noise source at the input of an impedance-matched network depends only on the temperature (in kelvin) and the bandwidth: .

In Equation (55), the noise power added by a network is considered separately and is expressed as an equivalent input noise .

The definition of noise figure considers an impedance-matched source resistance at temperature producing an input noise power . Figure 52a shows a network (an amplifier) where the input noise is produced by a source at temperature and the noise added by the network is .

Figure 52b shows an electrically equivalent model where the network is noiseless. The input noise is produced by a source at temperature and an equivalent input noise is produced by an additional source at temperature . The two noise sources are uncorrelated and therefore simply add together.



Figure 52. Equivalent circuits illustrating effective input noise temperature .

The temperature is called the effective input noise temperature and is always measured in kelvin. This is defined as the temperature of a fictitious noise source at the input of a two-port network or amplifier that would result in the same output noise power, when connected to a noise-free network or amplifier, as that of the actual network or amplifier connected to a noise-free source.

Note that in Figure 52, if the input noise source temperature was absolute zero (0 K), then there would be no noise at the input of the amplifier ( ). In this case, the only noise at the output would be the noise produced by the amplifier where .

Equation (55) then can be rewritten as:

(60)

where is the noise factor is the effective input noise temperature in kelvin is 290 K

Equation (60) shows that the noisiness of a network can be modeled as if it were caused by an additional noise source operating at the effective noise temperature . Powers from uncorrelated sources are additive so noise temperatures are also additive. A network that adds no noise at all has and

.

The temperature is often referred to as the effective noise temperature or just the noise temperature and sometimes as simply the “temperature,” even though it is not the physical tem-perature.

Gain

Noiseless

Gain Noise

a) Noisy amplifier




If the noise figure is known, the effective noise temperature is given by:

(61)

The noise figure and the effective noise temperature both represent the noise performance of devices. Figure 53 shows the relationship between the noise figure, the noise factor, and the noise temperature in K.

Figure 53. Noise figure [dB] and (noise factor) versus effective noise temperature .

Noise figure versus noise temperature

Although the noise figure and the effective noise temperature are both parameters that represent the noisiness of a network, there are cases where one is easier to use than the other. In terrestrial applications, the physical temperature is usually close to 290 K (16.85°C or 62.33°F). Since the noise figure is defined for this temperature, the noise figure is the parameter usually used for terrestrial applications. Noise figures for these applications typically fall in the range of 1 to 10 dB.

For satellite communications however, receivers typically have low noise figures, typically between 0.5 and 1.5 dB. Comparing two devices with low noise figures would require specifying the noise figure to several decimal places. In this case, it is usually more convenient to use the effective noise temperature since the numbers are larger. Besides, with satellite communications, the reference temperature of 290 K may not be appropriate. When using the noise temperature, no reference temperature is required.

Another you reason for using noise temperature instead of noise figure is that noise figure only applies to two-port devices (devices with both an input and an output) whereas noise temperature also applies to one-port devices (devices with only an output), such as antennas.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 50 100 150 200 250 300 350 400 450 500Effective noise temperature (K)

Noi

se fi

gure

or f

acto

r

[dB]

(noise factor)



Composite noise figure and noise temperature of cascaded elements

Friis developed formulas for determining the noise factor and the noise temperature of two-port elements connected in cascade. Each element may be a single component or a more complex network.

Figure 54. Noise factors and effective input temperatures of elements in cascade.

Equation (62) shows the Friis formula for the noise factor of cascaded elements:

(62)

where is the composite noise factor of the cascade is the noise factor of the jth element or stage is the gain of the jth element or stage is the number of elements or stages

Friis’s formula for effective input noise temperature is similar:

(63)

where is the composite effective input temperature of the cascade is the effective input temperature of the jth element or stage is the gain of the jth element or stage is the number of elements or stages

These equations show that the first stage in a network is most susceptible to add noise to the system, since the noise figure and noise temperature of the subsequent stages are reduced by the product of the gains of the preceding stages. It is therefore important that the first stage in the receiver have as low noise figure as possible, as well as high gain. This is why the first active component in a receiver is a low-noise amplifier (LNA).



Noise figure and noise temperature example

Figure 55a shows a network made up of two amplifiers in series. Figure 55b shows an electrically equivalent circuit. All impedances are matched (those of the sources, of the amplifiers, and of the load at the output). and are the noise factors of amplifier 1 and 2, respectively.

Figure 55. Two-stage network and equivalent circuit for determining noise figure.

The input noise and signal sources are shown in series. As these signals are uncorrelated, they simply add together.

For this example, we will assign values to each parameter and calculate the result.

Amplifiers 1 and 2 are identical; each amplifier has a gain and a noise figure . In linear terms, the gain and the noise factor for each amplifier. The signal at the input of the network .

We wish to calculate the noise figure of the entire network. The noise source at the input must therefore be at temperature since this is the temperature required by the definition of noise figure.

In the equivalent circuit, the first amplifier is represented showing three sources at its input: , , and .

