link characteristics and performance, 2 losses, radiated ... · pdf filefriis transmission...

© Festo Didactic 86312-00 61

When you have completed this exercise, you will be familiar with the various losses that affect a radio link. Knowing the transmitted power, as well as the losses and gains, you will be able to calculate the power at the input of a receiver.

The Discussion of this exercise covers the following points:

Effective isotropic radiated power of a directional antenna

Friis transmission equation

Free-space lossNotes on free-space loss.

Atmospheric attenuation and path loss

Feeder loss

Pointing loss

Polarization mismatch loss

Receiver input power

Effective isotropic radiated power of a directional antenna

An isotropic antenna radiates power uniformly in all directions. Its gain is equal to

one. If an isotropic antenna radiates the power , the radiation intensity (the power radiated per unit solid angle) is

(27)

With a radiating directional antenna, the radiation intensity is not uniform but is

maximal in the direction of maximum gain. In the direction where the gain is , the radiation intensity is

(28)

where is the effective isotropic radiated power [W]

For a directional antenna, the effective isotropic radiated power , also called the equivalent isotropic radiated power, is the power that a hypothetical isotropic antenna would emit in order to produce the same radiation intensity as the directional antenna in the direction of interest. In most cases, the direction of interest is the direction of maximum gain.

Losses, Radiated Power and Receiver Input Power

Exercise 2

EXERCISE OBJECTIVE

DISCUSSION OUTLINE

DISCUSSION

Exercise 2 – Losses, Radiated Power and Receiver Input Power Discussion

62 © Festo Didactic 86312-00

EIRP takes into account all losses (covered in the following sections) as well as the gain of the antenna. The EIRP allows comparing different antennas regardless of type or size. Knowing the EIRP and the distance between the transmitting and receiving antenna allows you to determine the amount of power the receiving antenna will collect.

Friis transmission equation

The power density (the amount of power passing through a unit area) produced

by an antenna radiating the power , at a distance from the antenna, in the direction of maximum gain , is:

(29)

where is the effective isotropic radiated power [W]

A receiving antenna whose effective aperture is receives the power which is proportional to the power density and the antenna’s effective aperture:

(30)

As shown in Equation (19), the gain of the receiving antenna is related to its effective aperture by:

(31)

Therefore:

(32)

where is the effective aperture of the receiving antenna is the gain of the receiving antenna

Harald Friis was a noted

radio engineer who worked

at Bell Laboratories. He

made pioneering contribu-

tions to radio propagation,

radio astronomy, and radar.



Putting this into Equation (30) gives:

(33)

Equation (33) was derived by Harald Friis and is known as the Friis transmission equation. It is one of the fundamental equations in antenna theory. It shows that, for antennas with specified gains, the received power will be greater for longer wavelengths (lower frequencies).

Free-space loss

Equation (33) can be rearranged as follows:

(34)

where is the free-space loss

The free-space loss or free-space path loss (FSPL) represents the ratio of the received and transmitted powers in a link between two isotropic

antennas (where ). Free-space loss represents the greatest single loss in any radio link.

Notes on free-space loss

Although the free-space loss represents a loss in power between transmitting and receiving antennas, free space in no way attenuates the signal. Instead, free-space loss is due to two factors: the spreading of the transmitted power and the effect of frequency on the receiving antenna’s effective aperture.

The term “free space” actually refers a vacuum. Attenuation due to molecules in the atmosphere is not part of free-space loss and is considered as a separate loss.

Power transmitted by antenna spreads out as it propagates through space. Only part of this power will be intercepted by the receiving antenna. The inverse square law states that the power intercepted per unit area is inversely proportional to the square of the distance from the source of the radiation. For

a transmitting isotropic antenna, the power density at a distance is:



The factor represents the spreading loss.

Free-space loss is defined with reference to isotropic antennas because the power radiated by an isotropic antenna would spread in a perfectly spherical manner. Free-space loss applies, however, to every antenna type.

