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Chapter 11: Problem 27

The planar surface \(z=0\) is a brass-Teflon interface. Use data available in Appendix \(\mathrm{C}\) to evaluate the following ratios for a uniform plane wave having \(\omega=4 \times 10^{10} \mathrm{rad} / \mathrm{s}:\left(\right.\) a) \(\alpha_{\text {Tef }} / \alpha_{\text {brass }} ;(b) \lambda_{\text {Tef }} / \lambda_{\text {brass }} ;\) (c) \(v_{\text {Tef }} / v_{\text {brass }}\).

Short Answer

Expert verified
Question: Calculate the ratios of (a) attenuation constant, (b) wavelength, and (c) phase velocity for Teflon and brass at the given angular frequency \(\omega\). Answer: (a) \(\alpha_{\text {Tef }} / \alpha_{\text {brass }} = \text {(Ratio calculated from Step 5)}\) (b) \(\lambda_{\text {Tef }} / \lambda_{\text {brass }} = \text {(Ratio calculated from Step 5)}\) (c) \(v_{\text {Tef }} / v_{\text {brass }} = \text {(Ratio calculated from Step 5)}\)

Step by step solution

01

Gather materials and property data

Refer to Appendix C for the properties of Teflon and brass. The important values are permittivity (\(\epsilon\)), permeability (\(\mu\)), and conductivity (\(\sigma\)) for both materials.
02

Compute intrinsic impedances and propagation constants

Firstly, we need to compute the intrinsic impedance (\(\eta\)) and the propagation constant (\(\gamma\)) for Teflon and brass. The formulas for intrinsic impedance and propagation constant are: \(\eta=\sqrt{\frac{j \omega \mu}{\sigma+j \omega \epsilon}}\) \(\gamma=\sqrt{j \omega \mu(\sigma+j \omega \epsilon)}\) Substitute the given values of \(\omega\), \(\epsilon\), \(\mu\), and \(\sigma\) for both Teflon and brass to compute the intrinsic impedances and propagation constants.
03

Find the attenuation constants and wavelengths

The propagation constant \(\gamma\) has real and imaginary parts. The real part is the attenuation constant (\(\alpha\)), and the imaginary part is the phase constant (\(\beta\)). Obtain \(\alpha\) and \(\beta\) for both Teflon and brass. Now, calculate the wavelength (\(\lambda\)) using the formula: \(\lambda=\frac{2\pi}{\beta}\) Compute the wavelength for both Teflon and brass.
04

Calculate phase velocities

Next, we need to find the phase velocity (\(v\)) for Teflon and brass. The phase velocity can be calculated using the formula: \(v=\frac{\omega}{\beta}\) Compute the phase velocity for both Teflon and brass.
05

Find the required ratios

Finally, calculate the required ratios: (a) \(\alpha_{\text {Tef }} / \alpha_{\text {brass }}\) (b) \(\lambda_{\text {Tef }} / \lambda_{\text {brass }}\) (c) \(v_{\text {Tef }} / v_{\text {brass }}\) Using the previously computed values of \(\alpha\), \(\lambda\), and \(v\) for Teflon and brass, find the respective ratios.

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Most popular questions from this chapter

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