Equations Flashcards
Range
Range = c Δt/2
Super heterodyne receiver
sc(t) * slo(t) = sin(2πfct)*sin(2πflot)
Intermediate frequency
fIF = fc - flo
Power density at range
Pr = Pt/4πR^2
Including gain
Pr = PtGt/4πR^2
Introducing the radar cross section
Pr = PtGtσ/4πR^2
Reflected power flux density received
Pr = PtGtσ/(4πR^2)^2
Antenna effective aperture
Ae = pa A
pa = efficiency term
Receiver gain
Gr = 4πAe/λ^2
Simple radar equation
Smin = Pr
Monastic radar Gt = Gr = G
Thermal or Johnson noise
N = kTo βn
Noise bandwidth
βn = (-∞ ∫ ∞) |H(f)|^2 df / |H(f0)^2
Noise figure
Fn = Nout/kToβnGa
Noise figure in terms of signal to noise ratio
Fn = (Sin/Nin) / (Sout/Nout)
Number of pulses
n = θbfp/θ(dot)s = θbfp/6ωm
Pre detection integration
(S/N)n = (S/N)1/n
where n is the number of pulses
Integration efficiency factor
Ei(n) = (S/N)1/n(S/N)n
Integration improvement factor
Ii(n) = nEi(n)
Average power of a pulse train waveform
Pav = Pt τ/Tp = Pt τ fp
Duty cycle
duty = τ/Tp = τfp = Pav/Pt
Maximum unanambigous range
Run = cTp/2 = c/2fp
Resolving ambiguities
n = ΔRapp/ΔRun
Multiple PRFs
Run,mprf = Run,1 (Run,2/(Run,2 - Run,1))(Run,3 / (Run,3 - Run,2))
Range resolution
resolution = cτ/2
Main lobe solid angle
θ = λ^2/Ae
Number of pulses for integration
n = fp Ti
Phase length
φ = 2π/λ x 2R
A moving target, the rate of change of phase
dφ/dt = ω = 4π/λ . dR/dt = 4π/λ . vr
Pulse compression ratio
τ/τ(comp) = ΔF/Δf
Time bandwidth product
τΔF
