A link budget is the ledger of every gain and loss between transmitter and receiver, ending in a number we can compare with what the receiver needs. It answers the first of the six questions: does the link close?
TERPSat Received Power
- Applies the received-power equation to the TERPSat downlink at the worst useful geometry (5° elevation)
Work the TERPSat Link
Given:
- At 5° elevation:
- Frequency:
- , ,
- ,
Calculate , , and
- EIRP:
- The spacecraft still transmits 10 W; antenna gain changes the on-axis equivalent
- Free-space path loss (edge cost):
- at 2574 km (vs. 167.9 dB overhead at 705 km)
- Received power:
- Does the link work? We still need noise, required performance, and margin
Check the Complete Ledger
- Follow the reference point; write every gain and loss with its sign
| Term | Value | Running power |
|---|---|---|
| 10 dBW | 10 dBW | |
| −1 dB | 9 dBW | |
| +8 dBi | 17 dBW | |
| −179.1 dB | −162.1 dBW | |
| +45 dBi | −117.1 dBW | |
| −2 dB | −119.1 dBW |
NOTE
- The path loss is enormous; the antenna gains are what make the link plausible
Predict Before Calculating
- What happens to received power if we double transmit power?
- What happens if we double range instead?
- What do we gain — and lose — by raising the elevation mask?
- Does adding a ground station necessarily strengthen this link?
Answer not on slide
- Double transmit power: ; double range: (from the decibel relationships slide)
- Raising the elevation mask: less edge path loss, less contact time (the elevation mask trade)
- Adding a ground station: see mission-owned vs. shared provider
Voyager 2 Received Power
Homework 2: Voyager 2
- Problem statement (lec03 slide 4, a screenshot of the Homework 2 handout): total received signal power for Voyager 2’s X-band link to DSS-43 (the 70 m antenna in Canberra), using the updated range with radio parameters from JPL’s January 1, 1996 budget (Ludwig and Taylor, Voyager Telecommunications, JPL DESCANSO 2002, Table 5-3)
- Given:
- Range 21,476,670,660 km, i.e. (21,476,670,660,000 m)
- , , ,
- 0 dB transmit feed loss; 0.42 dB other losses (pointing, atmosphere, and polarization combined)
Quantity Calculation Result 59.10 dBW ( in m, in GHz) 317.59 dB −184.90 dBW
- Is received power alone enough to predict data recovery?
- No — that needs noise: Signal-to-Noise Density (not on slide)
The Complete Link Budget: Lunar Link
Example Inputs and Assumptions
- Spacecraft → Earth, 8.4 GHz return link, range 384,400 km
- Spacecraft: 1 W transmitter, 0.3 m transmit dish, transmit line loss 0.60 dB
- Ground: 34 m receive dish, aperture efficiency 0.55
- Antenna temperature (off the lunar disk — see the Moon)
- Receive feed: 1 dB loss at 290 K
- Receiver NF = 0.69 dB ()
- Other losses: 0.1 dB atmosphere + 0.8 dB pointing + 0.5 dB polarization = 1.4 dB
- Tools (gain, path loss); diameter in meters, range in kilometers:
- Where do the 0.6 dB transmit loss and the 1 dB receive-feed loss go?
- Transmit line loss → EIRP
- At terminal A the signal has not yet passed through the receive feed → the feed loss lives in the noise ledger (and in G/T at A)
Signal Power at A
Lunar Link Signal Budget
Term Value Transmitter power +0.0 dBW Transmitter line loss −0.6 dB Transmit antenna gain (0.3 m) +25.8 dBi Free-space loss (384,400 km) −222.6 dB Atmosphere + pointing + polarization −1.4 dB Receive antenna gain (34 m) +66.9 dBi Received −131.9 dBW
- Plane A precedes the receive feed; at B the signal is 1 dB lower
System Noise at A
- All noise referred to antenna terminal A (two noise ledgers):
Lunar Link Noise at A
Antenna Feed emission, Receiver via feed, Total 30.0 K 75.1 K 62.9 K 168.0 K
- (G/T)
Signal-to-Noise Density
Lunar Link S/N₀
- , so
- With :
The Complete Budget in One View
- Transmit:
- Propagate: free space −222.6 dB; other losses −1.4 dB
- Collect: +66.9 dBi →
- Noise at A: , ,
- Compare:
- Design trades: more EIRP or G/T helps; more propagation loss hurts
NOTE
- This is the calculated S/N₀; modulation will determine what value is sufficient (Energy per Bit, Link Margin)
What Changes When We Point at the Moon?
- Same signal power, but the beam now sees the lunar disk: : 30 K → 230 K
-
- : 168.0 K → 368.0 K; : 22.3 → 25.7 dB-K
What Changes in the Budget?
| Change (everything else held fixed) | Effect |
|---|---|
| Double received signal power | |
| Double range (gains and temperatures fixed) | , so S/N₀ drops 6.0 dB |
| Double (signal budget fixed) | |
| Add 0.5 dB atmospheric loss |
- Weather: update both the atmospheric signal loss and the antenna noise — atmospheric emission can change G/T, so changes too (weather in the budget)
The Complete Link Calculation
Link Budget Equation (S/N₀ form)
- EIRP: transmitter power, transmit-line loss, and transmit antenna gain
- Losses: free space, atmosphere, pointing, and polarization
- G/T: receive gain and total system noise at one plane (receive-feed effects are already in G/T)
- The constant 228.6 is , for EIRP in dBW and G/T in dB/K
Lunar Link, One Line
- Noise and receiver references (Class 4): JPL DESCANSO Vol. 10, Ch. 2, System Noise Concepts with DSN Applications; NIST, Johnson-noise thermometry and SI defining constants; JPL Report 42-143, Follow-up Receiver Noise-Temperature Contribution; Keysight, Noise Figure Application / Noise Concepts; JPL DESCANSO Ch. 5, HEMT Low-Noise Amplifiers; Analog Devices AN-2622
- Further reading: DSN 810-005 Modules 104 and 105 (station and environmental noise); ITU-R P.838-3 (rain attenuation) and P.618-14 (Earth-space propagation); Condon & Ransom, Essential Radio Astronomy, Chs. 1–3; ITU-R P.525-5 (free-space attenuation)
The Complete Link Equation in Eb/N0
- Class 5 extends the budget past S/N₀ to the energy per bit the demodulator actually sees
Link Budget Equation (Eb/N₀ form)
- , where is the fraction of received signal power allocated to data (power allocation)
- , using the information bit rate
- ; and use the same reference plane
- Available must cover the requirement, implementation loss, and reserve (Link Margin)
The Remaining Trades
| Change | Budget effect | Mission cost |
|---|---|---|
| More data-channel EIRP | More available | Spacecraft power or antenna demands |
| Better G/T or lower losses | More available | Ground hardware, siting, or operations |
| Lower information bit rate | More energy per information bit | Longer delivery time |
| Different modulation / coding | May lower required | Bandwidth, complexity, or latency |
WARNING
- A lower requirement must come from a justified performance comparison at the same delivered error target
What If the Link Still Does Not Close?
- We have optimized power, antennas, receiver noise, losses, and data rate — and available still falls short of the requirement
- Could we transmit the bits in a way that requires less ?
- → Next class: Demodulation, BER, and Coding