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Everything You Ever Wanted to Know About Spacecraft Link Budgets . . .

Everything You Ever Wanted to Know About Spacecraft Link Budgets . . . But Were Afraid to Ask. Jan A. King Revised July 2005 VK4GEY. Terminology. S/N: You may have seen it written as: SNR It’s the “Signal-to-Noise Ratio”

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Everything You Ever Wanted to Know About Spacecraft Link Budgets . . .

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  1. Everything You Ever Wanted to Know About Spacecraft Link Budgets . . . But Were Afraid to Ask. Jan A. King Revised July 2005 VK4GEY Link Budgets - W3GEY / VK4GEY

  2. Terminology • S/N: You may have seen it written as: SNR It’s the “Signal-to-Noise Ratio” • Signal  Power Level of Signal in Occupied Bandwidth Units: dBW or dBm • Noise  Noise Power in Occupied Bandwidth or Receiver Filter Bandwidth. Units: dBW or dBm • So, S/N is dimensionless: Units are in dB Link Budgets - W3GEY / VK4GEY

  3. Terminology • C/N • C  Power of the signal but, expressed as a carrier with essentially no bandwidth. Units: dBm or dBW • N  Noise power in occupied bandwidth or receiver filter bandwidth. [It’s really QRN ] Units: dBm or dBW • So, C/N is dimensionless: Units are in dB Link Budgets - W3GEY / VK4GEY

  4. Terminology • For Our Purposes: S/N = C/N Let’s decide to use the more familiar S/N. Link Budgets - W3GEY / VK4GEY

  5. Exam No. 1 • A signal has a received power level of 1 mW and a noise level of 1 W. What is the S/N? ANSWER: 1 mW = .001 Watts S = 10 X Log ( 0.001) = 10 X (-3) = -30 dBW 1 W = 0.000001 Watts N = 10 X Log (0.000001) = 10 X(-6) = -60 dBW NOW: DON’T DIVIDE -> SUBTRACT: S/N = -30 – (-60) = 30 dB NOTE: The “Watts” Cancelled. Link Budgets - W3GEY / VK4GEY

  6. Terminology • C/No or S/No: • S,C  Signal (or Carrier) Power Units: dBm or dBW • No  Noise Power Per Unit of Bandwidth = Noise Power Density. [It’s really QRN density]. Units: dBm/Hz or dBW/Hz • S/No  Signal to Noise Power Density Ratio Units = dBW/(dBW/Hz) = dBHz • S/No is the S/N in a 1 Hz Bandwidth Link Budgets - W3GEY / VK4GEY

  7. Terminology • I and Io • I All the Power from an Interference Source [QRM] Units: dBm or dBW • Io Interference Power Density = Power per Unit of Bandwidth. [QRM Density]. Units: dBm/Hz or dBW/Hz Link Budgets - W3GEY / VK4GEY

  8. Terminology • S/(No + Io) • Signal to Combined Noise Plus Interference Power Density. • Units: dBHz • REMEMBER? -- How Do You Add dBs? Link Budgets - W3GEY / VK4GEY

  9. ANSWER: YOU DON’T! YOU MUST ADD THE TWO “UN-LOGGED” NUMBERS FIRST YUCK! Link Budgets - W3GEY / VK4GEY

  10. BITCH . . . Use The Link Model Instead And you Won’t Have to do this Calculation Link Budgets - W3GEY / VK4GEY

  11. Exam No. 2 • A signal is received at a power level of –60 dBm. The “white” noise in that receiver’s passband has a density of -110 dBm/Hz. There is also some interference from a broadcast station that is received at a density of –115 dBm/Hz. What is S/(No+Io)? ANSWER: • S is free; it’s –60 dBm • To add No and Io we must first “un-Log” the values, add them and “Re-Log” them: YUCK, Again! Link Budgets - W3GEY / VK4GEY

  12. Exam No. 2 (Continued) • No = -110 dBm/Hz = 1 X 10E-11 milliwatts/Hz • Io = -115 dBm/Hz = 3.16 X 10E-12 milliwatts/Hz • No+Io = (1X10E-11) + (3.16X10E-12) = 1.316X10E-11 mW/Hz • In dB: (No+Io) = 10 X Log (1.316X10E-11) = -108.8 dBm/Hz • NOW: S/(No+Io) = -60 –(-108.8) = 48.8 dBHz Link Budgets - W3GEY / VK4GEY

  13. Inserting a Transponder in a Link S/C TX EIRP S/C RX G/T ( ) S/No RX G/T TX EIRP UP (S/No) DOWN USERA USER B (S/No)TOTAL Link Budgets - W3GEY / VK4GEY