The effective aperture of an isotropic antenna is proportional to the wavelength of the signal:

The power received by an isotropic antenna from a transmitting isotropic antenna is therefore:

For two isotropic antennas, the free-space loss is equal to the ratio:

The free-space loss can be expressed in decibels as:

For a terrestrial line-of-sight microwave hop of 50 km, operating at a frequency of 10 GHz, the free-space loss is approximately 146 dB. For a 15 GHz Ku-band link to a geostationary satellite located 40 000 km from the earth station, the free-space loss is approximately 208 dB.

Although the free-space loss increases as the square of the frequency, other frequency sensitive factors may affect the received power. In Exercise 1, you saw that aperture antennas can operate over a broad frequency range and that the gain of an aperture antenna is approximately proportional to the square of the frequency. Hence, the combined gains of the transmitting and receiving antennas are roughly proportional to the frequency to the fourth power. As a result, increasing the frequency may increase the received power, even though it increases the free-space loss.

By substituting , the Friis transmission equation can also be written as:

(35)

where is the effective aperture of the transmitting antenna is the effective aperture of the receiving antenna



Atmospheric attenuation and path loss

Radio waves are attenuated to some extent as they pass through the atmosphere. At frequencies below 10 GHz, this attenuation is negligible. At higher frequencies, however, considerable losses occur near the resonant frequencies of the various molecules in the atmosphere, especially oxygen and water vapor, as shown in Figure 34. This figure shows the atmospheric attenuation for an atmosphere of typical temperature pressure and water vapor content.

Figure 34. Attenuation due to absorption by the atmosphere.

Atmospheric attenuation is denoted by . Path loss is the combination of the free-space loss and the atmospheric attenuation:

(36)

Feeder loss

An antenna usually consists of one or more reflecting or directive elements, such as a parabolic dish or parasitic wire elements, as well as an antenna feed which feeds the radio waves to the rest of the antenna structure. The feed is connected to the transmitting or receiving equipment by a feed line.

Feeds and feed lines are passive devices and therefore incur losses in signal power referred to as feeder loss.

If the power at the output of the transmitter is , then the power actually transmitted is:

(37)

where is the transmitter feeder loss

0.001

0.01

0.1

1

10

100

10 100

Sea level

9150 m Altitude

Frequency [GHz]

Att

en

ua

tio

n [

dB

/km

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O2 O2 H2O H2O



Likewise, the power at the input of the receiver is:

(38)

where is the receiver feeder loss

Most of this loss is due to attenuation in the feed line (feed-line loss).

Pointing loss

Directional antennas must be correctly aligned to ensure maximum power transfer. If the alignment is imperfect, the loss is referred to as pointing loss (or depointing loss). Pointing loss is a function of the misalignment angle. For a

parabolic antenna with small misalignment angles between 0 and :

(39)

where is the pointing loss of the transmitting antenna

is the pointing loss of the receiving antenna

is the misalignment angle of the transmitting antenna

is the misalignment angle of the receiving antenna is the 3 dB beamwidth of the transmitting antenna

is the 3 dB beamwidth of the receiving antenna

Therefore, the EIRP can be expressed as:

(40)


To ensure maximum power transfer between the transmitting and receiving antennas, the two antennas should have the same type of polarization and their polarizations should be correctly aligned.

Although linearly polarized antennas can be used to communicate with circularly

polarized antennas, there will be an antenna polarization mismatch loss of approximately 3 dB. For a transmitting and receiving antenna both using linear-polarization, the mismatch loss can, in theory, be infinite, as shown by

Equation (41). In practice, it can be up to 20 dB.



(41)

where is the antenna polarization mismatch loss

is the misalignment angle


Considering all the gains and losses mentioned above, the power at the input of the receiver is:

(42)

where is the power at receiver input

is the power at the transmitter output

is the power radiated

is the transmitting antenna pointing loss

is the transmitter feed-line loss

is the gain of the transmitting antenna

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

Equation (42) applies to a single link in a radio communication system. For a satellite communications system using a single satellite for example, the equation would be used to calculate the power at the input of the satellite repeater (the uplink). The equation would also be applied to calculate the power at the input of the earth station receiver (the downlink). For terrestrial microwave communication system, the equation would apply to each hop.

