Why does a TV loop have one turn?
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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Question
Why does a TV loop have one turn?
![Problem 6.5
A circular-loop TV antenna with 0.02-m² area is in the presence of a
uniform-amplitude 300-MHz signal. When oriented for maximum response, the loop I
develops an emf with a peak value of 30 (mV). What is the peak magnitude of B of
the incident wave?
Solution: TV loop antennas have one turn. At maximum orientation, Eq. (6.5)
evaluates to D = [B· ds
with magnitude B
we can express B as B = Bo cos (oI + ao) with @ =
arbitrary reference phase. From Eq. (6.6),
= +BA for a loop of area A and a uniform magnetic field
B|. Since we know the frequency of the field is f= 300 MHz,
2n x 300 × 10° rad/s and ao an
Vemf = –N =-A–[Bo cos(mt + a)] = AB90 sin(ot + o).
di
dt
Vemf is maximum when sin(wt + ao) = 1. Hence,
30 x 10 = AB0@=0.02 × Bo × 6r x 10*,
which yields Bo = 0.8 (nA/m).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5697e4d-cdc9-416d-9deb-b019c703ee3a%2Fbf989ac5-73cb-41ce-8458-c3edd8effd2a%2Feq8q9a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 6.5
A circular-loop TV antenna with 0.02-m² area is in the presence of a
uniform-amplitude 300-MHz signal. When oriented for maximum response, the loop I
develops an emf with a peak value of 30 (mV). What is the peak magnitude of B of
the incident wave?
Solution: TV loop antennas have one turn. At maximum orientation, Eq. (6.5)
evaluates to D = [B· ds
with magnitude B
we can express B as B = Bo cos (oI + ao) with @ =
arbitrary reference phase. From Eq. (6.6),
= +BA for a loop of area A and a uniform magnetic field
B|. Since we know the frequency of the field is f= 300 MHz,
2n x 300 × 10° rad/s and ao an
Vemf = –N =-A–[Bo cos(mt + a)] = AB90 sin(ot + o).
di
dt
Vemf is maximum when sin(wt + ao) = 1. Hence,
30 x 10 = AB0@=0.02 × Bo × 6r x 10*,
which yields Bo = 0.8 (nA/m).
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