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Transmitter which radiates a carrier frequency of 1850 MHZ for a vehicle moving 60 mph, calculate receive carrier frequency if the mobile is moving

(a) Directly towards the transmitter

(b) Directly towards away from the transmitter

(c) In the direction which is perpendicular to the direction of arrival of the transmitted signal

Mumbai University > Electronics and Telecommunication > Sem 7 > Mobile Communication

Marks: 10 M

Year: Dec 2013

1 Answer
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Given:
1) velocity of vehicle v=60miles/hr

2) Carrier frequency f=1850 MHz

Solution:

1 mile = 1609.344m

60 mile = 96560.64m/hr = 26.8224m/sec

$f = \frac{2π}{λ}$

$∴λ = \frac{2π}{f} = \frac{2π}{1850 ×10^6} = 0.1621 m$

We know Doppler shift $f_d$ is given by,

$f_d = \frac{v cosθ}{λ} ……. θ=0°$

$∴ f_d = \frac{26.8224×cos0}{0.1621}$

$ ∴ f_d = 165.40 Hz$

Case 1: when mobile moving directly toward the transmitter

Carrier frequency

$f1 = f + f_d = 1850 Mhz + 165.4 Khz = 1850.000165Mhz$

Case 2: when mobile moving directly away from the transmitter

Carrier frequency

$f2 = f - f_d = 1850 Mhz - 165.4 Khz = 1849.999835 Mhz$

Case 3: when mobile moving in the direction which is perpendicular to the direction of arrival of the transmitted signal

θ = 90°; cosθ=cos⁡ 90° = 0

$ ∴ f_d = \frac{26.8224 × cos⁡ 90}{0.1621} = {26.8224 × 0}{0.1621} = 0$

Thus carrier frequency $f3 = f + f_d = 1850 Mhz + 0 = 1850 Mhz$

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