Exercise 2 – Losses, Radiated Power and Receiver Input Power Procedure Outline


Equation (42) assumes that there are no impedance mismatches in the system. When there is an impedance mismatch between two components, some power is reflected back to the source and is wasted. This results in an additional loss called return loss.

The Procedure is divided into the following sections:

System startup

Preliminary measurements

Free-space lossSet up for measuring free-space loss. Notes on measuring the transmitted and received power. Determining the effective isotropic radiated power. Measuring the receiver input power. Calculating the free-space loss.



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 2 – Losses, Radiated Power and Receiver Input Power Procedure


Preliminary measurements

5. Make the connections shown in Figure 35. The antennas will be connected later.

Figure 35. Initial connections.

Free-space loss

In this section, you will set up the system in order to be able to move one of the antennas. You will vary the antenna separation distance as well as the frequency in order to determine the free-space loss in one RF link (the downlink). Since the repeater will act as the transmitter, the transmitter power will be the power at the RF OUTPUT of the repeater.

The objective of this section is to show that the free-space loss is proportional to the square of the range, and that it increases with frequency. Because of the small difference in frequency between channels, the fact that free-space loss is proportional to the square of the frequency may not be evident.

Digital Modulator

Up Converter1

Up Converter2

Down Converter 2

Down Converter 1

Earth Station Transmitter

Earth Station Receiver

Satellite Repeater

I Q I Q

I OUTPUT to

I INPUT

Q OUTPUT to

Q INPUT



Set up for measuring free-space loss

6. Set up the system so you can vary the downlink antenna separation distance between approximately 2.5 m and 0.5 m. You could add a table, as shown in Figure 36, for example, or you could place the antenna you will move on a small table with wheels. Make sure the antennas are at the same height.

Figure 36. Suggested set-up for moving one antenna.

Satellite Repeater

~2.5 m

~0.5 m



7. Make the connections shown in Figure 37. Connect two long cables to the antenna you intend to move.

Figure 37. Suggested connections for measuring free-space loss.

8. On the Earth Station Transmitter, make the following adjustments:

Data Source................................................... any Scrambler ...................................................... Off Clock & Frame Encoder ................................ Off

On the transmitter and on the receiver, choose the same Channel. Choose a channel that is not being used by another team in the same laboratory. If possible, choose channel D.

a Do not change the Channel for the duration of this exercise.

9. You will need to measure the power at the output of the Satellite Repeater. If you intend to use the Power Sensor on the repeater, adjust the distance between the two tables so the Power Sensor on the Satellite Repeater does not saturate.

b The maximum displayed level of the Power Sensor on the Satellite Repeater is approximately -6.7 dBm. While observing the power (or the voltage) at the repeater Power Sensor OUTPUT, move the table of the Satellite Repeater slightly toward or away from the transmitter. If the displayed power changes, the Power Sensor is not saturated.

If the displayed power does not change, and the three Level LEDs on the repeater are lit, then move the table away from the transmitter until the Power Sensor is no longer saturated, or slightly de-align one of the uplink antennas.

Digital Modulator

Up Converter1

Up Converter2

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

SMA-SMA adapter

Long cable

Large-Aperture Horn Antenna

(Downlink)

Large-Aperture Horn Antenna

(Downlink)



10. Set the range (the antenna separation distance) to approximately 2.5 m.

Optimize the alignment of the downlink antennas (see Aligning the antennas on page 38).

b If you are not using the Telemetry and Instrumentation Add-On, align the antennas to obtain the maximum voltage at the Power Sensor output of the receiver, or use a spectrum analyzer.

11. Decide how you will measure the power at the output of the repeater and at the input of the receiver.

Notes on measuring the transmitted and received power

The easiest way to measure the transmitted and received power, especially if you are using the Telemetry and Instrumentation Add-On, is to use the Power Sensors on these two modules. The Power Sensor of the repeater indicates the power at the RF output. The Power Sensor of the receiver, however, indicates the power at the output of Down Converter 2. You will have to subtract the gain of Down Converter 2 in order to obtain the power at the input of the receiver.

The sensitivity of the Power Sensors varies somewhat with frequency. Although this will induce small measurement errors, you will still be able to demonstrate the theory.