Signal

Input noise

Added noise

Amplifier 1 Amplifier 2

Signal

Input noise (Noise source

at )


a) Two-stage network


Matched source

Matched source Matched

source

Matched load

Matched load

Matched load



represents the signal:

mW

mW

represents the noise from the source at 290 K (for convenience, we will calculate noise in units of ):

represents the noise added by amplifier 1, referred to its input. Since the noise factor , from Equation (55):

The signal at the output of amplifier 1 (and at the input of amplifier 2) is:

The noise at the output of amplifier 1 (and at the input of amplifier 2) is:

The second amplifier can also be represented as having three sources at its input: , , and the noise added by amplifier 2: .

a The noise added by amplifier 2 is the same as the noise added by amplifier one, since they both have the same noise figure.

The signal at the output of amplifier 2 is:

The noise at the output of amplifier 2 is:

The signal-to-noise ratio at the input of the network is:



The signal-to-noise ratio at the output of the network is:

Therefore, the total noise factor of the entire network is:

From Equation (62), the theoretical noise factor for this network is:

The noise figure of the entire network is:

This example illustrates why the noise figure of a network depends mostly on the noise figure of the first stage of the network. According to the definition of noise figure, the noise at the input of the network must be equal to in order to calculate the noise figure of the network. The noise added by this first stage can be significant in proportion to its input noise. The deterioration of the signal-to-noise ratio in the first stage is therefore significant.

Since the first stage of the network amplifies this noise by its gain, and adds noise of its own, the noise at the input of the second stage is much greater than . Hence the noise added by the second stage is less significant, in proportion to its input noise, than the noise added by the first stage is to its input noise. Therefore, the deterioration of the signal-to-noise ratio in the second stage is much less than in the first stage.

With satellite communications, the received signal is very weak because of the great distance between the transmitter and the receiver. For this reason, the noise figure of the receiver must be very low. What changes in the circuit of Figure 55 would be most effective in reducing the total noise figure?

Table 26 shows the effect of certain changes that could be made in the components of the circuit of this example in an attempt to reduce the total noise figure. It also shows the effective input noise temperature of the entire network for each case.



Three parameters are shown in the table: , , and . The Example column shows the values already used in the example and which yield a total noise figure of 3.22 dB. The various changes and the results of each change are shown using columns of different colors.

Table 26. Effect of changing noise figure and gain.

Parameter Example Changes / Results

Gain 10 dB 50 dB

Noise figure 1 3 dB 0.5 dB 0.5 dB

Noise figure 2 3 dB 0.5 dB 0.5 dB

Total noise figure 3.22 dB 3.01 dB 3.03 dB 0.86 dB 0.53 dB

Effective input noise temperature

319 K 290 K 293 K 64 K 38 K

From Equation (62), we know that the gain of the last stage of the network has no effect on the total noise figure, so no change in is shown in the table.

In the green column, the gain of the first stage is changed from 10 dB to 50 dB (a 10 000-fold increase in gain). As a result, the total noise figure of the network becomes 3.01 dB, a reduction of approximately 0.2 dB. The improvement is small because increasing the gain of the first stage only reduces the noise contribution of the second stage.

In the purple column, the noise figure of the second amplifier is reduced from 3 dB to 0.5 dB. As a result, the total noise figure is reduced by approximately 0.2 dB, again a small improvement.

In the blue column, the noise figure of the first amplifier is changed from 3 dB to 0.5 dB. This causes the total noise figure to drop to 0.86 dB, an improvement of 2.36 dB.

The orange column of Table 26 shows the effect of reducing the noise figure of the second stage as well as that of the first stage. Although this would yield a small additional improvement of 0.33 dB, this improvement may not be enough to justify the cost of two low-noise amplifiers.

The bottom row of Table 26 shows the effective input noise temperature that corresponds to each total noise figure . As already mentioned, for low noise devices, it is often more convenient to use the effective input noise temperature, rather than the noise figure.



It is only when evaluating the noise figure of a network that the noise source is considered to be at the standard temperature of 290 K. Once the noise figure is known and the effective input noise temperature calculated, the noisiness of the entire network is equal to that of one noise-free amplifier with a resistance connected to its input whose temperature is equal to the physical temperature of the source, and an additional resistance whose temperature is equal to the effective input noise temperature of the network. This is illustrated in Figure 56.

Figure 56. Network and an equivalent one-stage circuit showing the physical source temperature and the effective input noise temperature .

Signal

Input noise

Added noise


Signal

Input noise

a) Two-stage network


Matched Source

Matched Load

Matched Source

Matched Load

Noiseless



Noise figure and noise temperature of an attenuator or a feed line

Figure 57 shows networks that include a passive, lossy device, such as an attenuator or a feed line.

Figure 57. Networks including an attenuator and a feed line.

Figure 58 shows a typical attenuator circuit with a matched input and output impedance.

Figure 58. Typical attenuator circuit.

