Range-dependent loss for rapidly scanning beam
calculates the range-dependent beam-dwell factor
fbd = beamdwellfactor(
fbd for an antenna at the specified range
hpbw, and scan rate
beamdwellfactor function assumes that the transmitter and receiver
antennas have equal beamwidth and an ideal Gaussian antenna pattern with no side
Calculate the beam-dwell factor for a surveillance radar at 100 linearly-spaced ranges in the interval
[0,100000] meters. Specify the beamwidth as
1 degree and the scan rate as
120 degrees per second.
r = linspace(0,100000); hpbw = 1; scanrate = 120; fbd = beamdwellfactor(r,hpbw,scanrate);
Plot the beam-dwell factor as a function of range. Before plotting, convert the range from meters to kilometers.
plot(r*0.001,fbd) grid on xlabel('Range (km)') ylabel('Beam-dwell Factor (dB)')
Range in meters, specified as a scalar or vector.
hpbw— Half-power beamwidth
Half-power beamwidth of the antenna in degrees, specified as a scalar or vector. If
hpbw is a vector, then
scanrate must be a
scalar or a vector of the same size.
fbd— Range-dependent beam-dwell factor
The rows of
fbd correspond to the ranges in
r. The columns depend on the sizes of
hpbw is a vector and
a scalar, then the columns of
fbd correspond to the
half-power beamwidths in
hpbw is a scalar and
a vector, then the columns of
fbd correspond to the scan
scanrate are both
vectors, then the columns of
fbd correspond to both the
half-power beamwidths in
hpbw and the scan rates in
The beam-dwell factor accounts for the misalignment between transmitter and receiver beam axes when a scanning system has a high scan rate and long-range targets.
The equation for the beam-dwell factor, Fbd, is
where the terms in the equation are:
L — Normalizing factor that brings Fbd to unity for ẟ = 0
ẟ = td / t0 — Fractional beamwidth scanned during the delay, where:
td = 2R / c — Time delay for a target, where R is the range and c is the wave propagation speed
t0 = θ3 / ωs — The time the system takes to continuously scan through one beamwidth, where θ3 is the half-power beamwidth and ωs is the scan rate
f(θ) — Antenna pattern
beamdwellfactor function assumes an ideal Gaussian antenna
pattern with no side lobes. The equation for the ideal Gaussian antenna pattern with no side
lobes, f(θ), is:
 Barton, David Knox. "Beam-Dwell Factor Fbd." In Radar Equations for Modern Radar, 362. Artech House Radar Series. Boston, Mass: Artech House, 2013.
 Barton, David Knox. "Antenna Patterns." In Radar Equations for Modern Radar, 147. Artech House Radar Series. Boston, Mass: Artech House, 2013.