Lect 05© 2012 Raymond P. Jefferis III1 Satellite Communications Link budget analysis Transmitted power Transmitting antenna gain Path loss Receiving antenna gain Receiver sensitivity

Lect 05© 2012 Raymond P. Jefferis III2 Tx Down-Link Budget Analysis Starting with transmitter link loss factors: –Power is reduced by system loss factors detuning losses, cabling losses, coupling losses, etc. –Power is reduced by antenna inefficiency, from beam sidelobes, for instance Dynamic losses – Backoff, beamwidth, and pointing losses Path loss factors –Free space loss –Atmospheric losses –Precipitation losses

Rx Down-Link Budget Analysis Receiver factors: –Receiver antenna gain – efficiency loss –Coupling, cabling, and detuning losses –Receiver sensitivity Noise factors –Input noise (natural factors) –Antenna, RF amplifier, and mixer noise Lect 05© 2012 Raymond P. Jefferis III3

Lect 05© 2012 Raymond P. Jefferis III4 Transmitted Power Usually specified in Watts Can be converted to dBW by, where, P t db = Transmitter power [dB-Watts] P t = Transmitter power [Watts]

Lect 05© 2012 Raymond P. Jefferis III5 Transmitted Power Usually specified in Watts Can be converted to dBm by, where, P t dbm = Transmitter power [dB-milliWatts] P t = Transmitter power [Watts]

Lect 05© 2012 Raymond P. Jefferis III6 Examples 05-01, Transmitter power = 20 Watts P t db = 10 log(20) = 13 dBW P t dbm = 10 log(20/10 -3 ) = 43 dBm Transmitter power = 75 Watts P t db = 10 log(75) = dBW P t dbm = 10 log(75/10 -3 ) = dBm

Lect 05© 2012 Raymond P. Jefferis III7 What does this specification mean? Intelsat GALAXY-11 at 91W (NORAD 26038) 39.1 dBW on C-Band (20W, 24 ch, Bw: 36 MHz) 47.8 dBW on Ku-Band (75/140W, 40 ch, Bw: 36 MHz) Transmitter power, is simultaneously distributed across all the available channels (CDMA) The satellite has four antennas, two for each band, and sequential channels are transmitted on one antenna in a band and received on the other. Shared channel (TDMA) Two possible interpretations (CDMA vs. TDMA)

Lect 05© 2012 Raymond P. Jefferis III8 Transmitter Antenna Gain For a circular antenna (parabolic dish), where, A e = Effective aperture [m 2 ]   = aperture efficiency d = aperture diameter [m] G = aperture antenna gain  = operating wavelength [m]

LECT 04© 2012 Raymond P. Jefferis III9 Circular Aperture Antenna The electric field of a circular aperture antenna can be calculated from: where, D/  gives the aperture diameter in wavelengths and ϕ is the angle relative to the normal to the plane of the aperture.

Lect 05© 2012 Raymond P. Jefferis III10 Example Ku-Band antenna 3dB beamwidth = 3˚ D/  = 25  = 0.63 G = 3886 G dBi = 36

Beamwidth – Circular Aperture Show demo. Lect 05© 2012 Raymond P. Jefferis III Lect

E-Field of a Circular Aperture Antenna Lect 05© 2012 Raymond P. Jefferis III Lect eps = 0.001; Diam = 20; Manipulate[e2 = (2.0/p*Diam)* (BesselJ[1, p*Diam*Sin[theta]])/Sin[theta]; Plot[Abs[e2], {theta, -p/6, p/6}, PlotRange -> {{-0.5, 0.5}, {0, 600}}, PlotStyle -> {Directive[Thick, Black]}], {Diam, 1, 25} ]

Lect 05© 2012 Raymond P. Jefferis III13 Antenna Gain vs Beamwidth Calculation eff = 0.63; beamw = 1; f = 12*10^9; c = *10^8; lam = c/f; Plot[app = 75.0/beamw; diam = app*lam; G = eff*p^2*app^2; lG = 10*Log[10, G]; lG, {beamw, 1, 5}, AxesLabel -> {Beamwidth [deg], Gain}]

Antenna Gain vs Beamwidth Result Lect 05© 2012 Raymond P. Jefferis III Lect

Link Budget – General Information The accounting of gains and losses over a link Other effects that can be considered –Fading –Reflections (multipath interference) –Ground absorption Excessive power losses can reduce a transmitted signal to levels below the receiver sensitivity in the presence of noise Lect 05© 2012 Raymond P. Jefferis III Lect

Lect 05© 2012 Raymond P. Jefferis III16 Link Budget Calculation (Downlink) Calculate power density of isotropic antenna Calculate effective radiated power (EIRP) using transmitter antenna gain and efficiency Calculate path loss Calculate receiving antenna aperture and gain Calculate received power at the earth station

