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# The Calculated Bit Error Rate of BPSK

Requirements: Solving for area of solar array (m2) and number of cells.

Solution

Power that must be produced by the solar cells P sa = power requirement = 1.30 kW

For multi-junction cells, power output P0 = 1300W/ (0.03*0.06) m2 = 722.22 W/m2

Beginning of life (BOL) power production capability, P BOL

= P0*I d*Cos Ɵ

= 722.22*0.82*Cos 6 = 588.98 kW/m2

End of life (EOL) power production capability, P EOL = L d* P BOL

L d = (1-degradation/year) design life = (1-0.03)8.5 = 0.77

P EOL = 0.77*588.98 kW/m2 = 453.51 W/m2

Solar array size to meet the requirement = Psa/ P

EOL = 1300/453.51 = 2.87 m2

Number of cells required = 2.87/ (0.03*0.06), approximately 1594 cells.

Question 2:

Given:

Batteries used –Nickel-Hydrogen batteries

Number of cycles around the Earth = 1×105

Requirement: Maximum DOD that we can use

Solution:

A Nickel-hydrogen battery used in 15000 cycles has 40% Depth of Discharge (DOD)

Therefore, the maximum DOD that we can use,

= 2.667 %.

The calculated value of DOD is expected to be less than 40% since a conservative depth of discharge is required for the larger number of cycles and since the spacecraft will take more time in space.

Question 3

Given:

Received power in the satellite, PR = 0.5 Pw,

Bit rate of the BPSK module Rb = 1.544 Mb/s and

Noise power density N0 = 0.5×10-19 J

PR = 0.5e-12 W

Rb = 1.544e6 b/s

N0 = 0.5e-19 J

Solution

To determine the bit error rate I used the equation for the ratio of the energy per bit to the noise power density.

= [0.5e-12/1.544e6]/ 0.5e-19

1.7601

The ratio was used to determine the corresponding bit error rate using the table of BER against Eb/ N0 for BPSK/QPSK module.

a)

This is the ratio of the energy per bit to the noise power density

b) Eb/ N0 = [0.5e-12/0.5e-19] = 1096.6332

c) Using fig. 16-16, the approximate BER was found to be 2×10-1