Attenuators and feed lines are both passive, impedance matched devices. The device loss is defined as:

(64)

where is the input power is the output power is the loss of the attenuator or line ( ) is the gain of the attenuator or line ( )

The noise figure for an attenuator or feed-line is defined the same way as for an active component, that is, considering an input noise source at the standard temperature of 290 K. When connected to a matched load, the input noise and the attenuator or feed-line together appear to the matched load as a simple noise

Input shuntOutput shunt

Series resistance

Amplifier

a) Attenuator

Attenuator

Amplifier

Feed line

Loss

a) Feed line

Loss



source at 290 K, providing that no components are higher than this temperature. The noise at the output of the attenuator (or line) is therefore .

If the input signal power to the attenuator or feed-line is , then the noise factor is:

(65)

where is the noise figure of the attenuator or feed-line is the loss of the attenuator or feed-line

Equation (65) shows that noise figure of an attenuator or of a lossy line is equal to its loss . This is because the signal-to-noise degradation results from the signal being attenuated while the noise level remains fixed.

The effective input noise temperature of a passive, lossy device with loss is related to its physical temperature:

(66)

where is the effective input noise temperature of a passive, lossy device is the physical temperature of the lossy device is the device loss

Note that, when the temperature of the lossy device is 290 K, the effective input noise temperature is:

(67)

where is the noise figure of the lossy device

Antenna noise temperature

Random noise is present at the terminals of a receiving antenna. A small part of this noise is thermal noise generated due to the antennas ohmic resistance. The remainder is noise the antenna picks up from other sources, both natural and man-made. The total amount of this noise can be represented as though it were thermal noise generated by a fictitious resistance at a temperature known as the effective antenna noise temperature or antenna noise temperature, or simply antenna temperature.

Only the noise factor is defined in reference to a standard temperature of 290K. The effective input noise temperature is not related to a standard tem-perature.

See also Equation (61).



The antenna noise temperature is the effective temperature such that the noise at the terminals of the antenna over a bandwidth is:

(68)

where is the noise produced by the antenna over the bandwidth is the bandwidth is Boltzmann’s constant

The amount of noise produced by an antenna depends on what the antenna “sees.” An antenna pointed at a clear sky picks up radiation that has been absorbed and released by molecules in the atmosphere. The antenna temperature depends on the frequency and the elevation angle of the antenna. The presence of clouds and especially of rain will increase the antenna temperature. The noise contribution from the sky is represented by the temperature .

In addition, the radiation from the ground may be captured by the side lobes of the antenna and to some extent by the main lobe is the elevation angle is small. The noise contribution from the ground is represented by the temperature .

Neglecting the small amount of noise due to the antenna’s ohmic resistance, the total antenna noise temperature is given by .

System noise temperature

Figure 59 shows a receiving system consisting of an antenna, a feed line, and a receiver. The antenna noise temperature is . The physical temperature of the feed line is . The loss of the feed line is equal to the reciprocal of its gain . The receiver has an effective input noise temperature .

Figure 59. System noise temperature.

From Equation (66) since the feed line acts as an attenuator with loss , its effective noise temperature is .

Antenna

System noise temperature (referred

to antenna output)

System noise temperature (referred

to receiver input)

Composite noise temperature

Feed line at

Receiver



The feed line and the receiver can be considered as two cascaded elements. The composite noise temperature of these two elements is determined by applying Equation (63):

(69)

where is the composite noise temperature of the feed line and receiver is the effective input noise temperature of the receiver is the effective noise temperature of the feed line is the loss of the feed-line

The system noise temperature or system temperature is similar in concept to the effective input noise temperature of a network. It is the temperature in kelvin of a fictitious resistance, placed at a specified point in a system made up of ideal (noiseless) components that would result in the same output noise power as produced by the actual system.

This fictitious resistance is usually considered to be located at the input of the receiver. One can say in this case that this is the “system temperature referred to the input of the receiver.”

Imagine first of all that this fictitious resistance is placed at the output of the antenna. In Figure 59, the system noise temperature referred to the output of the antenna is . Since the antenna acts as an noise source, the noise temperature of the entire system , referred to the output of the antenna, is simply equal to the sum :

(70)

where is the system noise temperature referred to the antenna output is the antenna noise temperature is the composite noise temperature of the feed line and receiver is the effective noise temperature of the feed line is the physical temperature of the feed line (often close to ) is the loss of the feed-line is the effective input noise temperature of the receiver

Now imagine that the fictitious resistance is placed at the input of the receiver, rather than at the output of the antenna. The temperature of this fictitious resistance is the system temperature referred to the input of the receiver.

How does the system temperature , referred to the receiver input, compare to the system temperature , referred to the antenna output? Referring to Figure 52 on page 118, recall that noise added by an amplifier with gain can be represented by a noise source at the input of a noiseless amplifier where

. The effective noise temperature of the amplifier is referred to the input of the amplifier. If the noise source was located at the output of the amplifier, rather than at the input, the added noise could be represented

Transmitter designers often prefer to refer the system noise temperature to the output of the antenna.

Receiver designers often prefer to refer the system noise temperature to the input of the receiver.



by , where is the noise temperature referred to the output. It follows that .