Link Budget Calculation (continued) Compare receiver input specifications with the calculated power levels at the receiver Add noise factors Calculate receiver input Signal/Noise ratio If this is inadequate, change accessible link factors Lect 05© 2012 Raymond P. Jefferis III Lect

The Isotropic (Ideal) Antenna The gains of antennas can be stated relative to an isotropic ideal antenna as G [dBi], where G > 0. This antenna is a (theoretical) point source of EM energy It radiates uniformly in all directions A sphere centered on this antenna would exhibit constant energy per unit area over its surface The gain of an isotropic antenna is 0 dBi Lect 05© 2012 Raymond P. Jefferis III Lect

EIRP Equivalent Isotropic Radiated Power – the equivalent power input that would be needed for an isotropic antenna to radiate the same power over the angles of interest LECT 04© 2012 Raymond P. Jefferis III Lect

Lect 05© 2012 Raymond P. Jefferis III20 Equivalent Isotropic Radiated Power - EIRP Where: (in the far-field only), EIRP = Equiv. isotropic rad. power [W] P t = Transmitted power [W] G t = Gain of lossless transmitting antenna (G t = 1 for lossless isotropic antenna) or, in dB units, EIRP dBW = P t dBW + G t dBi

Lect 05© 2012 Raymond P. Jefferis III21 Isotropic Radiated Flux Density where (in the far-field only), ψ = Transmitted power flux density (W/m 2 ) EIRP = Equiv. isotropic rad. power [W] r = Distance from transmitter Note: This is the EIRP per unit area of a sphere at radius r from an isotropic antenna.

Lect 05© 2012 Raymond P. Jefferis III22 Actual Transmitting Antenna Gain where (in the far-field only), EIRP eff = Effective EIRP [W] P t = Transmitted power [W] G t = Gain of a lossless (ideal) transmitting antenna  t = Transmitting antenna efficiency G te = Effective gain of transmitting antenna

Lect 05© 2012 Raymond P. Jefferis III23 Example 05-04: Ku-Band Satellite P t :75 [W] =>18.75 [dBW] Antenna diam:1.8 [m] Frequency:12 [GHz] Wavelength:0.025 [m] Antenna Eff.:0.62 [-2.1 dBW] Antenna Gain:45.02 [dBi] EIRP eff [dBW]

EIRP Calculation for Ku-band Example c = *10^8; (* m/sec *) freq = 12.0*10^9; (* Hz *) pt = 75.0;(* Watts *) ptdbW = 10*Log[10, pt]; (* dBW *) eff = 0.62; (* efficiency *) lam = c/freq; (* m *) diam = 1.8; (* m *) dl = diam/lam; gain = eff*(p*diam/lam)^2; loggain = 10*Log[10, gain];(* dB *) eirp = gain*pt;(* W *) dBW = 10*Log[10, eirp];(* dBW *) Print["EIRP = ", dBW, " [dBW]"] Lect 05© 2012 Raymond P. Jefferis III Lect

Lect 05© 2012 Raymond P. Jefferis III25 Free Space Path Loss Calculation Due to the spreading of transmitted energy Other losses will be accounted separately where,  = wavelength [m] r = transmission-reception distance [m]

Lect 05© 2012 Raymond P. Jefferis III26 Received Power (Gain & Losses) where, EIRP = Effective Isotropic Radiated Power  r = Antenna efficiency G r = Antenna gain (G = 1 for isotropic) d r = Antenna diameter [m] L p = Path loss  = wavelength [m]

Lect 05© 2012 Raymond P. Jefferis III27 Net Received Power Calculation EIRP = Eff. Isotropic Radiated Power  t/r = Antenna efficiency G t/r = Antenna gain D t/r = Antenna diameter [m] L p = Path loss λ = wavelength [m] R = transmitter-receiver distance [m]

Lect 05© 2012 Raymond P. Jefferis III28 Another Received Power Interpretation Where, P r = Received power [W] ψ r = Received flux density [W/m 2 ] A eff = Effective receiving antenna aperture [m 2 ]

Lect 05© 2012 Raymond P. Jefferis III29 Path Loss Summary Diagram

Lect 05© 2012 Raymond P. Jefferis III30 Power Ratio over Path Calculation where,  t = Efficiency of receiving antenna [-]  r = Efficiency of receiving antenna [-] G t = Antenna gain (G=1 for isotropic antenna) G r = Antenna gain (G=1 for isotropic antenna) λ = wavelength [m] d = distance between antennas [m]

Lect 05© 2012 Raymond P. Jefferis III31 Path Loss [dB]

Lect 05© 2012 Raymond P. Jefferis III32 Example 05-05: Ku-Band Satellite Receiving antenna diameter:0.9 [m] Frequency:12 [GHz] Wavelength:0.025 [m] Path length:42000 [km] Antenna Eff.:0.62 Receiving Antenna Gain:39 [dBi] EIRP eff 63.8 [dBW] Path gain (-loss): [dBW] Received power: [dBW]

