## Glossary of AERO230 Formulae

Created by Rasori

- Basic Electromagnetism

Wavevector - k = 2*pi / lambda

= 2*pi * f / c

lambda = wavelength

f = frequency

c = speed of light

- Decibels

two formats! - Power(dB) = 10 log10 (Power)

Power dBm = 10 log10 (Power(dBm))

Area dBsm = 10 log10 (Power(dBsm))

E(dBmicroV/meter) = 20 log10 (E(microV/meter)

- Radar Equations

Antenna Gain

Gr = Gt = ? - Gr = 4pi Ae / lambda^2 = Gt

Ae = Antenna effective area

lambda = wavelength

- Radar Equations

Gain transmitted - Gt = 4pi / (dTHETA dPHI)

dTHETA = angular beamwidth vertical

dPHI = angular beamwidth horizontal

- Radar Equations

Vertical Beamwidth

general / circular? - general:

dTHETA = lambda / 2a

circular:

dTHETA = 1.02 * lambda/2a

lambda = wavelength

a = aperture radius

- Radar Equations

Power Received - Pr = (Pt Gt Gr lambda^2 sigma Ls) / ((4pi)^3 R^4))

Pt = power transmitted

Gt = transmitter gain

Gr = receiver gain

lambda = wavelength

sigma = RCS radar cross section

Ls = Loss factor (0.3 - 0.5)

R = range

- Radar Equations

Radar Noise - N = k T0 B F

k = Boltzmann's Constant

= 1.38 * 10 ^(-23)J/K

T0 = temperature

B = bandwidth

F = "noise figure"

- Radar Equations

Signal-to-Noise Ratio - SNR = Pr/N =

(Pt Gt Gr lambda^2 Ls) / ((4pi)^3 R^4 N)

Pr = Power received

N = Noise

Pt = Power transmitted

Gt = Gain transmitted

Gr = Gain received

lambda = wavelength

Ls = loss factor (0.3 - 0.5)

R = range

- Radar Equations

Range Resolution

(rough) - dR = 0.8*c*t0

c = speed of light

t0 = pulse duration

- Radar Equations

Range accuracy - dR = c / (2B sqrt(2SNR))

c = speed of light

B = bandwidth

SNR = signal-to-noise ratio

- Radar Equations

Doppler Shift - fd = 2 vr / lambda

vr = radial velocity

lambda = wavelength

- Radar Equation

frequency (bandwidth) - fBW = 1 / t0

t0 = pulse length

- Radar Equations

Range and Max Range - R = c * tr / 2

Rmax = c / 2fPRF

c = speed of light

tr = time to recieve

fPRF = pulse repetition frequency

- Radar Equations

Two dopplers

Integration time

Frequency error

Radial Velocity error - tint = 1/dfd

df = 1/(tint sqrt(2SNR))

dvr = lambda / (2tint sqrt(2SNR))

tint = integration time

dfd = difference between doppler shifts

df = frequency error

SNR = signal-to-noise ratio

dvr = radial velocity error

lambda = wavelength

- Radar Equations

Radar Cross Section (RCS)

Summation of many scatterers - sigma = sum(sqrt(sigma-m) e^(j phi-m)

sigma = RCS

sigma-m = RCS of individual scatterer

phi-m = 2-way phase difference

- Radar Equations

Phased Array Radar - phi / 2 pi = (d sin(theta)) / lambda

phi = phase difference between elements

d = distance between elements

lambda = wavelength

- Radar Equations

Phased Array Radar

Gain GaTHETA - GaTHETA = abs(EaTHETA)^2 / N^2

= (sin^2(N pi (d/lambda) sin(theta)) / (N^2 sin^2(pi (d/lambda) sin(theta)))

EaTHETA = field intensity pattern

N = number of antennae in array

d = distance between antennae

lambda = wavelength

- Radar Equations

Synthetic Aperture Radar

cross-range resolution - dcr = R lambda / 2a

R = range to target

lambda = wavelength

a = antenna radius

- Radar Equations

Synthetic Aperture Radar

cross-range resolution to a - dcr = lambda / 2thetaB = 2a/2 = a

lambda = wavelength

thetaB = beamwidth

- Inertial Navigation Systems

Ring Laser Gyro - df = 4 A omega / (L lambda)

A = path area

omega = rate of rotation

L = path length

lambda = wavelength (laser average, in this case)

- Inertial Navigation Systems

Fibre Optical Gyro - dPHI = (8pi A N omega)/(c lambda)

A = path area

N = number of turns

omega = rate of rotation

c = speed of light

lambda = wavelength

- Intertial Navigation Systems

Schuler Frequency

theta..

and T - theta.. = (a - g sin(theta)) / Re = (a - gtheta) / Re

a = acceleration reading

gsin(theta) = horizontal error due to earth's rotation

Re = radius of the earth

gtheta = horizontal error again

T = 4pi sqrt(Re/g) = 84 minutes

- Radio Navigation Systems

LORAN - D = sqrt((x-x1)^2 + (y-y1)^2) - sqrt((x-x2)^2 + (y-y2)^2) = c*td

D = distance

x1,y1 / x2,y2 = fixed points

x, y = observer point

c = speed of light

td = time delay

- Imaging Systems

angular resolution - dTHETA = theta / N

dTHETA = angular resolution

theta = field of view (rads)

N = number of pixels

- Imaging Systems

Rayleigh Criterion - dTHETA = 1.22lambda / D

lambda = wavelength

D = aperture diameter

- Imaging Systems

Johnson Criteria (3) - Rd = (dX/3)/dTHETA

Rr = (dX/7)/dTHETA

Ri = (dX/11)/dTHETA

Rd = Range of Detection

Rr = Range of Recognition

Ri = Range of Identification

dX = Critical Dimension (smallest of height/width/length)

dTHETA = angular resolution

- Air Data Sensors

Pitot tube Airspeed

Indicated versus true? - Q = .5 rho V^2 = Pt - Ps

Q = dynamic pressure

rho = air density

V = airspeed

Pt = total pressure

Ps = static pressure

Indicated is without temperature reading