// CALCULATOR

Telemetry link budget, line by line.

A telemetry link budget is a single column of decibels: what the transmitter provides, minus what the path takes away, compared with what the demodulator needs. Fill in the column; the margin, the range at zero margin and the radio horizon follow.

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YOUR VALUES

Airborne transmitter

In the useful direction. In a bank, the airframe can mask a blade antenna by 10 to 20 dB.

Path

L band around 1,400 to 1,600 MHz, S band 2,200 to 2,400 MHz, C band around 5,090 to 5,250 MHz.

Polarisation, pointing, atmosphere, a fade allowance: whatever your range counts.

Ground station

The article's example: 30 dBi for a 1.8 m dish.

Receiver noise given as

The IF bandwidth set on the receiver. For reference, the 99% occupied bandwidth is ≈ 1.16 × the bit rate in PCM/FM and ≈ 0.78 × in SOQPSK-TG.

Demodulation
Requirement given as

The article's typical figure for PCM/FM at a bit error rate of 10⁻⁶: an Eb/N0 of 13 dB.

Line of sight

Above a smooth Earth: terrain is not taken into account.

RESULTS

Link margin

13.3 dB

Above the required Eb/N0 of 13.0 dB

Received power

−77.7 dBm

C/N 25.5 dB · Eb/N0 26.3 dB

Details
Transmitter power 10 W = +40.0 dBm
Cable, connector and filter losses −2.0 dB
Airborne antenna gain 0.0 dBi
EIRP +38.0 dBm
Free-space loss, 200 km at 2,300 MHz −145.7 dB
Other losses 0.0 dB
Ground antenna gain +30.0 dBi
Received power −77.7 dBm
Receiver noise, 6 MHz bandwidth, noise figure 3.0 dB −103.2 dBm
Carrier-to-noise ratio (C/N) 25.5 dB
Eb/N0 at 5 Mbit/s 26.3 dB
Required Eb/N0 13.0 dB
Margin 13.3 dB
Range
Free-space range at zero margin 926.4 km
Radio horizon, aircraft at 3,000 m, antenna at 10 m 238.8 km
At 200 km Within line of sight

HOW IT IS COMPUTED

Everything the transmitter provides, minus everything the path takes away.

Each line is in decibels, so the budget is a sum. The default values are the worked example of the PCM telemetry article: 10 W at 2,300 MHz over 200 km, 13.3 dB of margin.

Power in dBm

P(dBm) = 10 log₁₀(P in W) + 30

Decibels referred to one milliwatt: 10 W is +40 dBm, 1 W is +30 dBm.

Free-space loss

FSPL = 32.44 + 20 log₁₀(d in km) + 20 log₁₀(f in MHz)

The dominant term, between isotropic antennas. Doubling the distance costs 6 dB.

Received power

C = P − L_tx + G_tx − FSPL − L_other + G_rx

The first three terms are the EIRP, the power radiated in the useful direction.

Receiver noise

N = −174 dBm/Hz + 10 log₁₀(B in Hz) + NF

−174 dBm/Hz is the thermal noise density kT₀ at T₀ = 290 K. With a system noise temperature, 10 log₁₀(Tsys / 290 K) takes the place of NF.

C/N, Eb/N0 and margin

C/N = C − N · Eb/N0 = C/N + 10 log₁₀(B / Rb)

The margin is the difference with what the demodulator needs, in the same ratio. At a given received power, doubling the bit rate costs 3 dB of Eb/N0.

Range and horizon

d₀ = d × 10^(margin / 20) · d_h ≈ 4.12 × (√h₁ + √h₂) km

d₀ is where the margin reaches zero in free space. The radio horizon uses the standard effective Earth radius of 4/3 × 6,371 km, heights in metres; beyond it, there is no line of sight.

Free space and a clear line of sight: no multipath, no airframe masking, no rain. The airborne antenna gain is the optimistic line, and in practice the one that breaks the link: a bank away from the ground station can cost 10 to 20 dB in an instant. Keep the margin for that.

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