Interactive lessons on radar and electronic warfare calculations, built for training, engineering review and classroom demonstrations.
Use these subpages when you want a focused lesson with more graphics, real calculation examples and a technical explanation for each formula family.
Aperture, gain, beamwidth, sidelobes, field regions and polarization.
Radar equation, one-way links, pulse timing, range and resolution.
FSPL, Fresnel zones, earth bulge, horizon, two-ray and knife-edge effects.
J/S, burn-through, support jamming, communications jamming and deception offsets.
Noise figure, SQNR, ENOB, SINAD, dwell time, hits per scan and detection margins.
PDWs, PRI extraction, pulse sorting, RF/PW/AOA clustering, stagger, jitter and emitter tracks.
Radar cross section, scattering regions, simple target shapes and retroreflectors.
AOA, Watson-Watt, pseudo-Doppler, phase interferometry, array DF and bearing triangulation.
Complete section-by-section path covering every major formula family: EW concepts, frequency bands, antennas, propagation, receiver noise, ADC metrics, chaff, decoys, jamming, pulse/CW radar, detection, Doppler, horizon, radar equations, weather radar, RCS, retroreflectors and dB units.
Most EW math becomes manageable when all powers are in dB, distances are in one consistent unit, and wavelength is computed before range or aperture calculations.
Example. At 10 GHz, λ = 0.3 / 10 = 0.03 m. A target moving radially at 250 m/s creates a Doppler shift near 16.7 kHz.
Example. 500 W is 27 dBW because 1000 W is 30 dBW and 500 W is 3 dB lower.
Free-space path loss describes one-way spreading loss. The radar equation adds the two-way path, antenna gain, wavelength, target RCS, receiver noise and losses.
The curve shows the fourth-power range penalty for a point target. A 2x increase in range costs 12 dB in the two-way radar equation.
In this energy form, Pt * tau is pulse energy, G concentrates energy toward the target and back, sigma is target radar cross section, and k*T is thermal noise density. Losses reduce the available margin.
Jamming-to-signal ratio compares jammer power entering the radar receiver to the target echo. Burn-through occurs where the real target echo becomes strong enough to overcome the jammer by the radar's required margin.
For self-protection, jammer and target are collocated, so jammer power falls as one-way range squared while the target echo falls as two-way range to the fourth power. That is why jamming is powerful at long range and less dominant at short range.
The crossing point is the burn-through range for the selected J/S threshold. It is an engineering training model; operational systems add waveform, processing, polarization and ECCM effects.
Support jamming becomes a geometry problem. If the support jammer is in a radar sidelobe, the gain ratio Gs - Gm can be a large penalty. Stand-in jamming improves J/S by reducing Rj, while stand-off jamming usually needs more ERP or a better antenna geometry.
Pulse timing defines what the radar can measure without ambiguity and what ranges are hidden during transmit or recovery time.
Doppler shift is the signature of radial motion. It is central to moving-target indication, velocity tracking and velocity deception concepts.
A radar does not measure a mathematical point. It measures energy inside a range-angle cell. Range resolution comes from pulse width or bandwidth; angular resolution comes from beamwidth.
RCS is the equivalent reflective area that would return the measured echo. It is not simply geometric size: aspect, material, frequency, polarization and resonance matter.
| Target class | Approx. RCS | dBsm |
|---|---|---|
| Small bird / nano UAV | 0.01 m2 or less | -20 dBsm or less |
| Cruise missile class | 0.1 to 0.5 m2 | -10 to -3 dBsm |
| Fighter aircraft class | 1 to 10 m2 | 0 to 10 dBsm |
| Truck / small vessel class | 100 to 1000 m2 | 20 to 30 dBsm |
| Large ship class | 10,000 m2 or more | 40 dBsm or more |
This section expands the guide into a full-course reference. Each topic gives the operational meaning, the principal equations and a short engineering example or usage note.
Electronic warfare is organized around sensing the spectrum, attacking hostile spectrum use and protecting friendly systems.
| ES | Detect, intercept, identify, locate and analyze electromagnetic emitters. |
| EA | Use noise, deception, expendables or directed energy to reduce hostile radar or communications effectiveness. |
| EP | Design and tactics that reduce hostile EW effectiveness: LPI, agility, filtering, sidelobe control, ECCM and emission control. |
Training example. If an intercept receiver measures frequency, bandwidth, modulation and bearing, it supports both threat identification and jammer assignment.
Band naming is a language for mission planning. The same frequency can imply antenna size, propagation behavior, atmospheric loss, Doppler sensitivity and likely emitter class.
| VHF/UHF | Longer wavelength, larger antennas, useful for long-range surveillance and communications. |
| L/S/C | Common surveillance, air-defense and weather radar ranges. |
| X/Ku/K/Ka | Shorter wavelength, narrower beams, higher resolution, more atmospheric sensitivity. |
| ISM bands | Unlicensed industrial, scientific and medical allocations often used by commercial radios and drones. |
Near-field and far-field boundaries tell you when simple plane-wave assumptions are valid.
Example. A 2 m aperture at 10 GHz has λ = 0.03 m, so far field starts near 267 m.
Antenna gain describes directional concentration of radiated energy. Aperture efficiency captures the difference between ideal and practical antennas.
Example. At the same aperture, moving from S band to X band increases theoretical gain because wavelength is shorter.
Beamwidth sets angular resolution and determines how much area is illuminated at a given range.
