Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![**Problem Statement**
If a wave with a frequency of 110 MHz propagates in free space, find the propagation constant, \(\gamma\).
---
**Explanation**
The propagation constant, \(\gamma\), is a measure of how a wave propagates through a medium. It is a complex number that indicates the change in amplitude and phase of the wave as it travels. In free space, the propagation constant can be calculated in terms of the angular frequency (\(\omega\)) and the speed of light (\(c\)).
\[
\gamma = j\frac{\omega}{c}
\]
where:
- \(\omega = 2\pi f\)
- \(f = 110 \text{ MHz} = 110 \times 10^6 \text{ Hz}\)
- \(c \approx 3 \times 10^8 \text{ m/s}\)
Calculate \(\omega\) and then solve for \(\gamma\).](https://content.bartleby.com/qna-images/question/53cd4567-e9c0-49bc-8f29-7fe4db37c68a/85a7100e-7e8f-4759-9099-85139f376ef9/haaqf6_processed.jpeg)
Transcribed Image Text:**Problem Statement**
If a wave with a frequency of 110 MHz propagates in free space, find the propagation constant, \(\gamma\).
---
**Explanation**
The propagation constant, \(\gamma\), is a measure of how a wave propagates through a medium. It is a complex number that indicates the change in amplitude and phase of the wave as it travels. In free space, the propagation constant can be calculated in terms of the angular frequency (\(\omega\)) and the speed of light (\(c\)).
\[
\gamma = j\frac{\omega}{c}
\]
where:
- \(\omega = 2\pi f\)
- \(f = 110 \text{ MHz} = 110 \times 10^6 \text{ Hz}\)
- \(c \approx 3 \times 10^8 \text{ m/s}\)
Calculate \(\omega\) and then solve for \(\gamma\).
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