second largest signal. The direction of an incoming signal, within the arc described by two antennas with a squint angle of Φ, may be obtained by comparing the relative powers of the signals received. When the signal is on the boresight of one of the antennas, the signal at the other antenna will be about 12 dB lower. When the signal direction is halfway between the two antennas, signal levels will be equal and approximately 3 dB lower than the boresight value. At other bearing angles, φ, some intermediate ratio of the signal levels will give the direction. If the antenna main lobe patterns have a Gaussian characteristic, and the signal powers are described in logarithmic terms (e.g. decibels (dB) relative to the boresight value), then there is a linear relationship between the bearing angle φ and the power level difference, i.e. φ ∝ (P1(dB) - P2(dB)), where P1(dB) and P2(dB) are the outputs of two adjacent channels. The thumbnail shows a typical plot. To give 360° coverage, antennas of a circular array are chosen, in pairs, according to the signal levels received at each antenna. If there are N antennas in the array, at angular spacing (squint angle) Φ, then Φ = 2π/N radians (= 360/N degrees). Basic equations for two-port DF If the main lobes of the antennas have a Gausian characteristic, then the output P1(φ), as a function of bearing angle φ, is given by where G0 is the antenna boresight gain (i.e. when ø = 0), Ψ0 is one half the half-power beamwidth A = -ln(0.5), so that P1(ø)/P10 = 0.5 when ø = Ψ0 and angles are in radians. The second antenna, squinted at Phi and with the same boresight gain G0 gives an output Comparing signal levels, The natural logarithm of the ratio is Rearranging This shows the linear relationship between the output level difference, expressed logarithmically, and the bearing angle ø. Natural logarithms can be converted to decibels (dBs) (where dBs are referred to boresight gain) by using ln(X) = X(dB)/(10.log10(e)), so the equation can be written Three-channel DF Improvements in bearing accuracy may be achieved if amplitude data from a third antenna are included in the bearing processing. For three-channel DF, with three antennas squinted at angles Φ, the direction of the incoming signal is obtained by comparing the signal power of the channel containing the largest signal with the signal powers