Satellite Link Design Joe Montana IT 488 - Fall 2003

1. Satellite Link Design Joe Montana IT 488 - Fall 2003

2. Agenda • Basic Transmission Theory • Review of Decibel • Link Budget • System Noise Power (Part 1)

3. Basic Transmission Theory

4. Link Budget parameters • Transmitter power at the antenna • Antenna gain compared to isotropic radiator • EIRP • Flux density at receiver • Free space path loss • System noise temperature • Figure of merit for receiving system • Carrier to thermal noise ratio • Carrier to noise density ratio • Carrier to noise ratio

5. Isotropic Radiator • Consider an Isotropic Source (punctual radiator) radiating Pt Watts uniformly into free space. • At distance R, the area of the spherical shell with center at the source is 4pR2 • Flux density at distance R is given by Eq. 4.1 W/m2

6. Isotropic Radiator 2 Isotropic Source Distance R Pt Watts Power Flux Density: Surface Area of sphere = 4pR2 encloses Pt. W/m2

7. Antenna Gain • We need directive antennas to get power to go in wanted direction. • Define Gain of antenna as increase in power in a given direction compared to isotropic antenna. (Eqn 4.2) • P() is variation of power with angle. • G() is gain at the direction . • P0 is total power transmitted. • sphere = 4p solid radians

8. Antenna Gain 2 • Antenna has gain in every direction! Term gain may be confusing sometimes. • Usually “Gain” denotes the maximum gain of the antenna. • The direction of maximum gain is called “boresight”.

9. Antenna Gain 3 • Gain is a ratio: • It is usually expressed in Decibels (dB) G [dB] = 10 log10 (G ratio) The world’s most misused unit ?? (we will see more on dBs later)

10. EIRP - 1 • An isotropic radiator is an antenna which radiates in all directions equally • Antenna gain is relative to this standard • Antennas are fundamentally passive • No additional power is generated • Gain is realized by focusing power • Similar to the difference between a lantern and a flashlight • Effective Isotropic Radiated Power (EIRP) is the amount of power the transmitter would have to produce if it was radiating to all directions equally • Note that EIRP may vary as a function of direction because of changes in the antenna gain vs. angle

11. EIRP Pt Pout Lt HPA EIRP - 2 • The output power of a transmitter HPA is: Pout watts • Some power is lost before the antenna: Pt =Pout/Lt watts reaches the antenna Pt = Power into antenna • The antenna has a gain of: Gt relative to an isotropic radiator • This gives an effective isotropic radiated power of: EIRP = PtGtwatts relative to a 1 watt isotropic radiator

12. Power Flux Density - 1 • We now want to find the power density at the receiver • We know that power is conserved in a lossless medium • The power radiated from a transmitter must pass through a spherical shell on the surface of which is the receiver • The area of this spherical shell is 4pR2 • Therefore spherical spreading loss is 1/4pR2

13. Power Flux Density - 2 • Power flux density (p.f.d.) is a measure of the power per unit area • This is a regulated parameter of the system • CCIR regulations limit the p.f.d. of any satellite system • CCIR regulations are enforced by signatory nations • Allowable p.f.d. varies w.r.t. elevation angle • Allows control of interference • Increasing importance with proliferation of LEO systems

14. Received Power • We can rewrite the power flux density now considering the transmit antenna gain: • The power available to a receive antenna of area Ar m2 we get: (Eqs. 4.4, 4.6) (Eqn. 4.3)

15. Effective Aperture • Real antennas have effective flux collecting areas which are LESS than the physical aperture area. • Define Effective Aperture Area Ae: • (Eqn. 4.5) • Where Aphy is actual (physical) aperture area. • Very good: 75% • Typical: 55% •  = aperture efficiency

16. Effective Aperture - 2 • Antennas have (maximum) gain G related to the effective aperture area as follows: • Where: • Ae is effective aperture area.