Usage note. Use radians for θ in beam-solid-angle and resolution-cell calculations.
Line-of-sight links can fail even when the optical path looks clear, because obstructions inside the Fresnel zone cause diffraction and phase cancellation.
Example. Long microwave links need tower height for both curvature and Fresnel clearance, not only direct visual sight.
Ground reflection can interfere with the direct wave. Terrain edges can add diffraction loss.
Usage note. FSPL is a clean first estimate; two-ray and diffraction explain why real low-altitude links fluctuate.
Atmospheric gas, rain, fog and polarization mismatch reduce received power. Below about 10 GHz, atmospheric loss is often small for short paths; above that it can dominate.
Example. Cross-polarized antennas may lose around 10 dB or more depending on target and propagation environment.
Noise factor and noise figure describe how much a receiver degrades signal-to-noise ratio.
Example. NF = 3 dB means F ≈ 2, so equivalent input noise temperature is about 290 K.
Digital receivers are limited by quantization and distortion as well as thermal noise.
Example. A 12-bit ideal converter gives about 74 dB SQNR before practical clock, front-end and distortion losses.
Chaff creates many resonant dipoles in a radar resolution cell, while corner reflectors and lenses create high passive RCS.
Usage note. Real chaff behavior depends on cloud density, wind, polarization, radar resolution and time since deployment.
Active decoys receive, modify and retransmit radar-like signals to create false range, velocity or angle information.
Example. A 1 µs retransmission delay creates a false range offset near 150 m.
For communications, the useful signal is usually one-way, so geometry differs from monostatic radar burn-through.
Example. A jammer half the distance to the receiver gains 6 dB in geometry over a transmitter twice as far away.
Pulse compression transmits a long energetic pulse and processes it into a narrow range response.
Example. 20 MHz bandwidth gives range resolution about 7.5 m, even if the transmitted pulse is much longer.
Duty cycle links peak power, pulse width, PRF and average transmitter power.
Example. 1 MW peak power, 10 µs pulse and 1 kHz PRF gives D = 1% and average power = 10 kW.
CW radar measures Doppler well but not range unless modulation is added. FMCW maps beat frequency to range.
Example. A 100 MHz FMCW sweep gives about 1.5 m range resolution.
Detection is probabilistic because target echo, noise and clutter fluctuate.
Usage note. More hits can improve integration gain, but scanning too slowly may reduce tactical update rate.
Low PRF helps unambiguous range; high PRF helps unambiguous velocity. One waveform cannot maximize both.
Example. At 10 GHz and PRF = 3 kHz, vunamb is only about 22.5 m/s, so ambiguity resolution is needed for fast aircraft.
The radio horizon is extended by normal atmospheric refraction. Abnormal refraction and ducting can extend or reduce coverage.
Example. A 20 m radar and 1000 m target give line-of-sight distance near 149 km.
The one-way link equation applies to communications, data links, radar warning receivers and secondary radar paths.
Example. Every doubling of one-way range costs about 6 dB.
Real radar range is often limited by accumulated losses from propagation, antenna pattern, processing, fluctuation and hardware.
Example. Adding 6 dB total loss reduces radar range by about 29% because range follows the fourth root.
Swerling models describe how target RCS fluctuates with scan or pulse. They drive fluctuation loss in detection calculations.
Usage note. Smooth, nonfluctuating targets need less detection margin than rapidly fluctuating complex targets.
Weather is a volume target: the illuminated volume grows with range, so the range dependence differs from a point target.
Example. A rain cell fills more resolution volume at long range, partly offsetting spreading loss.
The ratio of target size to wavelength controls scattering behavior.
Usage note. Very small targets can become dramatically more visible as frequency increases.
Simple formulas are idealized and assume favorable aspect and conducting surfaces. Real RCS is aspect-dependent and can change by tens of dB.
Example. A flat plate normal to the radar can have much larger RCS than its physical area suggests.
Retroreflectors deliberately send energy back toward the source and can produce very large RCS for calibration or decoy use.
Usage note. One larger reflector is often cleaner than many small reflectors because phase interference can make the pattern irregular.
Absolute dB units attach a physical reference to a logarithmic value.
| dBm | Power relative to 1 mW. |
| dBW | Power relative to 1 W. |
| dBV | Voltage relative to 1 V. |
| dBµV | Voltage relative to 1 µV. |
| dBi | Antenna gain relative to an isotropic radiator. |
| dBsm | Radar cross section relative to 1 m2. |
Example. 47 dBm = 50 W, because 47 dBm = 17 dBW.
Use consistent units before calculating. Mixed kilometers, meters, GHz and Hz are the most common source of wrong answers.
| c0 | Speed of light, approximately 3 × 108 m/s. |
| f, λ | Frequency and wavelength. |
| R | Range or link distance. |
| Pt, Pr | Transmit and receive power. |
| G | Antenna gain. |
| σ | Radar cross section. |
| τ, PRT, PRF | Pulse width, pulse repetition time and pulse repetition frequency. |
| k, T, B | Boltzmann constant, temperature and bandwidth. |
One-way links scale as R^2. Monostatic radar echoes scale as R^4. That single difference explains many EW range and burn-through effects.
Start with wavelength, convert all gains and losses, compute clean radar performance, then add jammer geometry and required J/S margin.
The calculators are simplified training models. Real systems also include waveform, processing, antenna pattern, polarization, propagation and tactical geometry effects.