This also holds if the amplifier is replaced by a feed line whose gain . The system temperature , referred to the output of the feed line (the input of the receiver) is therefore:

(71)

where is the system noise temperature referred to the receiver input is the system noise temperature referred to the antenna output is the gain of the feed line (less than 1) is the loss of the feed-line is the antenna noise temperature is the feed-line physical temperature is the receiver effective noise temperature

Both system noise temperatures and take into account the noise produced by the antenna, the feed line, and the receiver. The noise temperature is called the system noise temperature at the receiver input.

Composite temperature of the antenna and feed line

In many terrestrial systems, the antenna temperature and the feed line physical temperature are both close to 290 K. When , this is also their composite temperature, regardless of the feed-line loss:



Link performance and receiver figure of merit

The performance of an individual link is evaluated as the ratio of the received carrier power to the noise power spectral density . The ratio has units of hertz (Hz).

The received carrier power is simply the power received at the input of the receiver. From Equation (42) on page 77:

(72)

where is the carrier power (power at receiver input) is the power at the transmitter output is the gain of the transmitting antenna is the transmitting antenna pointing loss is the transmitter feed-line loss is the free-space loss is the atmospheric attenuation is the gain of the receiving antenna is the receiving antenna pointing loss is the receiver feed-line loss is the antenna polarization mismatch loss is the effective isotropic radiated power is the path loss is the composite receiving gain

The noise power spectral density at the receiver input is proportional to the system noise temperature referred to the receiver input:

(73)


Therefore, the carrier power to the noise power spectral density at the receiver input is:

(74)

The carrier power to the noise power spectral density is the key parameter in evaluating the performance of a link.



Although Equation (74) was derived by determining the values at the receiver input, the ratio is independent of the point chosen in the receiving chain as long as the carrier power and the system noise power spectral density are calculated (not measured) at the same point. This is because the system temperature is calculated as though all components are ideal (noiseless) and all of the noise in the system results from a single, fictitious noise source at the receiver input.

Because the components of the receiver are not ideal, each component adds noise. For this reason, the ratio can only be directly measured at the output of the RF front end (at the input of the demodulator).

The ratio of the composite receiving gain to the system noise temperature is called the figure of merit of the receiving equipment.

Link budget

The objective of link performance analysis is to determine whether the communication system will provide the expected performance. The link budget compares the actual ratio to the ratio required to give the expected performance. The actual ratio should exceed the required ratio by a certain margin.

Performance analysis is carried out by calculating each of the terms of Equation (74) separately.

Link budget example

The following example analyzes the performance of the downlink between a satellite repeater (the transmitter) in a geostationary satellite and an earth-station receiver. The values used in this example are given in the tables below.

First, the is calculated:

The transmitter power in this example is 10 W. The earth station is within the 3 dB beamwidth of the downlink antenna. The values for this example are shown in Table 27.



Table 27. Calculating the EIRP.

Item Symbol Value Value (dB)

Transmitter power 10 W 40 dBm

Transmitter antenna gain 35 dBi

Maximum transmitter antenna pointing loss 3 dB

Transmitter antenna feed-line loss 1 dB

Effective isotropic radiated power (12 589 W) 71 dBm

a When necessary, both the absolute value and the value in decibels are given in the example tables. Values in parentheses are shown for information only; conversion into these values is not necessary for the calculations.

The path loss is calculated for a range of 40 000 km, a downlink frequency of 11 GHz, and an atmospheric attenuation of 0.3 dB.

Table 28. Calculating the path loss.


Distance 40 000 km

Frequency 11 GHz

Free-space loss 3.4 x 1020 205.3 dB

Atmospheric attenuation 0.3 dB

Path loss 205.6 dB

The composite receiver gain is calculated using the values in Table 29, assuming there is no polarization mismatch loss:



Table 29. Calculating the composite receiver gain.


Receiver antenna gain (100 000) 50 dB

Receiver antenna pointing loss 0.5 dB

Receiver antenna feed-line loss 1.26 1 dB

Polarization mismatch loss 0 dB

Composite receiving gain 70 795 48.5 dB

The earth station antenna points to a clear sky; its temperature is 65 K. The feed line temperature , however, is 290K. The noise figure of the receiver is 1 dB. The receiver antenna feed-line loss is given in Table 29.

The system noise temperature is calculated using:

Table 30. Calculating system noise temperature.


Antenna temperature 65 K

Feed line temperature 290 K

Receiver noise figure 1.26 1 dB

Receiver noise temperature 75.4 K

System noise temperature 186.8 K

The figure of merit of the receiver is . The link performance is characterized by the value :



Table 31. Calculating figure of merit and .


Figure of merit (380.2 K-1) 25.8 dB K-1

Boltzmann’s constant 1.38E-23 W K-1 Hz-1

-198.6 dBm K-1 Hz-1

Link performance figure 89.8 dBHz

The link budget says a great deal about the overall system design and performance. When the system is being designed, a minimal value is calculated that will provide the desired performance, and a link margin is added. The system is then designed to meet this value while making trade-offs between the system cost and various other constraints.

For example, if the system described above required a value of 83 dB, then a system built respecting parameters given in the tables would have a link margin of 6.8 dB.

Analog and digital figures of merit

An important figure of merit for an analog system is the average signal-to-noise ratio or at the input of the demodulator.

