Radar Fundamentals

The electronic principle on which radar operates is very similar to sound-wave reflection. If you shout toward a rocky canyon, you hear an echo; knowing the speed of sound lets you estimate distance. Radar does the same with electromagnetic energy at the speed of light.

RADAR is an acronym: Radio Detection And Ranging. The term was officially coined in November 1940 by U.S. Navy Lieutenant Commander Samuel M. Tucker and F. R. Furth, and was adopted by the Allied powers by agreement in 1943.

A primary radar set has five functional blocks: Transmitter -> Duplexer -> Receiver <- Antenna <- Indicator. The transmitter produces the short, high-power RF pulses. The duplexer alternately switches the antenna between transmitter and receiver — necessary because the high-power pulse would destroy the receiver if allowed to enter it simultaneously. The receiver amplifies and demodulates the returned echo signal. The antenna both radiates the pulse and captures the echo. The indicator — classically a PPI scope — converts echo timing into a geographical display: range as radial distance from centre, bearing as the sweep angle.

The PPI scope displays echoes as bright blips. The longer the pulse was delayed by travel time, the further from the centre the blip appears. The direction of the deflection matches the direction the antenna is pointing at the moment of reception. This two-dimensional map of azimuth and range is the fundamental radar picture that air traffic control, military surveillance, and weather systems all build on.

Backscatter is the key physics term: it is the fraction of scattered energy that travels back in the direction of the incident ray — back toward the transmitter. A larger, more reflective target produces stronger backscatter and therefore a stronger echo signal.

The fundamental range equation is R = c₀ · t / 2, where c₀ is the speed of light (3 × 10⁸ m/s) and t is the measured round-trip time. The factor of two appears because the pulse must travel to the target and back — twice the range. A round-trip time of 1 µs corresponds to a range of approximately 150 m; 1 ms corresponds to 150 km.

Maximum unambiguous range (Rmax) constrains how far the radar can reliably see. If the next pulse is transmitted before the previous echo returns, the receiver cannot determine which pulse the echo belongs to — a range ambiguity. The boundary is set by the Pulse Repetition Time (PRT): Rmax = c₀ / (2 · fp), where fp is the Pulse Repetition Frequency. A PRF of 1 000 Hz gives PRT = 1 ms and Rmax = 150 km. Raising the PRF shortens Rmax; lowering it extends Rmax but reduces data rate.

Minimum range (Rmin) — sometimes called the blind range — is the closest distance a target can be and still be detected. A monostatic radar uses a single antenna for both transmitting and receiving; during transmission, the receiver is switched off by the duplexer. A target so close that its echo returns while the transmitter is still firing, or while the duplexer is recovering, is eclipsed. The formula is Rmin = c₀ · (τ + t_recovery) / 2, where τ is pulse width and t_recovery is the duplexer recovery time. A 1 µs pulse typically gives Rmin ≈ 150 m — generally acceptable. Pulse-compression radars with long coded waveforms (tens to hundreds of µs) suffer large Rmin values.

The angular determination of a target is governed by antenna directivity — the ability of the antenna to concentrate transmitted energy in a particular direction. A highly directive antenna produces a narrow beam; the target bearing is simply the direction the antenna is pointing when the echo signal strength peaks.

True bearing is the angle between true north and the line pointing directly at the target, measured clockwise in the horizontal plane. Relative bearing is the same angle measured from the vessel's or aircraft's own heading line. Most tactical displays work in true bearing after a GPS or gyro north-reference is applied. Older radar sets required an expensive compass or trigonometric survey; modern sets resolve north automatically from GPS.

Azimuth accuracy depends on antenna beamwidth: a narrower beam means greater pointing precision. The peak echo method — finding the antenna angle that maximises return signal — is used by search radars. Weapons-control and guidance radars use automatic tracking circuits that lock onto the pointing angle of maximum return.

Elevation angle (ε) is the angle between the horizontal plane and the line of sight, measured in the vertical plane. It is positive above the horizon and negative below. Knowing both slant range R and elevation angle ε, target height h is computed: h ≈ R · sin(ε) (for short ranges where Earth's curvature can be ignored).

Height-finding radars use a very narrow fan beam scanned in elevation. A 3D radar combines azimuth rotation with electronic elevation scanning to provide range, bearing, and height in a single system. Search radars that do not scan in elevation are 2D sensors — they give range and bearing but not height, requiring a separate height-finder to build a full 3D track.