The most accurate way to measure these powers is to use a spectrum analyzer (or a power meter, if you have one). However, it may be inconvenient to move the instrument between the repeater and the receiver.

If you will be using the Power Sensor on the receiver, enter the gain of Down Converter 2 below. Enter the cable loss of a long cable at 9 GHz. (Refer to your measurements Exercise 1 for these two values).

Table 17. Initial values for free-space loss measurements.

Cable loss 2.4 dB

Down Converter 2 Gain 28.9 dB

Determining the effective isotropic radiated power

12. Choose three equally-spaced Channels to use (A, C, and E, or B, D, and F). Enter these channels and their downlink frequencies in the first two rows of Table 18.



Table 18. Transmitted power and antenna gain (using the repeater as a transmitter).

Channel

Frequency

GHz

Radiated power*

dBm

Transmitter power

dBm

Transmitter antenna gain (large horn)

dBi

Transmitter antenna feed-line loss

(2 long cables) dB

Effective isotropic radiated power

dBm

* does not apply if you are measuring the transmitted power using the Power Sensor on the repeater.

If you are measuring the power at the output of the repeater using a spectrum analyzer, connect the RF OUTPUT to the spectrum analyzer using two long cables (the same cables used to connect the antenna).

The measured power is the radiated power . Enter this power for each channel in the third row of Table 18. As this measurement is affected by loss in the cable, add the cable loss to each value to determine the transmitter power for each channel and enter these values in the fourth row.

b Don’t forget that the transmitting antenna is connected to the repeater using two long microwave cables.

Cable loss does not affect the Power Sensor on the repeater. If you measure the power at the output of the repeater using the Power Sensor,

you can enter these values directly as the transmitter power for each channel in the fourth row.

Refer to the measurements you made in Exercise 1 in the section Gain of the large-aperture horn antenna versus downlink frequency and enter the antenna gain for each channel in the fifth row of Table 18.

In the last row of the table, calculate and enter the effective isotropic radiated power for each channel.

Measuring the receiver input power

13. Plan to make received power measurements at four different ranges between

approximately 2.5 m and 0.5 m (the range is the downlink antenna



separation distance). Make sure the double-length cable is long enough to move one of the down link antennas to the different ranges.

Position the antennas at the farthest range and then optimize the antenna alignment. Changing the Channel on both the transmitter and the receiver, enter the measured power in either Table 19 or Table 20. If you are using the Power Sensor on the repeater, enter the values in Table 19; otherwise, enter the values in Table 20.

Table 19. Power at receiver IF 2 OUTPUT (if using Power Sensor).

Channel:

Range Measured power

If you are measuring the received power using the Power Sensor, subtract the gain of Down Converter 2 from each measured value and enter the result in Table 20.

Table 20. Power at receiver RF INPUT.

Channel:

Range Receiver input power

Calculating the free-space loss

14. Using Table 21, calculate the free-space loss for each range and each channel, making the following assumptions:

Since the antenna alignment is optimized each time you move the

antenna, the pointing losses are and .

Since the antennas are correctly polarized, the polarization loss .

Since the range is very short, the atmospheric attenuation .

The transmitting and receiving antenna gains are equal .



With these assumptions, Equation (42) can be written as:

Therefore:

Table 21. Free-space loss measurements (decibels).

Channel:

Receiver antenna gain (large horn):

Feed-line loss:

Range Free-space loss

In Table 22, convert the free-space loss values from decibels to absolute values using:

Table 22. Free-space loss measurements (absolute values).

Channel:

Frequency:

Range Free-space loss Range squared



Using the results in Table 22, plot the free-space loss versus the range

squared for each frequency in Figure 38.

Figure 38. Free-space loss.

Describe the relationship between the free-space loss and the range between the transmitting and receiving antennas.

How does free-space loss vary with frequency?

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

1,100,000

1,200,000

1,300,000

1,400,000

1,500,000

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Range squared

Fre

e-s

pa

ce

lo

ss



15. Calculate the theoretical free-space loss values (absolute values, not decibels) for the same ranges and frequencies and enter them into Table 23. Then plot these values in Figure 38.

Table 23. Theoretical free-space loss.

