Everything You Ever Wanted to Know About Spacecraft Link Budgets . . . But Were Afraid to Ask. Jan A. King Revised July 2005 VK4GEY 11/14/2018 Link Budgets - W3GEY / VK4GEY

You may have seen it written as: SNR It’s the “Signal-to-Noise Ratio” 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY Terminology For Our Purposes: S/N = C/N Let’s decide to use the more familiar S/N. 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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. 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY Terminology S/(No + Io) Signal to Combined Noise Plus Interference Power Density. Units: dBHz REMEMBER? -- How Do You Add dBs? 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY ANSWER: YOU DON’T! YOU MUST ADD THE TWO “UN-LOGGED” NUMBERS FIRST YUCK! 11/14/2018 Link Budgets - W3GEY / VK4GEY

BITCH . . . Use The Link Model Instead And you Won’t Have to do this Calculation 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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! 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Inserting a Transponder in a Link S/C RX G/T S/C TX EIRP ( ) S/No RX G/T TX EIRP UP (S/No) DOWN USER A USER B (S/No)TOTAL 11/14/2018 Link Budgets - W3GEY / VK4GEY

Who’s Responsible? EIRP and G/T -> That’s Who CHARACTERISTIC: ESTABLISHES: USER EIRP and S/C “G” S (S/C Received Signal Power) S/C “T” No (S/C Received Noise Power Density) S/C EIRP and USER “G” S (User Received Signal Power) USER “T” No User Received Noise Power Density UPLINK DOWNLINK 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY The MAGIC Formula! For a Spacecraft Link Using a “Bent Pipe” Transponder: (S/No) = 1 1 1 (S/No) (S/No) TOTAL + UP DOWN 11/14/2018 Link Budgets - W3GEY / VK4GEY

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… 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY Exam No. 3 R total = ? R1= 1K  R2= 1 Meg  11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY Magic Formula Results 11/14/2018 Link Budgets - W3GEY / VK4GEY

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. 11/14/2018 Link Budgets - W3GEY / VK4GEY

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. 11/14/2018 Link Budgets - W3GEY / VK4GEY

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). 11/14/2018 Link Budgets - W3GEY / VK4GEY

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: 11/14/2018 Link Budgets - W3GEY / VK4GEY

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… 11/14/2018 Link Budgets - W3GEY / VK4GEY

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: 11/14/2018 Link Budgets - W3GEY / VK4GEY

Eb/No = S/N x Brx/fb NOTE: 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Link Budgets - W3GEY / VK4GEY 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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Signal Amplitude (dBW) Two Tone Intermodulation Method (Useful for Narrowband Signal Structures) Signal Amplitude (dBW) f1 f2 2f2 – f1 2f1 – f2 3f1 – 2f2 3f2 – 2f1 fc Frequency  11/14/2018 Link Budgets - W3GEY / VK4GEY

Signal Amplitude (dBW) 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 fc Frequency  11/14/2018 Link Budgets - W3GEY / VK4GEY

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) 11/14/2018 Link Budgets - W3GEY / VK4GEY

Noise Power Ratio Method (Useful for Wideband Signal Structures) Signal Amplitude (dBW) Amplifier Input Signal B - 40 dB fc Frequency  11/14/2018 Link Budgets - W3GEY / VK4GEY

Signal Amplitude (dBW) Amplifier Output Signal Noise Power Ratio [ “Slot IM” ] Method Signal Amplitude (dBW) Amplifier Output Signal B - 40 dB - 15 dB IMR (Via NPR) = 15 dB fc Frequency  11/14/2018 Link Budgets - W3GEY / VK4GEY

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 11/14/2018 Link Budgets - W3GEY / VK4GEY

Want a Copy of the Link Model? Contact me at: w3gey@amsat.org 11/14/2018 Link Budgets - W3GEY / VK4GEY