Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 28

A large ground-based transmitter radiates \(10 \mathrm{~kW}\) and communicates with a mobile receiving station that dissipates \(1 \mathrm{~mW}\) on the matched load of its antenna. The receiver (not having moved) now transmits back to the ground station. If the mobile unit radiates \(100 \mathrm{~W}\), what power is received (at a matched load) by the ground station?

Short Answer

Expert verified
Answer: The power received by the ground station is 10 μW.

Step by step solution

01

Ratio of Received Power to Transmitted Power for First Transmission

Calculate the ratio of the received power (1 mW) to the transmitted power (10 kW) during the first transmission: \(g_1=\frac{1 \mathrm{~mW}}{10 \mathrm{~kW}}\) Convert the units into the same scale: \(g_1=\frac{1 \mathrm{~mW}}{10000 \mathrm{~W}}=\frac{1\times 10^{-3}\mathrm{~W}}{1\times 10^{4}\mathrm{~W}}=10^{-7}\) So, the ratio \(g_1\) for the first transmission is \(10^{-7}\).
02

Calculate the Ratio of Received Power to Transmitted Power for the Second Transmission

Let's say the ground station receives a power of P after the mobile unit transmits the signal with a power of 100 W. Then the ratio of the received power to the transmitted power for the second transmission will be: \(g_2=\frac{P}{100 \mathrm{~W}}\)
03

Calculate the Received Power

Since the mobile unit did not move between the two transmissions, the ratio of the received power to the transmitted power must be the same in both cases (\(g_1=g_2\)): \(10^{-7} = \frac{P}{100 \mathrm{~W}}\) Now, solve for P: \(P = 10^{-7} \times 100 \mathrm{~W} = 10^{-7} \times 10^{2} \mathrm{~W}\) \(P= 10^{-5} \mathrm{~W}\) So, the power received by the ground station is \(10^{-5}\mathrm{~W}\) or 10 μW.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A short dipole-carrying current \(I_{0} \cos \omega t\) in the \(\mathbf{a}_{z}\) direction is located at the origin in free space. \((a)\) If \(k=1 \mathrm{rad} / \mathrm{m}, r=2 \mathrm{~m}, \theta=45^{\circ}, \phi=0\), and \(t=0\), give a unit vector in rectangular components that shows the instantaneous direction of \(\mathbf{E}\). (b) What fraction of the total average power is radiated in the belt, \(80^{\circ}<\theta<100^{\circ}\) ?

A monopole antenna extends vertically over a perfectly conducting plane, and has a linear current distribution. If the length of the antenna is \(0.01 \lambda\). what value of \(I_{0}\) is required to \((a)\) provide a radiation-field amplitude of \(100 \mathrm{mV} / \mathrm{m}\) at a distance of \(1 \mathrm{mi}\), at \(\theta=90^{\circ} ;(b)\) radiate a total power of 1 W? Assume free space above the plane.

Consider a lossless half-wave dipole in free space, with radiation resistance, \(R_{\mathrm{rad}}=73\) ohms, and maximum directivity \(D_{\max }=1.64\). If the antenna carries a 1-A current amplitude, \((a)\) how much total power (in watts) is radiated? \((b)\) How much power is intercepted by a \(1-\mathrm{m}^{2}\) aperture situated at distance \(r=1 \mathrm{~km}\) away? The aperture is on the equatorial plane and squarely faces the antenna. Assume uniform power density over the aperture.

Write the Hertzian dipole electric field whose components are given in Eqs. (15) and (16) in the near zone in free space where \(k r<<1\). In this case, only a single term in each of the two equations survives, and the phases, \(\delta\) and \(\delta_{\theta}\), simplify to a single value. Construct the resulting electric field vector and compare your result to the static dipole result (Eq. (36) in Chapter 4). What relation must exist between the static dipole charge, \(Q\), and the current amplitude, \(I_{0}\), so that the two results are identical?

Design a two-element dipole array that will radiate equal intensities in the \(\phi=0, \pi / 2, \pi\), and \(3 \pi / 2\) directions in the \(H\) plane. Specify the smallest relative current phasing, \(\xi\), and the smallest element spacing, \(d\).
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Wave Optics

Read Explanation

Kinematics Physics

Read Explanation

Medical Physics

Read Explanation

Electricity and Magnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free