Resolution is the ability to distinguish two separate targets. Accuracy is how closely the measured position of a single target matches its true position. A radar can have excellent accuracy — placing a lone aircraft within metres of its true position — while having poor resolution that merges two nearby aircraft into one blip. These properties improve through different engineering levers.

Range resolution (ΔR) is the minimum separation in range between two targets on the same bearing for them to appear as two distinct returns. The theoretical limit is half the pulse width expressed as a distance: ΔR = c₀ · τ / 2. A 1 µs pulse gives ΔR = 150 m. Two aircraft separated by less than this distance in range will merge into a single elongated blip. Pulse-compression systems decouple range resolution from pulse width: a long coded pulse achieves the resolution of a short pulse after compression, determined by transmitter bandwidth rather than pulse width.

Angular (azimuth) resolution is the minimum angular separation at which two targets at the same range appear as distinct returns. It is set by the antenna's −3 dB beamwidth Θ: two targets must be separated by more than Θ to be resolved. At slant range R, this corresponds to a linear separation SA ≈ R · Θ (with Θ in radians). Narrower beamwidths — achieved with larger antennas — produce better angular resolution. At 100 km range with a 1° beam, SA ≈ 1.75 km.

The accuracy vs resolution distinction matters for EW and intelligence work. A signal intercept may accurately geolocate an emitter while being unable to resolve two co-located emitters into separate tracks. Conversely, high resolution enables discrimination of closely spaced contacts that accuracy alone cannot separate.

A pulsed radar transmits a short burst of RF energy, then listens for echoes, then transmits again. This cycle repeats at the Pulse Repetition Frequency (PRF) — the number of pulses emitted per second. The reciprocal is the Pulse Repetition Time (PRT), also called the interpulse period: PRT = 1/PRF.

Within each PRT, time is divided between the transmit phase (pulse width τ) and the listen/receive phase. The receive phase starts after the duplexer switches from TX to RX, which takes a short recovery time. The receive window closes just before the next transmit pulse to prevent interference.

Pulse width (τ) determines both energy per pulse (longer pulse = more energy) and the minimum range and range resolution. Narrow pulses are preferred for resolution and short Rmin but deliver less energy per pulse, reducing maximum detection range.

Duty cycle (D) is the fraction of time the transmitter is active: D = τ / PRT = τ × PRF. A transmitter running for 1 µs in a 1 ms period has D = 1/1000 = 0.001, or 0.1%. Duty cycle links peak power to average power: P_avg = P_peak × D. Average power matters more than peak power for energy-on-target and thermal limits. Modern pulse-compression radars maximise duty cycle with coded long pulses, achieving high average power while maintaining fine resolution after compression.

The core timing trade-off is: higher PRF -> shorter PRT -> shorter Rmax -> higher duty cycle -> more average power. Radar designers choose PRF based on the required unambiguous range; everything else follows.

The radar range equation describes how received echo power depends on transmit power, antenna characteristics, range, and the target's reflectivity. The simplified monostatic form is:

Pe = (PS · G² · λ² · σ) / [(4π)³ · R⁴]

where Pe is received echo power, PS is transmit power, G is antenna gain, λ is wavelength, σ is the radar cross section of the target, and R is slant range. Because R appears in the denominator to the fourth power, doubling range reduces received power by a factor of 16. This is the fundamental reason long-range radar requires very high transmit power or large antenna apertures.

Rearranging for the maximum range at which Pe equals the minimum detectable signal:

Rmax = ⁴√[(PS · G² · λ² · σ) / ((4π)³ · Smin)]

Increasing any of PS, G², or σ improves range; improving receiver sensitivity (lower Smin) does the same.

Radar Cross Section (RCS, σ) is the target-specific quantity that quantifies how much electromagnetic energy is backscattered toward the radar. It is expressed in square metres and depends on: the physical geometry and exterior features of the target, the direction of illumination (aspect angle), the radar's operating frequency, and the electrical properties of the target surface. RCS is not the physical cross-sectional area — a corner reflector far smaller than 1 m² can have an RCS of 1 000 m². A large transport aircraft has RCS of order 10–100 m² broadside; a fighter aircraft 1–5 m²; a stealth aircraft < 0.01 m². Measures to reduce RCS — shaping, radar-absorbing material, internal weapon carriage — constitute stealth technology.

For analytics work, the practical implication is: the same radar will detect a high-RCS tanker at much longer range than a low-RCS drone. Range assessments must account for the target's RCS, which is often uncertain and aspect-dependent, not a fixed number.