  14. Who’s Responsible?EIRP and G/T -> That’s Who UPLINK DOWNLINK Link Budgets - W3GEY / VK4GEY

  15. The MAGIC Formula! • For a Spacecraft Link Using a “Bent Pipe” Transponder: (S/No) = 1 1 1 (S/No) (S/No) TOTAL + DOWN UP Link Budgets - W3GEY / VK4GEY

  16. How Does the Magic Formula Work? • NOTE: It’s the Same Formula as the Parallel Resistor Formula. • (S/No)TOTAL will be  (S/No)UP or (S/No)DOWN, Whichever is Smaller. • For Finite Values of (S/No)UP and (S/No)DOWN, the Total Link Result will ALWAYS be Poorer than the Poorest of the Two Links. WATCH… Link Budgets - W3GEY / VK4GEY

  17. Exam No. 3 Rtotal = ? R2= 1 Meg  R1= 1K  Link Budgets - W3GEY / VK4GEY

  18. Exam No. 3 Result: • R total = 999.0   1K • The 1 Meg Ohm Resistor had ALMOST NO Effect on the Total Circuit Resistance. • The Circuit was Dominated by the 1 K Ohm Resistor. • RTOTAL was LESS than the Smallest Resistor Link Budgets - W3GEY / VK4GEY

  19. Magic Formula Results Link Budgets - W3GEY / VK4GEY

  20. Working Toward a Result • At This Point in the Link there is a Fork in the Road. We have Computed the S/No for the Overall Link, including the transponder. • We Must Decide if the Signal We are Passing Through the System is an Analogue Signal (like FM or SSB) or a Digital Signal (like FSK or PSK). • If the Signal is Analogue, We Do the Following: • Determine the Bandwidth of the Filter Just in Front of the Receiver’s Detector (that’s the Discriminator for FM or the Product Detector if it is SSB) [It’s probably 12 to 15 kHz if it’s an FM Receiver and 2.7 to 3.0 kHz if it’s an SSB Receiver]. • Calculate this bandwidth in dB-Hz: Brx(dB) = 10xlog(B) dBHz • Subtract This Number from the S/No or S/(No + Io) you have computed above. Here’s another exam. Link Budgets - W3GEY / VK4GEY

  21. Working Toward a Result (2) • Exam No. 4: An SSB receiver at the end of a satellite link sees a signal with a mean signal-to-noise power density ratio of 49 dBHz. What is the peak signal-to-noise ratio of the signal at the output of the receiver’s product detector if the receivers pre-detection bandwidth is 3.0 kHz? • S/No = 49 dBHz • B(dB) = 10*log(3000 Hz) = 34.8 dBHz • S/N = S/No – Brx(dB) = 14.2 dB • This is the average S/N for the SSB signal. The peak S/N for SSB is approximately 10 dB higher than the average so, the resulting S/N that the user “hears” is about 24 dB. Link Budgets - W3GEY / VK4GEY

  22. Working Toward a Result (3) • If the signal you are interested in is a digital signal there is a preferred way to proceed, especially if the signal uses an optimum modulation type such as PSK. PSK is a signal type for which we can build what is known as a matched filter. Such a receiver system will be virtually lossless and will add no more thermal noise (that’s “white noise” or “Additive Gaussian White Noise (AWGN)” should we want to get technical about it) than is absolutely necessary. To get a result, the process is similar to the analogue approach but, slightly different. • We first determine the data rate we want to pass through our receiver demodulator. • Then we assume we can build a “matched filter” in the demodulator (this is, in fact, a practical assumption). Link Budgets - W3GEY / VK4GEY

  23. Working Toward a Result (4) • Then we determine the matched filter bandwidth required to receiver the data rate selected. In doing this we assume that each bit per second occupies exactly 1 Hz of spectrum (bandwidth). So it looks like this (example): • Data Rate = 9600 bps • Matched Filter Bandwidth = 9600 Hz • Matched Filter Bandwidth in dBHz = 10*log (9600) = 39.8 dBHz • Then we subtract the matched filter bandwidth occupied by our signal from the previously calculated S/No or S/(No+Io). • This result (in simple dB) is called the Eb/No: that’s the Energy per bit to Noise Power Density Ratio. This result tells you the energy received in one single bit divided by the noise power in every single Hz of the receiver’s matched filter. • Here’s the next Exam: Link Budgets - W3GEY / VK4GEY