As mentioned before, the ratio is independent of the point chosen in the receiving chain as long as the carrier power and the system noise power spectral density are calculated at the same point. Since is the noise power in the bandwidth of 1 Hz, the can be converted into a signal-to-noise ratio by multiplying by the bandwidth of the receiver:

(75)

where is the signal power at the demodulator input is the noise power at the demodulator input is the carrier power at a certain point in the receiver chain is the noise power spectral density at the same point is the bandwidth of the receiver

In digital communication systems, the figure of merit is usually used. Consider a digital signal that conveys information one bit of the time at a bit rate . Each bit has a duration . The energy per bit is therefore

. The relation between and is:

(76)

where is the energy per bit is the bit rate

Exercise 3 – Noise and the Link Budget Procedure Outline


Equation (76) shows that the ratio is a normalized expression of the signal-to-noise ratio.

a Measuring the ratio is beyond the scope of this manual.

The Procedure is divided into the following sections:

System startup Noise figure

Set up for measuring noise figure. Measuring received carrier power and RF front end gain. Measuring the gain of the preamplifier. Measuring the receiver output noise power. Calculating the receiver noise figure and effective input noise temperature.

System noise temperature Link budget

a Before carrying out the following exercise Procedure, be sure to read Appendix F Noise Measurement Using a Spectrometer on page 187.

System startup

1. If not already done, set up the system and align the antennas visually as shown in Appendix B.

2. Make sure that no hardware faults have been activated in the Earth Station Transmitter or the Earth Station Receiver. b Faults in these modules are activated for troubleshooting exercises using DIP

switches located behind a removable panel on the back of these modules. For normal operation, all fault DIP switches should be in the “O” position.

3. Turn on each module that has a front panel Power switch (push the switch into the I position). After a few seconds, the Power LED should light.

4. If you are using the optional Telemetry and Instrumentation Add-On:

Make sure there is a USB connection between the Data Generation/Acquisition Interface, the Virtual Instrument, and the host computer, as described in Appendix B.

Turn on the Virtual Instrument using the rear panel power switch. b If the TiePieSCOPE drivers need to be installed, this will be done automatically in Windows 7 and 8. In Windows XP, the Found New Hardware Wizard will appear (it may appear twice). In this case, do not connect to Windows Update (select No, not this time and click Next). Then select Install the software automatically and click Next.

Start the Telemetry and Instrumentation application. In the Application Selector, do not select Work in stand-alone mode. b If the Telemetry and Instrumentation application is already running, exit

and restart it. This will ensure that no faults are active in the Satellite Repeater.

PROCEDURE OUTLINE

PROCEDURE

Exercise 3 – Noise and the Link Budget Procedure


Noise figure

Set up for measuring noise figure

5. Position the Earth Station Receiver, its antenna, and the spectrum analyzer so that you can easily connect this antenna to either to the RF INPUT of the Earth Station Receiver or to the input of the spectrum analyzer without putting tension on the cable.

a During this exercise, you will connect the antenna at the Earth Station Receiver to the RF INPUT of the Earth Station Receiver and then directly to the input of the spectrum analyzer. It is important to be able to make these connections without putting tension on the cable as this could move the antenna or change its orientation.

6. Make the connections shown in Figure 60 (you will require the RF Amplifier and the spectrum analyzer, but do not connect them now). In this exercise, the external RF Amplifier will be used as a spectrum analyzer preamplifier when measuring the noise power, as described in Appendix F. The RF Amplifier and the spectrum analyzer will be connected later as required.

a In this exercise, the RF Amplifier is referred to as the “preamplifier.”

Figure 60. Connections for an unmodulated carrier.

7. On the Earth Station Transmitter and the Earth Station Receiver, select a Channel not being used by another system in the same laboratory.

Digital Modulator

Up Converter1

Up Converter 2

RF OUTPUT

Down Converter 2

Down Converter 1

Earth Station Transmitter

Earth Station Receiver

Satellite Repeater

RF OUTPUT

I Q I Q

I OUTPUT to

I INPUT

Q OUTPUT to

Q INPUT

Spectrum Analyzer

Preamplifier (RF Amplifier)

Long cable

Large-Aperture Horn Antenna

(Uplink)

Large-Aperture Horn Antenna

(Downlink)

Small-Aperture Horn Antenna

(Uplink)

Small-Aperture Horn Antenna

(Downlink)



On the Earth Station Transmitter, make the following adjustments:

Data Source................................................... Sampler Scrambler ...................................................... Off Clock & Frame encoder ................................. Off

The signal at the output of the Digital Modulator is an unmodulated carrier. The RF OUTPUT signal from the transmitter is the same unmodulated carrier shifted up to the uplink frequency.

8. Align the antennas and optimize the alignment (see Aligning the antennas on page 38). Make sure the knob on the mast of the antenna at the Earth Station Receiver is tight.

Adjust the Gain control on the Earth Station Receiver so that the green Level LED is lit.