Class Activity Compute the path loss of the previous example in dBW. Compute the received power of the previous example in dBW. Lect 05© 2012 Raymond P. Jefferis III Lect

Activity Results f = 12 GHz [12000 MHz] λ= [m] => (-32 dBW) P t = dBW η t G t = dBW η r G r = 39.0 dBW r = 42,000 km => ( dBW) P r = = [dBW] Lect 05© 2012 Raymond P. Jefferis III Lect

Lect 05© 2012 Raymond P. Jefferis III35 Activity Calculation c = *10^8; f = 12.0*10^9; lam = c/f; r = 42.0*10^6; pwrTx = 75.0; dAntTx = 1.8; effAntTx = 0.62; gAntTxEff = effAntTx*(p*dAntTx/lam)^2; gAntTxEffdB = 10 Log[10, gAntTxEff]; EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB; Lp = (lam/(4*p*r))^2; LpdB = 10 Log[10, Lp]; dAntRx = 0.9; effAntRx = 0.62; gAntRxEff = effAntRx*(p*dAntRx/lam)^2; GAntRxEffdB = 10 Log[10, gAntRxEff]; PrdB = EIRPdB + LpdB + GAntRxEffdB; Print["Path Loss ", LpdB, " [dB]"]; Print["Rcv pwr = ", PrdB, " [dBW]"];

Lect 05© 2012 Raymond P. Jefferis III36 Example: Ku-Band Link Tx power:10 [Watts] Rx and Tx antenna diameters:3.0 [m] Frequency:12 [GHz] Path length:35,900 [km] Antenna Efficiencies 0.55 Antenna Gains:48.93[dBi] EIRP eff [dBW] Path gain (-loss): [dBW] Received power: [dBW]

Example Ku-Band Calculation f = 12.0*10^9; Bw = 36.0*10^6; c = *10^8; lam = c/f; r = 35.9*10^6; (* Tx EIRP CALC. *) pwrTx = 10.0; pwrTxdB = 10 Log[10, pwrTx]; dAntTx = 3.0; effAntTx = 0.55; gAntTxEff = effAntTx*(p dAntTx/lam)^2; gAntTxEffdB = 10 Log[10, gAntTxEff]; EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB; (* Path Loss *) Lp = (3.0*10^8/(4*p*f*r))^2; (* Path Loss [DB] *) LpdB = 10 Log[10, Lp]; (* Rx Antenna CALC. *) dAntRx = 3.0; effAntRx = 0.55; gAntRxEff = effAntRx*(p dAntRx/lam)^2; GAntRxEffdB = 10 Log[10, gAntRxEff]; (* Received Power [DB] *) PrdB = EIRPdB + LpdB + GAntRxEffdB; (* Received Power [W] *) PrWatts = 10^(PrdB/10); Lect 05© 2012 Raymond P. Jefferis III37

Lect 05© 2012 Raymond P. Jefferis III38 Conversion to Frequency Base where, (P t ) dB = Transmitted power [dBW] (P r ) dB = Received power [dBW] (L p ) dB = Path loss power [dBW] (G t/r ) dB = Transmitting or receiving antenna gain f = frequency [Hz] R = distance [m]

Lect 05© 2012 Raymond P. Jefferis III39 Example Calculation: Ku-Band f = 12 GHz [12000 MHz] P t = 18.7 dBW G t = 45 dBi G r = 39 dBi R = 42, 000 km P r = = dBW Note: Considering free space loss only

Workshop 05 Please do all work indicated on the Workshop 05 handout. You may use a spreadsheet or a mathematics package (Mathematica ® is recommended) for your calculations Document ALL work and calculations Submit as a written Workshop report. Lect 05© 2012 Raymond P. Jefferis III40

Lect 05© 2012 Raymond P. Jefferis III41 Workshop 05 Calculations c = *10^8; f = 12.0*10^9; lam = c/f; r = 42.0*10^6; pwrTx = 75.0; pwrTxdB = 10 Log[10, pwrTx]; dAntTx = 1.8; effAntTx = 0.62; gAntTxEff = effAntTx*(p dAntTx/lam)^2; gAntTxEffdB = 10 Log[10, gAntTxEff]; EIRPdB = 10 Log[10, pwrTx] + gAntTxEffdB; Lp =(3.0*10^8/(4*p*f*r))^2; LpdB =10 Log[10, Lp]; dAntRx = 0.9; effAntRx = 0.62; gAntRxEff = effAntRx*(p dAntRx/lam)^2; GAntRxEffdB = 10 Log[10, gAntRxEff]; PrdB = EIRPdB + LpdB + GAntRxEffdB;

End Lect 05© 2012 Raymond P. Jefferis III42