17. Aperture Antennas • Aperture antennas (horns and reflectors) have a physical collecting area that can be easily calculated from their dimensions: • Therefore, using Eqn. 4.7 and Eqn. 4.5 we can obtain the formula for aperture antenna gain as: Typical values of : • Reflectors: 50-60% • Horns: 65-80 %

18. Aperture Antenna Types • HORN • Efficient, Low Gain, Wide Beam • REFLECTOR • High Gain, Narrow Beam, May have to be deployed in space Let’s concentrate on the REFLECTORS in the next slides

19. Reflector Types Symmetrical, Front-Fed Offset, Front-Fed Offset-Fed, Cassegranian Offset-Fed, Gregorian

20. Reflector Antenna -1 • A rule of thumb to calculate a reflector antenna beamwidth in a given plane as a function of the antenna dimension in that plane is given by: (Eqn. 3.2) degrees • The approximation above, together with the definition of gain (previous page) allow a gain approximation (for reflectors only): • Assuming for instance a typical aperture efficiency of 0.55 gives:

21. Antenna Beamwidth Peak (i.e. maximum) GAIN Angle between the 3 dB down points is the beamwidth of the antenna

22. Back to Received Power… • The power available to a receive antenna of effective area Ar = Ae m2 is: (Eqn. 4.6) Where Ar = receive antenna effective aperture area = Ae • Inverting the equation given for gain (Eq. 4.7) gives: Inverting…

23. Back to Received Power… • Substituting in Eqn. 4.6 gives: Friis Transmission Formula (Eqn. 4.8) • The inverse of the term at the right referred to as “Path Loss”, also known as “Free Space Loss” (Lp): Therefore…

24. More complete formulation • Demonstrated formula assumes idealized case. • Free Space Loss (Lp) represents spherical spreading only. • Other effects need to be accounted for in the transmission equation: • La = Losses due to attenuation in atmosphere • Lta = Losses associated with transmitting antenna • Lra = Losses associates with receiving antenna • Lpol = Losses due to polarization mismatch • Lother = (any other known loss - as much detail as available) • Lr = additional Losses at receiver (after receiving antenna)

25. Transmission Formula • Some intermediate variables were also defined before: Pt =Pout/Lt EIRP = PtGt Where: • Pt = Power into antenna • Lt = Loss between power source and antenna • EIRP = effective isotropic radiated power • Therefore, there are many ways the formula could be rewritten. The user has to pick the one most suitable to each need.

26. Link Power Budget Tx EIRP Transmission: HPA Power Transmission Losses (cables & connectors) Antenna Gain Antenna Pointing Loss Free Space Loss Atmospheric Loss (gaseous, clouds, rain) Rx Antenna Pointing Loss Reception: Antenna gain Reception Losses (cables & connectors) Noise Temperature Contribution Rx Pr

27. Review of Decibel

28. That’s a lot of zeros! Why dB? • There is a large dynamic range of parameters in satellite communications • A typical satellite antenna has a gain of >500 • Received power flux is about one part in 100,000,000,000,000,000,000of the transmitted power • Wouldn’t it be nice to have a better way to write these large numbers? • dB also lets many calculations be addition or subtraction!

29. What is a dB? • Decibel (dB) is the unit for 10 times the base 10 logarithmic ratio of two powers • For instance: gain is defined as Pout/Pin (where Pout is usually greater than Pin) • in dB: • Similarly loss is:

30. A Dangerous Calculation in dB! • dB ratios must NEVER be calculated as 20 times the base 10 logarithmic ratio of voltages Unless of course its more convenient, in which case you must be very, very careful. Here’s why: If these calculations are performed for say a (passive)transformer with winding ratios of 4 output turns per input turn, Vout = 4 when Vin = 1. If the last term is neglected, the gain appears to be G = 20log(4) = 12 dB. This is a curious result for a passive device! If the last term is used, Rout = 16 for Rin = 1, so the last term is -12 dB. This restores the balance at G = 0 as expected for an ideal passive device. This term is usually forgotten (with tragic results!)

31. Using Decibels - 1 Rules: • Multiply A x B: (Add dB values) • Divide A / B: • (Subtract dB values)

32. Using Decibels - 2 Rules: • Squares: (Multiply by 2) • Square roots: • (Divide by 2)

33. Thinking in dB • Its useful to be able to think in dB Note that 18 is 2*3*3. Since: 2 = 3 dB and: 3 = 4.8 dB you can find 18 in dB in your head by adding 3 + 4.8 + 4.8 = 12.6 You don’t even need a calculator! This is really handy for checking link budgets quickly.