Measuring received carrier power and RF front end gain

In this section, you will measure the carrier power at the input of the receiver and at the output of the RF front end (the IF 1 OUTPUT) with the Gain control set to maximum. This will allow you to calculate the maximum gain on the RF front end, which consists of Down Converter 2 and Down Converter 1.

9. Taking care not to change the orientation of the antenna, disconnect the cable at the RF INPUT of the Earth Station Receiver and connect it to the input of the spectrum analyzer, as shown in Figure 61. The antenna should not move at all (i.e. its orientation should not change). If it does move, reconnect it to the Earth Station Receiver and realign the antennas.

Figure 61. Measuring . b As the signal received by the antenna is very weak, no attenuation will be required on the spectrum analyzer. Use averaging, if necessary, to reduce fluctuations. Use a marker or a cursor to read the power of the spectral line.

Enter the measured input carrier power in the first column of Table 32.

Down Converter 2

Down Converter 1


Spectrum Analyzer




Table 32. Maximum gain of the receiver RF front end.

[dBm]

[dBm] [dB]

Table 32. Maximum gain of the receiver RF front end.

[dBm] [dBm] [dB]

-45.5 1.57 47.1

You can expect the carrier at the IF 1 OUTPUT of the receiver to be approximately 45 dB above the signal received by the antenna. On the spectrum analyzer, select the appropriate scale and input attenuation level required in order to avoid overloading the instrument (if you are using the Telemetry and Instrumentation Add-On, connect the 20 dB Attenuator to the Frequency Converter and add 20 dB to the displayed level).

Being very careful not to move the antenna, disconnect the cable from the input of the spectrum analyzer and connect it to the RF INPUT of the Earth Station Receiver, as shown in Figure 62. Use the remaining long cable to connect the IF 1 OUTPUT to the spectrum analyzer.

Figure 62. Measuring .

On the Earth Station Receiver, turn the Gain control to the maximum position and measure the carrier power at the IF 1 OUTPUT using the required settings and attenuation. Enter this value into Table 32.

Calculate the gain of the receiver and enter this into Table 32.

Measuring the gain of the preamplifier

10. The gain of the preamplifier (RF Amplifier) is approximately 20 dB. However, it is preferable measure its gain more precisely.

On the Earth Station Receiver, reduce the Gain control until the peak on the spectrum analyzer is approximately -20 dBm (considering any attenuation used). Do not change the Gain setting for the rest of this section. Note the power in the first column of Table 33.

Down Converter 2

Down Converter 1


Spectrum Analyzer




Table 33. Preamplifier gain calculation.

[dBm]

[dBm]

[dB]

Table 33. Preamplifier gain calculation.

[dBm] [dBm] [dB]

-19.7 -0.1 19.6

11. Disconnect the spectrum analyzer from the receiver.

Power off the receiver and disconnect the power cable on the rear panel of the receiver.

Connect the RF amplifier directly to the IF 1 OUTPUT of the receiver, as shown in Figure 63, using a male SMA-SMA adapter. Tighten the connectors so that they are snug but not over tightened. A small wrench for this purpose is provided in the Accessories.

Figure 63. RF Amplifier connected to the IF 1 OUTPUT of the receiver.

The RF Amplifier is powered by the receiver power supply as shown in Figure 63. Connect the power cable from the receiver power supply to the connector on the bottom of the RF Amplifier. Plug the power cable from the RF Amplifier into the power connector on the rear panel of the receiver.

Power on the receiver.

RF Amplifier

Cable from receiver power supply

Cable to receiver power input (on rear panel)

RF Amplifier output



12. Connect the spectrum analyzer as shown in Figure 64.

Figure 64. Measuring preamplifier gain.

Note the power of the peak displayed on the spectrum analyzer in the second column of Table 33. Calculate the gain of the preamplifier.

Measuring the receiver output noise power

13. Disconnect the cable at the RF INPUT of the Earth Station Receiver and connect a 50 load (a matched load) in its place.

Figure 65. Measuring .

Power off the Earth Station Transmitter. This will reduce extraneous noise.

On the Earth Station Receiver, turn the Gain control to the maximum position and measure the noise level at the output of the preamplifier using the spectrum analyzer. Enter this value as in Table 34.

a As mentioned in Appendix F, it is preferable to use a wide span on the spectrum analyzer as this collects more noise power.

Fill in the other rows of Table 34 using the appropriate units. b Most spectrum analyzers display the resolution bandwidth corresponding to the selected span. If this is not the case, consult the user’s manual of the spectrum analyzer.

The Averaging correction depends on the type of averaging used on the spectrum analyzer. For video averaging or video filtering, this is +2.5 dB. For power (RMS) averaging, it is 0 dB. For FFT spectrum analyzers, it is also 0 dB.

Down Converter 2

Down Converter 1


Spectrum Analyzer

Preamplifier (RF Amplifier) 50

Down Converter 2

Down Converter 1


Spectrum Analyzer




For most conventional spectrum analyzers, the Equivalent noise bandwidth correction required may range from approximately -0.2 dB to -0.5 dB. If this value is not specified in the user documentation, a value of -0.5 dB is recommended. For FFT spectrum analyzers, this correction is 0 dB.

