Aero 250 Equations

Question 1

SNR(dB)

Answer 1

10log(Ps/Pn)

Question 2

Modulation factor, mu

Answer 2

KaAm = Am/m

Question 3

Channel capacity, C

Answer 3

BcLog2(1 + SNR) = BcLog(P/BcN0)

Question 4

Carrier power, Pc

Answer 4

(Ac^2)/2

Question 5

Angle modulated signal power, P

Answer 5

(A^2)/2

Question 6

Carson’s rule

Answer 6

Banglemod = 2(B + ∆f) = 2B(ß + 1), where ß = ∆f/B

Question 7

Sampling frequency, fs

Answer 7

1/Ts

Question 8

Bit number, N

Answer 8

Log2(L), where L is the quantisation level.

Question 9

Range, R

Answer 9

0.5ct, where t is transit time.

Question 10

Range resolution, ∆R

Answer 10

c/2Bp, where Bp is the pulse bandwidth

Question 11

Pulse bandwidth, Bp

Answer 11

1/Tp, where Tp is the pulse duration

Question 12

Duty cycle, d

Answer 12

Tp/Tpri, where Tpri is the pulse repetition interval.

Question 13

Max range, Rmax

Answer 13

c/2fprf, where fprf is the pulse repetition frequency.

Question 14

Average power (radar)

Answer 14

dPpeak, where Ppeak is the peak power.

Question 15

SNRintegrated

Answer 15

GI SNRperpulse

Question 16

Beamwidth, ∆theta

Answer 16

1.22lambda/2a, where a is the radius of the circular aperture.

Question 17

Cross range resolution, ∆Rc

Answer 17

2RSin(∆theta/2)

Question 18

Range accuracy, sigmaR

Answer 18

∆R/√(2SNR) = c/2Bp√(2SNR)

Question 19

Angular accuracy, sigmaA

Answer 19

∆theta/1.6√(2SNR)

Question 20

Doppler shift, fd

Answer 20

2Vr/lambda, where Vr is the radial velocity

Question 21

Integration time for two doppler shifts, Tint

Answer 21

1/∆fd

Question 22

Doppler shift error, sigmafd

Answer 22

∆fd/√(2SNR)

Question 23

Radial velocity error, sigmaVr

Answer 23

lambda∆fd/2√(2SNR)

Question 24

Rayleigh criterion

Answer 24

∆theta = 1.22lambda/D

Question 25

Angular resolution, ∆theta

Answer 25

theta/N

Question 26

Noise power, N

Answer 26

kT0BF, where T0 is the temperature of the electronics, and F is the noise figure of the electronics.

Question 27

Antenna gain, G

Answer 27

4π/(∆theta)^2