34. References in dB • dB values can be referenced to a standard • The standard is simply appended to dB • Typical examples are:

35. Link Budget

36. Translating to dBs • The transmission formula can be written in dB as: • This form of the equation is easily handled as a spreadsheet (additions and subtractions!!) • The calculation of received signal based on transmitted power and all losses and gains involved until the receiver is called “Link Power Budget”, or “Link Budget”. • The received power Pr is commonly referred to as “Carrier Power”, C.

37. Link Power Budget Now all factors are accounted for as additions and subtractions Tx EIRP • Transmission: • + HPA Power • Transmission Losses • (cables & connectors) • + Antenna Gain • Antenna Pointing Loss • Free Space Loss • Atmospheric Loss (gaseous, clouds, rain) • - Rx Antenna Pointing Loss • Reception: • + Antenna gain • Reception Losses • (cables & connectors) • + Noise Temperature Contribution Rx Pr

38. 4 Easy Steps to a GoodLink Power Budget • First, draw a sketch of the link path • Doesn’t have to be artistic quality • Helps you find the stuff you might forget • Next, think carefully about the system of interest • Include all significant effects in the link power budget • Note and justify which common effects are insignificant here • Roll-up large sections of the link power budget • Ie.: TXd power, TX ant. gain, Path loss, RX ant. gain, RX losses • Show all components for these calculations in the detailed budget • Use the rolled-up results in build a link overview • Comment the link budget • Always, always, always use units on parameters (dBi, W, Hz ...) • Describe any unusual elements (eg. loss caused by H20 on radome)

39. Simple Link Power Budget

40. Why calculate Link Budgets? • System performance tied to operation thresholds. • Operation thresholds Cmin tell the minimum power that should be received at the demodulator in order for communications to work properly. • Operation thresholds depend on: • Modulation scheme being used. • Desired communication quality. • Coding gain. • Additional overheads. • Channel Bandwidth. • Thermal Noise power. We will see more on these items in the next classes.

41. Closing the Link • We need to calculate the Link Budget in order to verify if we are “closing the link”. Pr >= Cmin  Link Closed Pr < Cmin Link not closed • Usually, we obtain the “Link Margin”, which tells how tight we are in closing the link: Margin = Pr – Cmin • Equivalently: Margin > 0  Link Closed Margin < 0  Link not closed

42. Carrier to Noise Ratios • C/N: carrier/noise power in RX BW (dB) • Allows simple calculation of margin if: • Receiver bandwidth is known • Required C/N is known for desired signal type • C/No: carrier/noise p.s.d. (dbHz) • Allows simple calculation of allowable RX bandwidth if required C/N is known for desired signal type • Critical for calculations involving carrier recovery loop performance calculations

43. System Figure of Merit • G/Ts: RX antenna gain/system temperature • Also called the System Figure of Merit, G/Ts • Easily describes the sensitivity of a receive system • Must be used with caution: • Some (most) vendors measure G/Ts under ideal conditions only • G/Ts degrades for most systems when rain loss increases • This is caused by the increase in the sky noise component • This is in addition to the loss of received power flux density

44. System Noise Power

45. System Noise Power - 1 • Performance of system is determined by C/N ratio. • Most systems require C/N > 10 dB. (Remember, in dBs: C - N > 10 dB) • Hence usually: C > N + 10 dB • We need to know the noise temperature of our receiver so that we can calculate N, the noise power (N = Pn). • Tn (noise temperature) is in Kelvins (symbol K):

46. System Noise Power - 2 • System noise is caused by thermal noise sources • External to RX system • Transmitted noise on link • Scene noise observed by antenna • Internal to RX system • The power available from thermal noise is: where k = Boltzmann’s constant = 1.38x10-23 J/K(-228.6 dBW/HzK), Ts is the effective system noise temperature, andB is the effective system bandwidth We will see more on calculating Ts next class.