The virtual Spectrum Analyzer of the Telemetry and Instrumentation Add-On is an FFT spectrum analyzer.

Table 34. Measuring noise power at IF 1 OUTPUT.

Measured preamplifier output noise power

Preamplifier gain

Spectrum analyzer Span

Resolution bandwidth for this Span

Averaging correction

Equivalent noise bandwidth correction

Corrected receiver output noise power in RBW

Receiver output noise power spectral density

Table 34. Measuring noise power at IF 1 OUTPUT.

Using the Telemetry and Instrumentation Add-On:

Measured preamplifier output noise power -49.8 dBm

Preamplifier gain 19.6 dB

Spectrum analyzer Span 5 MHz/div. Resolution bandwidth for this Span 302 734 Hz Averaging correction 0 dB

Equivalent noise bandwidth correction 0 dB Corrected receiver output noise power in RBW

-69.4


-124.2 dBm/Hz

Using a conventional spectrum analyzer and power averaging (example):


Preamplifier gain 19.6 dB

Spectrum analyzer Span 300 MHz Resolution bandwidth for this Span 3 MHz Averaging correction 0

Equivalent noise bandwidth correction -0.5 dB Corrected receiver output noise power in RBW

-59.1 dBm


-123.9 dBm/Hz



Using a conventional spectrum analyzer and video averaging (example):


Preamplifier gain 19.6

Spectrum analyzer Span 300 MHz Resolution bandwidth for this Span 3 MHz Averaging correction 2.5 dB

Equivalent noise bandwidth correction -0.5 dB Corrected receiver output noise power in RBW

-59.1 dBm


-123.9 dBm/Hz

Calculating the receiver noise figure and effective input noise temperature

14. Using the receiver gain from Table 32, the receiver input noise power spectral density from Equation (56), and the receiver output noise power spectral density from Table 34 (all in dB), calculate the noise figure of the Earth Station Receiver.

Calculate the noise factor of the receiver and the equivalent input noise temperature .


15. Make sure the Earth Station Transmitter is turned off.

While observing the spectrum analyzer display, remove the 50 load at the RF INPUT of the receiver and connect the antenna. Is the noise level at the IF 1 OUTPUT different with the antenna connected rather than the 50 load?

No, there was no change in the displayed noise level.



What can you conclude about the noise temperature of the antenna and cable together as compared to the noise temperature of the 50 load?

The noise temperature of the antenna and cable together is the same as that of the 50 load, that is, .

16. Considering that the antenna temperature and the feed cable temperature are both 290K, calculate the system temperature referred to the input of the receiver.

To check your calculation, recall the definition of system temperature . Then calculate what the output noise power spectral density of the receiver would be using this system temperature. Compare the results of your calculation with the receiver output noise power spectral density determined in Table 34.

The system temperature, referred to the input of the receiver, is the temperature in kelvin of a fictitious resistance, placed at the receiver input in a system made up of ideal (noiseless) components that would result in the same output noise power as produced by the actual system.

The output noise power spectral density of such a system with a gain of 47.1 dB is calculated as follows:

This is exactly the same receiver output noise power spectral density measured in Table 34.



Link budget

In this section, you will calculate the figure of merit of the receiver. You will also value for the downlink and compare this with the measured value.

17. Measure the distance between the downlink antennas and enter this in Table 35.

Measure the power at the output of the repeater. If you use the Power Sensor on the repeater (via telemetry), you can measure this power directly. If you use a spectrum analyze, you must take into consideration the cable loss. Enter this power in Table 35.

Then fill in the remainder of the table. These values will be used in subsequent calculations and should be entered in the following tables as required.

Table 35. Initial values for link budget.

Channel

Downlink frequency (from Table 1 on page 32)

GHz

Distance

m

Transmitter power

dBm

Gain of small-aperture horn antenna

(from Table 10 on page 56) dBi

Gain of large-aperture horn antenna

(from Table 12 on page 59) dBi

Receiver noise figure

(from Step 14 on page 143) dB

Receiver noise temperature

(from Step 14 on page 143) K



Table 35. Initial values for link budget.

Channel

Downlink frequency (from Table 1 on page 3232)

9.0 GHz

Distance

(measured) 2.01 m

Transmitter power

or -12.4 dBm

Gain of small-aperture horn antenna

(from Table 10 on page 56) 14.2 dBi

Gain of large-aperture horn antenna

(from Table 12 on page 59) 18.4 dBi

Receiver noise figure (from Step 14 on page 143)

2.7 dB


(from Step 14 on page 143) 249 K

18. Fill in Table 36 making the necessary calculations.

Table 36. Calculating downlink EIRP (using the repeater as a transmitter).


Transmitter power

Transmitter antenna gain (small horn)


Transmitter antenna feed-line loss

Effective isotropic radiated power

a When necessary, both the absolute value and the value in decibels are given in the example tables. Values in parentheses are shown for information only; conversion into these values is not necessary for the calculations.



Table 36. Calculating downlink EIRP (using the repeater as a transmitter).