  24. Working Toward a Result (5) • Exam No. 5: A PSK receiver has received a signal via a satellite transponder at an S/(No+Io) value of 50 dBHz. The data rate of the BPSK signal is 9600 bits per second. What is the resultant Eb/No of the signal? • S/(No+Io) = 50.0 dBHz • The matched filter bandwidth for this signal is 9600 Hz • B(dB) = 10*log(9600Hz) = 39.8 dBHz • Eb/No = S/(No+Io) – B(dB) = 50.0 – 39.8 = 10.2 dB • This is the result of the digital link…BUT… Link Budgets - W3GEY / VK4GEY

  25. Working Toward a Result (6) • We would like to know just one more thing for a digital signal. At the Eb/No performance level we have obtained, what is the “quality” of the data stream? • One way to think about this is to ask, how many errors will be made in any given messsage (say, in a packet or a frame of a block of data)? There is such a parameter and it is known as the BIT ERROR RATE (or B.E.R.). There is also an equivalent parameter for FRAME ERROR RATE or PACKET ERROR RATE. • Putting Aside the Mathematical Process of Deriving the Relationship between Bit Error Rate and Signal-to-Noise Ratio, the Results are Shown as Follows: Link Budgets - W3GEY / VK4GEY

  26. For any given modulation type, such as BPSK shown here, there is a relationship between the received signal Eb/No and the Bit Error Rate you should expect for your system. • NOTE: • Eb/No = S/N x Brx/fb • S/N is the same as C/N • Brx = the receive pre-detection filter bandwidth • fb = system data rate Link Budgets - W3GEY / VK4GEY

  27. The “Bottom Line” – Link Margin • The bottom line of a link budget is an expression of the “margin” that exists for the link. The margin (typically measured in dB) is the amount of additional loss the link will “tolerate” while still achieving the desired Bit Error Rate (B.E.R.). These losses could come from a variety of unforseen sources not covered here. • Link Margin (dB) = Required Eb/No (for a given B.E.R.) – the Eb/No achieved in your link Budget. (Example): • Eb/No Achieved: 18 dB • Required Eb/No: 10.6 dB (for a 10E-6 BER; BPSK) • Eb/No Margin: 7.4 dB Link Budgets - W3GEY / VK4GEY

  28. Intermodulation • Distortion Products Produced by the User or Spacecraft Transmitter. • These Distortion Products are Created by Power Amplifier: • Non-Linear Transfer Characteristics (A) • Saturation Characteristics (B) B A POUT PIN Link Budgets - W3GEY / VK4GEY

  29. Two Tone Intermodulation Method(Useful for Narrowband Signal Structures) Signal Amplitude (dBW) f1 f2 2f2 – f1 2f1 – f2 3f1 – 2f2 3f2 – 2f1 Frequency  fc Link Budgets - W3GEY / VK4GEY

  30. Two Tone Intermodulation Method(Useful for Narrowband Signal Structures) IMR (Two Tone) = 9 dB - 3 dB Signal Amplitude (dBW) f1 f2 -9 dB [Hard Limiter] 2f2 – f1 2f1 – f2 3f1 – 2f2 3f2 – 2f1 Frequency  fc Link Budgets - W3GEY / VK4GEY

  31. Noise Power Ratio Method(Useful for Wideband Signal Structures) Notch Filter Amplified Wideband Signal (Output) Wideband Signal (Bandwidth B) HPA fc Amplifier Input Signal (Test Point) Link Budgets - W3GEY / VK4GEY

  32. Noise Power Ratio Method(Useful for Wideband Signal Structures) Signal Amplitude (dBW) Amplifier Input Signal B - 40 dB fc Frequency  Link Budgets - W3GEY / VK4GEY

  33. Noise Power Ratio [ “Slot IM” ] Method Signal Amplitude (dBW) Amplifier Output Signal B - 40 dB - 15 dB IMR (Via NPR) = 15 dB fc Frequency  Link Budgets - W3GEY / VK4GEY

  34. Incorporating Intermodulation Into the Link Model • Intermodulation is an “Io” term (an Interference term). • It must be added to the No terms to create an overall result: 1 S/No (Total) = 1 + 1 S/No S/Io • To Perform this calculation is of the same degree of difficulty as we ecountered in Exam No. 2. • Instead of Performing This Calculation You May Use the Link Model. Effect of Intermod on Adjacent Transponder Users Link Budgets - W3GEY / VK4GEY

  35. Want a Copy of the Link Model? • Contact me at: w3gey@amsat.org Link Budgets - W3GEY / VK4GEY

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