LoRa / FSK Modulation & Doppler Shift Analyzer

Compare LoRa spreading factors (SF7–SF12), sensitivity, 32-byte time-on-air, and LEO horizon Doppler shift limits.

LoRa / FSK & Carrier Settings
LoRa Spreading Factor
Channel bandwidth
Receiver noise figure (NF)
MHz
km
Receiver sensitivity−132.0 dBmReq SNR: −15.0 dB · NF: 6.0 dB
Equivalent bit rate977 bps
32-byte Time-on-Air453 ms
Static offset limit (±0.25·BW)±31.25 kHzHorizon Doppler: ±10.23 kHz
Doppler drift tolerance per symbol (¼ bin)30.5 HzZenith drift: 1.21 Hz/sym (148 Hz/s)
Symbol duration T_s8.19 ms

DETERMINISTIC PHYSICS & DATA METHODOLOGY

How This Calculator Works

Source modules: lib/physics/lora.ts, lib/physics/orbit.ts

Evaluates Semtech SX1276/SX1262 LoRa chirp spread spectrum (CSS) sensitivity, packet Time-on-Air, static frequency capture range, and intra-symbol Doppler rate limits against circular-LEO horizon shift and overhead slew rate.

Governing Equations & Physical Model

LoRa CSS sensitivity & symbol duration
S_rx = −174 + 10·log₁₀(BW) + NF + SNR_req(SF),   T_sym = 2^SF / BW

Uses Semtech AN1200.22 required SNR (−7.5 dB at SF7 down to −20.0 dB at SF12) and low-data-rate optimization DE = 1 when T_sym ≥ 16 ms.

Static Doppler capture vs. intra-symbol drift rate
Δf_pull = ±0.25·BW,   Δf_sym,max = BW / (4 · 2^SF),   df/dt|_zenith = (f₀/c)·(R_E/(R_E+h))·(v²/h)

Checks both Semtech AN1200.14 static offset pull-in and ¼-FFT-bin per-symbol chirp demodulation stability during overhead TCA.

Inputs, Parameters & Units

ParameterUnitPhysical definition
SF, BW7–12, kHzLoRa spreading factor and chirp channel bandwidth (62.5–500 kHz).
NFdBReceiver front-end noise figure (6.0 dB bare SX1276/62; 3.5 dB with external LNA).
f₀, hMHz, kmRF carrier frequency and circular LEO altitude.

Assumptions & Validity Limits

  • Time-on-Air assumes a 32-byte explicit-header CRC-enabled frame at coding rate 4/5 with an 8-symbol preamble.
  • Overhead Doppler slew rate evaluates exact zenith closest approach (worst-case df/dt).

Worked Default Reference Case

Default SF10 / 125 kHz LoRa at 436.7 MHz, 525 km (NF = 6.0 dB)

Achieves −132.0 dBm sensitivity (977 bps equivalent, 453 ms for 32 B); horizon Doppler (±10.23 kHz) stays well within ±31.25 kHz capture, and zenith drift (1.21 Hz/symbol) stays far below the 30.5 Hz ¼-bin limit.

Receiver sensitivity
−132.0 dBm (977 bps)
32-byte frame Time-on-Air
453 ms (T_s = 8.19 ms)
Horizon Doppler vs pull-in
±10.23 kHz vs ±31.25 kHz
Zenith drift vs ¼-bin limit
1.21 Hz/sym vs 30.5 Hz
Model Validation & Analytical Test SuiteLoRa CSS vs FSK in LEO Technical Note

Engineering Specifications, Equations & Topic Hubs

TOPIC HUB · TOP.03 // COMMSRF Communications, Link Budgets & Antenna Deployment
TECHNICAL NOTE · NL-TN-2026-013LoRa from low Earth orbit
SATWIKI SPECIFICATION · SQ-SS-009Antennas & deployment mechanisms
COURSE MODULE 06UHF / LoRa Link Budgets, Antennas & Doppler