Section 5.6 · Home exercises · 7 of 7
Home exercise 5.6.7: A loop antenna for AM radio
About the home exercises of Section 5.6
Home exercises 5.6.1–5.6.3 belong to the lecture, Home exercises 5.6.4–5.6.7 to the exercise lecture.
A loop antenna for AM radio
#The wave of Problem 5.6.6 arrives with , , on a loop of turns of radius in the -plane.
- Find the amplitude of of the wave in air.
- Is the loop small? Find the amplitude of the emf ( turns give times the emf of one).
- An ideal mixer gives with , the local oscillator has . Which frequencies leave the mixer, and what amplitude passes the low-pass filter?
- How must the loop be turned to receive nothing?
Use the results of Problem 5.6.6 with numbers: in air, for a small loop, and the product-to-sum identity for the mixer. The emf is the rate of change of the flux of through the loop, so it vanishes when lies in the plane of the loop.
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and . The correction factor of Problem 5.6.6 is : the loop is very small.
The mixer output contains , that is and . The low-pass filter passes
The flux is , with the normal of the loop. It vanishes when , that is when the loop lies in a plane that contains the axis, such as the - or the -plane.
Per turn the emf is , and , since in air.
Portable AM radios use the same principle with a ferrite rod inside a small coil, which multiplies the flux by the rod's effective permeability. The null of (d) is sharp, and turning the radio until the station disappears points the rod along the direction of travel: this is how a loop finds a transmitter (Exercise 5.6.15).