Answered: The transmitter and receiver antennas…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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The transmitter and receiver antennas used in a long range microwave communication system operating at 9 GHz are identical and separated by 10km from each other. The receiver power must be at least 10*10^-6 W to meet the receiver's signal to noise ratio. Assuming that both antennas are aligned for maximum reception and are polarization compatible, what should be the gain of the transmit and receive antennas in dB when the input power of the transmitter antenna is 10W

Expert Solution

Step 1

Given: In a long-range microwave communication system,

Operating frequency, f=9 GHz

So, the wavelength will be:

$λ = \frac{c}{f} = \frac{3 \times 10^{8}}{9 \times 10^{9}} = 0.0333 m$

The transmitter and receiver antennas used are identical and separated by 10km from each other, so the distance between the antennas is:

$R = 10 k m = 10^{4} m$

The receiver power (to maintain signal-to-noise ratio) is:

$P_{r} = 10 μ W = 10 \times 10^{- 6} W$

The input transmitter power is:

$P_{t} = 10 W$

Assuming that both antennas are aligned for maximum reception and are polarization compatible, so

$G_{0 r} = G_{0 t}$

To find: The gain of the transmit and receive antennas in dB?

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