Channel:

Frequency:

Range Free-space loss Range squared

How does the free-space loss vary with the range? What is the effect of frequency on the free-space loss?


16. Calculate the theoretical received power for each range and each frequency used in the previous steps, making the following assumptions:

Since the antenna alignment is optimized each time you move the

antenna, the pointing losses are and .

Since the antennas are correctly polarized, the polarization loss .

Since the range is very short, the atmospheric attenuation .

With these assumptions, Equation (42) can be written as:

Use the values from Table 18. Use the same antenna gain and feed-line loss values used in Table 21. Use the theoretical free-space loss values from Table 23.



Table 24. Theoretical receiver input power.

Channel: A C E

Frequency:

Range Theoretical receiver input power

0.44

0.87

1.37

2.01

Plot the theoretical receiver input power versus range in Figure 39. Then plot the measured values from Table 20.

Figure 39. Receiver input power.

How did the measured values compare with the theoretical values?


In this section, you will mount one antenna using a swivel clamp. The swivel clamp, allows you to depolarize the antenna in order to measure the polarization mismatch loss.

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

0.0

0.0 0.5 1.0 1.5 2.0 2.5

Range [m]

Po

we

r [d

Bm

]



17. Mount one of the antennas in the system on the mast using the swivel clamp, as shown in Figure 40.

Figure 40. Horn antenna mounted with swivel clamp.

18. Adjust the antenna for as best you can for vertical polarization, as shown in Figure 41.

Figure 41. Antenna mounted on swivel clamp with 0° depolarization.

Align the antennas. Then set the Gain control on the receiver so that the red + LED barely lights. While observing this LED, optimize the antenna alignment very carefully to ensure that the main lobes of the two antennas are perfectly aligned.

Vertical polarization

Swivel clamp

Shaft



Measure the received power using either a spectrum analyzer or the Power Sensor of the receiver. Enter this value in Table 25.

a If you use the Power Sensor on the receiver, it is not necessary to subtract the gain of Down Converter 2 since the objective of this step is to determine the difference in received power due to two polarization mismatch loss.

Table 25. Polarization mismatch loss.

Received power with 0° depolarization

dBm

Received power with 45° depolarization

dBm

Measured depolarization loss

dB

Calculated depolarization loss

dB

19. Tilt the antenna so that it is depolarized by 45° as shown in Figure 42.

Figure 42. Antenna mounted on swivel clamp with 45° depolarization.

Align the antennas. Then set the Gain control on the receiver so that the red + LED barely lights. While observing this LED, optimize the antenna alignment very carefully to ensure that the main lobes of the two antennas are perfectly aligned.

45°

Exercise 2 – Losses, Radiated Power and Receiver Input Power Conclusion


b Make several small adjustments, if necessary, until you are sure that the main beams of the two antennas are perfectly aligned. Then tighten the knob on the swivel clamp and make sure that the received power level has not changed.

Measure the received power using either a spectrum analyzer or the Power Sensor of the receiver. Enter this value in Table 25.

a If you use the Power Sensor on the receiver, it is not necessary to subtract the gain of Down Converter 2 since the objective of this step is to determine the difference in received power due to two polarization mismatch loss.

Calculate the measured polarization mismatch loss.

Then calculate the theoretical polarization mismatch loss using Equation (41) on page 67.

Compare the measured and calculated polarization mismatch losses.

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

In this exercise, you became familiar with the various losses that affect a radio link. You measured the free-space loss four different ranges and frequencies and confirmed that the free-space loss is proportional to the square of the range. You also observed that free-space loss is higher at higher frequencies. You saw that by considering the different gains and losses, it is possible to calculate the power at the input of a receiver.

1. What is the greatest single loss in a radio link? Give the formula for this loss.

2. What two factors contribute free-space loss?

CONCLUSION

REVIEW QUESTIONS

Exercise 2 – Losses, Radiated Power and Receiver Input Power Review Questions


3. Why is it important that the transmitting and receiving antennas have the same polarization?

4. Give the formula containing three factors for calculating the power at the input of the receiver.

5. What causes atmospheric attenuation and how does this loss vary with frequency?

link characteristics and performance, 2 losses, radiated ... · pdf filefriis transmission...

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