Transmitter power 0.058 mW -12.4 dBm

Transmitter antenna gain (small horn) 14.2 dBi


Transmitter antenna feed-line loss 2.4 dB

Effective isotropic radiated power (0.87 mW) -0.6 dBm

[dBm] [dB]

19. Calculate the path loss using:

Table 37. Calculating path loss.


Distance

Frequency

Free-space loss

Atmospheric attenuation 0 dB

Path loss

Table 37. Calculating path loss.


Distance 2.01 m

Frequency 9 GHz

Free-space loss 5.74x105 57.6 dB

Atmospheric attenuation 0 dB

Path loss 57.6 dB



20. The composite receiver gain is calculated using the equation:

When all values are expressed in decibels, the composite receiver gain is:

Table 38. Calculating composite receiver gain.


Receiver antenna gain

Receiver antenna pointing loss 0 dB

Receiver antenna feed-line loss

Polarization mismatch loss

Composite receiving gain

Table 38. Calculating composite receiver gain.


Receiver antenna gain (large horn) 18.4 dB

Receiver antenna pointing loss 0 dB

Receiver antenna feed-line loss 1.58 2.4 dB

Polarization mismatch loss 0 dB

Composite receiving gain 39.8 16.0 dB

21. Both the antenna and the feed line are at room temperature (290 K).

The system noise temperature is calculated using:





Antenna temperature

Feed line temperature

Receiver noise figure





Antenna temperature 290 K

Feed line temperature 290 K

Receiver noise figure 1.86 2.7 dB

Receiver noise temperature 249 K

System noise temperature 539 K

22. The figure of merit of the receiver is . The link performance is characterized by the value :

When the values , , , , and are expressed in decibels, the equation is:



Figure of merit

Boltzmann’s constant

Link performance figure





Figure of merit 0.074 K-1 -11.3 dB/K

Boltzmann’s constant 1.38E-23 W K-1 Hz-1 -198.6 dBm K-1 Hz-1

Link performance figure 129.1 dBHz

[dB ] [all in dB]

23. Use the values measured in Table 32 and Table 34 to determine the link performance figure at the IF 1 OUTPUT of the receiver.

Table 41. Measured link performance figure.

Carrier power

dBm

Noise power spectral density

dBm/Hz


dBHz

How does the value determined by measurement in Table 41 compare with the calculated value in Table 40?

Table 42. Measured link performance figure.

Carrier power

1.57 dBm

Noise power spectral density

-124.2 dBm/Hz


125.8 dBHz

The measured value and the calculated value are fairly close.

24. When you have finished using the system, exit any software being used and turn off the equipment.

Exercise 3 – Noise and the Link Budget Conclusion


In this exercise, you measured the noise figure of the receiver and calculated the receiver noise temperature. Then you determined the system noise temperature referred to the input of the receiver and calculated the figure of merit . You also calculated the value for the system.

1. Describe additive white Gaussian noise (AWGN)

Additive white Gaussian noise (AWGN) is a model for noise in communications channels. It describes noise as additive (adding positive and negative random values to the amplitude of the signal), white (having equal noise power per unit bandwidth over all frequencies of interest) and Gaussian (having a normal amplitude probability distribution).

2. What is the noise figure of a device?

The noise figure is the degradation or decrease of the signal-to-noise ratio as the signal passes through the device.

3. What is the noise temperature of a device?

The noise temperature, or more precisely, the effective input noise temperature of a device, is the source noise temperature in kelvin in a device that will result in the same output noise power, when connected to a noise-free device, as that of the actual device connected to a noise-free source

4. Define the system noise temperature.

The system noise temperature is the temperature in kelvin of a fictitious resistance, placed at a specified point in a system made up of ideal (noiseless) components that would result in the same output noise power as produced by the actual system.

5. What is the importance of the ratio of a communications link?

The ratio (carrier power to the noise power spectral density) determines the performance of a link.

CONCLUSION

REVIEW QUESTIONS


Bibliography

Agilent Technologies, Spectrum Analysis Basics, Application Note 150 (5952-0292.pdf).

Agilent Technologies, Spectrum and Signal Analyzer Measurements and Noise, Application Note (5966-4008E.pdf).

Antenna-theory.com, http://www.antenna-theory.com.

Chartrand, Mark R., Satellite Communications for the Nonspecialist, Bellingham, SPIE Press, 2004, ISBN 0-8194-5185-1.

Haslett, Christopher, Essentials of Radio Wave Propagation, Cambridge, Cambridge University Press, 2008, ISBN 978-0-511-37112-7.

Hewlett Packard, Spectrum Analysis noise figure measurements, Application Note 150-9 (5952-9229.pdf).

Maral, Gérard and Bousquet, Michel, Satellite Communications Systems, Fourth Edition, Chichester, John Wiley & Sons, 2002, ISBN 978-0-471-49654-0.

Miller Technology, Inc., Equivalent Noise Bandwidth (ENB), Technical Note TN129.

SKLAR, Bernard. Digital Communications Fundamentals and Applications, Second Edition, Upper Saddle River, N.J., Prentice Hall Inc., 2001 ISBN 978-0-13084-788-7

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